Project 2 - Rankine cycle Simulator

ABSTARCT

This report is regarding MATLAB code for determining state points parameters of Rankine Cycle Simulator in relation to user inputs and additionally plotting T-S and H-S plots. The theory about Rankine cycle simulator working is explained and finally Net work output, work ratio and the thermal efficiency are also calculated. The step-by-step code generation in MATLAB and logic is explained and errors appeared during process of successful execution of code and steps are taken to resolve them. Additionally, evidence of errors is documented in the report.

THEORY

The following paragraphs gives a brief account on thermodynamics and Rankine Cycle working.

THERMODYNAMICS

It is science of the relationship between heat, work, temperature, and energy. In wide sense, it deals with the transfer of energy from one point to another and from one form to another form. The crucial concept is that heat is a form of energy corresponding to a definite amount of mechanical work. Thermodynamics is the study of the effects of work, heat, and energy on a system. Thermodynamics is only concerned with macroscopic (large-scale) changes and observations.

In thermodynamics, the following are predominantly used technical terms for better understanding.

1. System: it is prescribed region of space or finite quantity of matter nearby an envelope/casing called the boundary.

the following are three types of system:

1. Closed System: there is no mass transfer, but heat transfer takes place with surroundings and system.
2. Open System: there is mass transfer and heat transfer between surroundings and system.
3. Isolated System: there is no mass transfer and no heat transfer between surroundings and system.
4. Surrounding: the space and matter external to the thermodynamic system and outside boundary is called the surrounding.
5. Universe: it is combination of system and the surroundings put together are called universe.
6. State: the distinctive circumstance of the system at particular point of time and described by properties.
7. Process: the line(path) of series or succession of points through which the system passes during transformation from one state to another state is called process.
8. Cycle: the process of going through various states and returning to initial state of system is called cycle.

All of thermodynamics can be expressed in terms the following:

-Temperature (T)

-Internal Energy (U)

-Entropy (S)

-Heat (Q)

-Work(W)

THERMODYNAMICS PROCESS FOR CLOSED SYSTEM

The following are the thermodynamic process:

1. Isothermal process: it is a constant temperature process. The heat flow into or out of the system must be slow enough to maintain thermal equilibrium. The energy entering system must leave with work.

For ideal gases, if ΔT is zero, ΔU = 0

Therefore, Q = W

2. Isobaric Process: is a constant pressure process. ΔU, W, and Q are generally non-zero, but calculating the work done by an ideal gas is straightforward.

W = P·ΔV

3. Isochoric Process: is a constant volume process. When the volume of a system doesn’t change, it will do no work on its surroundings. W = 0. Heating gas in a closed container is an isochoric process

ΔU = Q

4. Polytropic Process: is a thermodynamic process that obeys the relation: where p is the pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer. The exponent nis known as the polytropic index and it may take on any value from 0 to ∞, depending on the particular process.

pVⁿ = constant

5. Adiabatic Process: it is the process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression. It can be either reversible or irreversible. Following are the essential conditions for the adiabatic process to take place: First, the system must be perfectly insulated from the surrounding. Second, the process must be carried out quickly so that there is a sufficient amount of time for heat transfer to take place.

PV^γ = constant

P is the pressure of the system

V is the volume of the system

γ is the adiabatic index and is defined as the ratio of heat capacity at constant pressure C_p to heat capacity at constant volume C_v.

6. Isentropic Process: An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. It is a special case of an adiabatic process in which there is no transfer of heat or matter. It is a reversible adiabatic process. An isentropic process can also be called a constant entropy process. In engineering such an idealized process is very useful for comparison with real processes.

Since there is change in internal energy (dU) and changes in system volume (∆V), so, the entahlpy of the system, which is defined as:

H = U + pV

dH = dQ + Vdp

dH = TdS + Vdp

THERMODYNAMICS LAWS:

The following are the laws of thermodynamics which used to determine heat, work, energy, enthalpy and entropy.

1.Zeroth Law of Thermodynamics: If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

2.First Law of Thermodynamics: In cyclic process the cyclic integral of the heat transfer to the system is equal to the cyclic integral of the work transfer to the surroundings. The internal energy of an isolated system is constant. A closed system may exchange energy as heat or work. Let us consider a close system at rest without external fields.

The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics. The first law gives the relationship between heat transfer, work done, and the change in internal energy of a system. The First Law is often called the conservation of energy law.

Mathematically stated, for a control mass undergoing a cyclic process such as in Joule’s experiment and for consistent set of units

∫dQ_{from system}= ∫dW_{on system}

or ∫dQ_{from system}- ∫dW_{on system} = 0

The important thing to remember is that the first law states that the energy is conserved always.

Sign convention , the work done by a system on the surroundings is treated as a positive quantity. Likewise, energy transfer as heat to the system from the surroundings is assigned a positive sign. With the sign convention one can write:∫dQ = ∫dW

Consequences of the first law: Suppose a system is taken from state 1 to state 2 by the path 1-a-2 and is restored to the initial state by the path 2-b-1, then the system has undergone a cyclic process 1-a-2-b-1. If the system is restored to the initial state by path 2-c-1, then the system has undergone the cyclic change 1-a-2-c-1. Let us apply the first law of thermodynamics to the cyclic processes 1-a-2-b-1 and 1-a-2-c-1 to obtain

∫_1-a-2dQ+ ∫_2-b-1dQ - ∫_1-a-2dW - ∫_2-b-1dW =0

∫_1-a-2dQ+ ∫_2-c-1dQ - ∫_1-a-2dW - ∫_2-c-1dW=0

Subtracting, we get

∫_2b1dQ- ∫_2c1dQ –( ∫_2b1dW - ∫_2c1dW) =0

We know that the work is a path function and hence the term in the bracket is non-zero. Hence, we find

∫_2b1dQ = ∫_2c1dQ

That is heat is also a path function.

Energy is a property of the system: By rearranging we can have

∫_2b1 (dQ - dW) = ∫_2c1 (dQ - dW)

It shows that the integral is the same for the paths 2-b-1 and 2-c-1, connecting the states 2 and 1. That is, the quantity ∫ (dQ - dW) does not depend on the path followed by a system, but depends only on the initial and the final states of the system. That is ∫ (dQ - dW) is an exact differential of a property. This property is called energy (E). It is given by

dE = dQ-dW

E = KE + PE +U

where U is the internal energy. Therefore,

dE = d(KE) + d(PE) + dU = dQ-dW

Quit often in many situations the KE or PE changes are negligible.

dU = dQ – dW

An isolated system does not exchange energy with the surroundings in the form of work as well as heat. Hence dQ = 0 and dW = 0. Then the first law of thermodynamics reduces to dE = 0 or E₂ = E₁ that is energy of an isolated system remains constant.

3.Second Law of Thermodynamics: it introduces the notion of entropy (S), a measure of system disorder. It is about the quality of energy. It states that as energy is transferred or transformed, more and more of it is wasted. The Second Law also states that there is a natural tendency of any isolated system to degenerate into a more disordered state.

This law is also described two scientist statement:

KELVIN-PLANK STATEMNT: it is impossible to construct a device that will operate in cycle and produces no effect other than the rising of a weight and the exchange of heat with a single reservoir.

CLAUSIUS STATEMNT: It is impossible to construct a device that operates in a cycle and produce no effect other than the transfer of heat from cooler body to hotter body.

4. Third Law of Thermodynamics: It is impossible to reach a temperature of absolute zero. This is another statement of third law, the entropy of a true equilibrium state of a system at T = 0 K is zero. Strictly speaking, this is true only if the quantum mechanical ground state is non-degenerate. If it is degenerate, the entropy at T = 0 K is a small constant, not 0!)

Absolute entropy can be written as S=kBlogW, where

W is the number of available microstates

k_B is the Bolzmann constant

Provided that the ground state is unique (or W=1), the entropy of a perfect crystal lattice as defined by Nernst’s theorem is zero provided that its ground state is unique, because log(1) =0.

The third law of thermodynamics is sometimes stated as follows: The entropy of a perfect crystal at absolute zero is exactly equal to zero.

At zero kelvin the system must be in a state with the minimum possible energy, thus this statement of the third law holds true if the perfect crystal has only one minimum energy state. Entropy is related to the number of possible microstates, and with only one microstate available at zero kelvin the entropy is exactly zero.

Principles of thermodynamics are useful for power cycle for of electric power generation (i.e net power output) and to study refrigeration & heat pump which requires input of net power.
Classification of thermodynamics power cycles can be done into two types:

1. Vapor cycle working fluid exists in liquid phase during one part of the cycle (i.e from condenser outlet to Boiler) and mixed phase wit in the steam boiler and in vapor phase at the Boiler outlet.
2. Gas cycle working fluid during the cycle remains in gas phase.

Steam power generation units run on vapor power cycle using water as the working fluid.
Under this section attempt is made to familiarize the readers with the concepts of ideal vapor cycle called Rankine cycle.

Entropy: it is the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system.

Enthalpy: it is a concept used in science and engineering when heat and work need to be calculated. When a substance changes at constant pressure, enthalpy tells how much heat and work was added or removed from the substance. Enthalpy is similar to energy, but not the same. Enthalpy, the sum of the internal energy and the product of the pressure and volume of a thermodynamic system. In symbols, the enthalpy, H, equals the sum of the internal energy, E, and the product of the pressure, P, and volume, V, of the system: H = E + PV.

RANKINE CYCLE: It is the basic operating cycle for all power plants where a working fluid is continuously changing its phase from liquid to vapor and vice-versa. It is well known as modified Carnot cycle , where condensation process is continued until the steam condensed in to water.

Rankine cycle is also defined: if the working fluid in a vapor cycle passes through various components of the power plant without irreversibility and frictional pressure drop, then the cycle is called as Ideal Rankine Cycle.

Many of the impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely in the condenser. The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants. The ideal Rankine cycle does not involve any internal irreversibility. The below picture depicts Rankine cycle.

PROCESS_1-2 ISENTROPIC COMPRESSION: Water enters the pump as state 1 as saturated liquid and is compressed isentropically to the operating pressure of the boiler.

PROCESS_2-3 CONST PRESSURE HEAT ADDITION: Saturated water enters the boiler and leaves it as superheated vapor at state 3.

PROCESS_3-4 ISENTROPIC EXPANSION: Superheated vapor expands isentropically in turbine and produces work.

PROCESS_4-1 CONST PRESSURE HEAT REJECTION: High quality steam is condensed in the condenser.

Energy Analysis of the Ideal Rankine Cycle: All four components of the Rankine cycle are steady-state steady-flow devices. The potential and kinetic energy effects can be neglected. The first law per unit mass of steam can be written as:

steady-flow energy equation:

The thermal efficiency can be interpreted as the ratio of the area enclosed by the cycle on a T-s diagram to the area under the heat-addition process.

Deviation of actual vapor power cycles from idealized one: The actual vapor power cycle differs from the ideal Rankine cycle as a result of irreversibility in various components. Fluid friction and heat loss to the surroundings are the two common sources.

The below picture depicts the deviation:

Based on the variation the thermal efficiency of pump and turbine changes. The below are formulas.

INCREASE THE EFFICIENCY OF THE RANKINE CYCLE: the following are methods to enhance efficiency. The basic idea behind all the modifications to increase the thermal efficiency of a power cycle is the same: Increase the average temperature at which heat is transferred to the working fluid in the boiler, or decrease the average temperature at which heat is rejected from the working fluid in the condenser.

Lowering the Condenser Pressure (Lowers T__{low, avg}): To take advantage of the increased efficiencies at low pressures, the condensers of steam power plants usually operate well below the atmospheric pressure. There is a lower limit to this pressure depending on the temperature of the cooling medium.

Side effect: Lowering the condenser pressure increases the moisture content of the steam at the final stages of the turbine.

Superheating the Steam to High Temperatures (Increases T_high,avg)

Both the net work and heat input increase as a result of superheating the steam to a higher temperature. The overall effect is an increase in thermal efficiency since the average temperature at which heat is added increases. Superheating to higher temperatures decreases the moisture content of the steam at the turbine exit, which is desirable. The temperature is limited by metallurgical considerations. Presently the highest steam temperature allowed at the turbine inlet is about 620°C.

Increasing the Boiler Pressure

For a fixed turbine inlet temperature, the cycle shifts to the left and the moisture content of steam at the turbine exit increases. This side effect can be corrected by reheating the steam. Increasing the operating pressure of the boiler leads to an increase in the temperature at which heat is transferred to the steam and thus raises the efficiency of the cycle. The below is the picture depicts.

Note that for a fixed turbine inlet temperature, the cycle shifts to the left and the moisture content of the steam at the turbine exit increases. This undesirable side effect can be corrected by reheating the steam.

The Ideal Reheat Rankine Cycle

To take advantage of the increased efficiencies at higher boiler pressure without facing the excessive moisture at the final stages of the turbine, reheating is used. In the ideal reheating cycle, the expansion process takes place in two stages, that is the high-pressure and low-pressure turbines.

The total heat input and total turbine work output for a reheat cycle become:

The incorporation of the single reheat in a modern power plant improves the cycle efficiency by 4 to 5 percent by increasing the average temperature at which heat is transferred to the steam.

The Ideal Regenerative Rankine Cycle

The regeneration process in steam power plants is accomplished by extracting (or bleeding) steam from turbine at various stages and feed that steam in heat exchanger where the feedwater is heated. These heat exchangers are called regenerator or feedwater heater (FWH). FWH also help removing the air that leaks in at the condenser (de-aerating the feedwater). There are two types of FWH’s, open and closed.

Open (Direct‐Contact) Feedwater Heaters

An open FWH is basically a mixing chamber where the steam extracted from the turbine mixes with the feedwater exiting the pump. Ideally, the mixture leaves the heater as a saturated liquid at the heater pressure. The following are the features of the OFWH:

- Simple

- inexpensive

- good heat transfer characteristics

- bring feedwater to the saturation state

- a pump is required for each FWH

Based on above figure, the heat and work interactions of a regenerative Rankine cycle with one FWH can be expressed per unit mass of steam flowing through the boiler as:

Thermal efficiency of the Rankine cycle increases as a result of regeneration since FWH raises the average temperature of the water before it enters the boiler. Many large power plants have as many as 8 FWH’s.

Closed Feedwater Heaters

In closed FWH, heat is transferred from the extracted steam to the feedwater without any mixing taking place. Thus; two streams can be at different pressures, since they don’t mix. In an ideal closed FWH, the feedwater is heated to the exit temperature of the extracted steam, which ideally leaves the heater as a saturated liquid at the extraction pressure. The below T-S diagram depicts it.

The below is the picture that depicts Ideal regenerative Rankine cycle with a closed FWH.

The following features of Closed FWH:

- More complex (internal tubing)

- less effective (no mixing)

- do not require a pump for each FWH

The "dryness fraction", x, gives the fraction by mass of gaseous water in the wet region, the remainder being droplets of liquid.

The ratio of the compressor work to the turbine work is called the back-work ratio. Sometimes, more than one-half of the turbine work may be used by the compressor.

UNITS

The following are units of the parameters involved:

T- Temperature °C

p -Pressure bar

h- Enthalpy kJ/kg

v -Specific volume m3/kg

rho -Density kg/ m3

s -Specific entropy kJ/(kg °C)

u- Specific internal energy kJ/kg

Cp -Specific isobaric heat capacity kJ/(kg °C)

Cv- Specific isochoric heat capacity kJ/(kg °C)

work done by turbine- KJ/Kg

work done on pump- KJ/Kg

net work done- KJ/Kg

specific heat consumption- Kg/kWh

MATLAB CODE STEP-BY-STEP DESCRIPTION

The following are various steps involved in generating code to determine the various parameters for Rankine cycle efficiency. Initially, MATLAB code ask user to input his choice to calculate efficiency of Rankine cycle or not, then MATLAB code takes inputs from the user to determine parameters at various states in the Rankine cycle, further, the code will calculate work done on pump, turbine work, net work, heat input for heating condensed water and finally thermal efficiency and specific heat consumption. The following are steps involved:

1.Starting code with comment box to inform about what is purpose MATLAB code and using ‘close all‘, ‘clear all’, ‘clc’ functions. The 'clear all': this function removes all variables, functions and MEX-files from-memory and leaving workspace empty. The 'close all': This function will close all the figure handles are visible and hidden figure handles. The 'clc': function clears text from function window.

close all

clear all

clc

2. I used ‘while’ loop to ask the user to provide his choice of interest to calculate the parameters of Rankine cycle.

while(1)

3. I used 'cprintf.m' function to show all the process of Rankine Cycle Simulator in color font. The below is the code

cprintf('Blue','\n RANKINE CYCLE SIMULATION \n\n')

cprintf('Red','1-2 ISENTROPIC EXPANSION IN THE TURBINE \n')

cprintf('Magenta','2-3 CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSOR \n')

cprintf('Red','3-2 ISENTROPIC COMPRESSION IN THE PUMP \n')

cprintf('Magenta','4-1 CONSTANT PRESSURE HEAT ADDITION BY THE BOILER \n')

4. Here, I asked user opinion of calculating Rankine cycle efficiency or not based on his choice, I used ‘if-else’ function to proceed further. User input is important.

I_P=input('\n DO YOU WANT TO CALCULATE RANKINE CYCLE DETAILS ? Y or y/N or n:','s');

I_P_U=upper(I_P);

When user presses ‘y’ or ‘Y’, the MATLAB will proceed to execute the code to calculate parameters.

if I_P_U=='Y'

5. Now, I used the ‘close’ function to close all the figure window plots, there are any so that I could plot new plots for Temperature Vs Entropy and Enthalpy Vs Entropy plots based on user input parameters.

close(figure(1),'reset')

close(figure(2),'reset')

6. Now, I used the ‘input’ function for providing user input for turbine inlet pressure, temperature and input to the condenser pressure of the steam or combination of liquid and vapor.

PRESS_1=input(' ENTER THE TURBINE INLET PRESSURE (in bar): ');

TEMP_1=input('\n ENTER THE TURBINE INLET TEMPERATURE (in Degree Celsius): ');

PRESS_2=input('\n ENTER THE INSIDE CONDENSOR PRESSURE (in bar): ');

7. I used ‘Xsteam.m’ function file which consist of certain parameters required for the calculations. Steam and water properties for MATLAB based on the "International Association for Properties of Water and Steam Industrial Formulation 1997 (IAPWS IF-97). A full implementation of the IF-97 standard that provides very accurate steam and water properties in ranges from 0-1000 bar and 0-2000°C. Provided thermodynamic properties are:

Temperature
Pressure
Enthalpy
Specific volume
Density
Specific entropy
Specific internal energy
Specific isobaric heat capacity
Specific isochoric heat capacity
Speed of sound
Viscosity
Vapor fraction

All properties can be calculated with the inputs, p and T known, p and h known, h and s known and some with pressure and density known. X Steam are a full implementation of the IF-97 formulation including all regions and all backward functions for good calculation speed. The code is speed optimized with pressure and enthalpy as inputs for dynamic simulations.

Now, I extracted specific heat for liquid and vapor states for given pressures at state 1 and state 2.

SPEC_HEAT_1_LIQUID=XSteam('CpL_p',PRESS_1);

SPEC_HEAT_1_VAPOUR=XSteam('CpV_p',PRESS_1);

SPEC_HEAT_2_LIQUID=XSteam('CpL_p',PRESS_2);

SPEC_HEAT_2_VAPOUR=XSteam('CpV_p',PRESS_2);

Where

CpV_p -saturated vapor heat capacity

CpL_p -saturated liquid heat capacity

8. Correspondingly, I used the ‘XSteam.m’ function to extract saturation temperature for given pressures at state1 and state 2.

SAT_TEMP_P1=XSteam('Tsat_p',PRESS_1);

SAT_TEMP_P2=XSteam('Tsat_p',PRESS_2);

Where, Tsat_p -saturation temperature at given pressure

At the same time, I am verifying the input temperature is greater or equal to saturation temperature for given pressure at state 1, for that I used ‘if-else’ function.

if not (TEMP_1>=SAT_TEMP_P1)

cprintf('_red','You entered Inlet Temperature less than Saturation Temperature\n')

cprintf('_blue','\n Please enter the Inlet Temperature greater or equal to Saturation Temperature\n')

else

9. Once, above condition passed, then, I am using ‘XSteam.m’ function for extracting all the saturated entropy, enthalpy for both liquid and vapor phases for all the state points .

Saturation properties at state1

ENTHALPY_VAP_STATE_1=XSteam('hV_p',PRESS_1);

ENTROPY_VAP_STATE_1=XSteam('sV_p',PRESS_1);

ENTHALPY_LIQ_STATE_1=XSteam('hL_p',PRESS_1);

ENTROPY_LIQ_STATE_1=XSteam('sL_p',PRESS_1);

Saturation properties at state2

ENTHALPY_VAP_STATE_2=XSteam('hV_p',PRESS_2);

ENTROPY_VAP_STATE_2=XSteam('sV_p',PRESS_2);

Saturation properties at state3

ENTHALPY_LIQ_STATE_3=XSteam('hL_p',PRESS_2);

ENTROPY_LIQ_STATE_3=XSteam('sL_p',PRESS_2);

Saturation properties at state4

ENTHALPY_LIQ_STATE_4=XSteam('hL_p',PRESS_1);

ENTROPY_LIQ_STATE_4=XSteam('sL_p',PRESS_1);

Uniformly, I utilized XSteam.m function to obtain entropy and enthalpy at state 1 with respect to pressure and temperature at state 1.

ENTHALPY_1=XSteam('h_pT',PRESS_1,TEMP_1);

ENTOPRY_1=XSteam('s_pT',PRESS_1,TEMP_1);

Based on Rankine cycle, constant pressure heat rejection by the condenser constant pressure heat addition, so pressure at state 4 is equal to pressure at state 1, likewise, pressure at state 3 is equal to pressure at state 2.

PRESS_4=PRESS_1;

PRESS_3=PRESS_2;

Now, I obtained enthalpy , entropy and temperature for the state 3 using XSteam.m function.

ENTHALPY_LIQ_STATE_3=XSteam('hL_p',PRESS_3);

ENTHALPY_3=ENTHALPY_LIQ_STATE_3;

ENTROPY_LIQ_STATE_3=XSteam('sL_p',PRESS_3);

ENTOPRY_3=ENTROPY_LIQ_STATE_3;

SAT_TEMP_P3=XSteam('Tsat_p',PRESS_3);

TEMP_3=SAT_TEMP_P3;

It is known fact that for isentropic expansion process the entropy at state 2 is equal to entropy at state 1.

ENTOPRY_2=ENTOPRY_1;

Between state 2 to state 3 is constant pressure heat rejection and temperature remaining same and there are entropy changes. Entropy in liquid phase and vapor phase are extracted form ‘XSteam.m’ function.

TEMP_2=TEMP_3;

ENTROPY_LIQ_STATE_2=XSteam('sL_p',PRESS_2);

ENTROPY_VAP_STATE_2=XSteam('sV_p',PRESS_2);

Now , I would be calculating dryness fraction .The steam dryness fraction is used to quantify the amount of water within steam. If steam contains 10% water by mass, it's said to be 90% dry, or have a dryness fraction of 0.9. From state 1 to state 2 is isentropic expansion process, where we get output through the turbine. Once work is obtained the power of steam get lower and it will be in the phase of both liquid and vapor, so at this point I would be calculating dryness fraction with help of entropy, entropy liquid phase and entropy vapor phase at state 2.

X2=(ENTOPRY_2-ENTROPY_LIQ_STATE_2)/(ENTROPY_VAP_STATE_2-ENTROPY_LIQ_STATE_2);

Simultaneously, I procure vapor and liquid phase of enthalpy at state2 with respect to pressure state 2 from XSteam.m function.

ENTHALPY_VAP_STATE_2=XSteam('hV_p',PRESS_2);

ENTHALPY_LIQ_STATE_2=XSteam('hL_p',PRESS_2);

Now, I determine the enthalpy at state 2, by using dryness fraction, vapor and liquid phase of enthalpy at state2.

ENTHALPY_2=ENTHALPY_LIQ_STATE_2+X2*(ENTHALPY_VAP_STATE_2-ENTHALPY_LIQ_STATE_2);

It is fact that the process of isentropic compression gives us the entropies same, the entropy at state 4 is equal to entropy at state 3.

ENTOPRY_4=ENTOPRY_3;

For determining temperature at state 4, I have to calculate Gama which is obtained specific isobaric heat capacity and specific isochoric heat capacity. The following is the code

SPEC_ISO_CHO_CAPACITY_4=XSteam('Cv_ps',PRESS_4,ENTOPRY_4);

SPEC_ISO_BAR_CAPACITY_4=XSteam('Cp_ps',PRESS_4,ENTOPRY_4);

GAMA_4=SPEC_ISO_BAR_CAPACITY_4/SPEC_ISO_CHO_CAPACITY_4;

TEMP_4=TEMP_3*((PRESS_4/PRESS_3)^((GAMA_4-1)/(GAMA_4)));

After above calculations, I convert pressure at state 3 and state 4 converted from ‘bar’ to ‘mpa’ as I calculate the work done on pump using pressure and volume at state 3.

VOLUME_3=XSteam('vL_p',PRESS_3);

WORK_PUMP=VOLUME_3*(PRESS_4_mpa-PRESS_3_mpa)*1000;

ENTHALPY_4=ENTHALPY_3-WORK_PUMP;

INLET_HEAT=ENTHALPY_1-ENTHALPY_4;

10. At this point, I determine work output produced by turbine, net work done, thermal efficiency, back work ratio and SSC(specific heat consumption). The following is the code.

TURBINE_WORK=ENTHALPY_1-ENTHALPY_2;

NET_WORK=TURBINE_WORK-WORK_PUMP;

THERMAL_EFF=(NET_WORK*100)/INLET_HEAT;

BACK_WORK_RATIO=WORK_PUMP/TURBINE_WORK;

SSC=3600/TURBINE_WORK;

11. Here, I used ‘for’ loop function for determining the liquid and vapor lines. The temperature ranges are established using ‘linspace’ function. The below is the code.

TEMP_RANGE=linspace(1,TEMP_1,1000);

for i=1:length(TEMP_RANGE)

ENTHALPY_LIQ_STATE(i)=XSteam('hL_T',TEMP_RANGE(i));

ENTHALPY_VAP_STATE(i)=XSteam('hV_T',TEMP_RANGE(i));

ENTROPY_LIQ_STATE(i)=XSteam('sL_T',TEMP_RANGE(i));

ENTROPY_VAP_STATE(i)=XSteam('sV_T',TEMP_RANGE(i));

end

12. I printed parameters like temperature, pressure, enthalpy, entropy for state 1, state2, sate3 and state 4 using functions like ‘cprintf’ for color font and ‘fprintf’ to print to display in the command window for output.

% PRINTING THERMODYNAMIC PROPERTIES AT STATE 1

cprintf('Blue','\n\n THE OUPUTS OF THE RANKINE CYCLE')

cprintf('Blue','\n\n AT STATE POINT 1')

fprintf('\n PRESSURE_1: %f BAR',PRESS_1)

fprintf('\n TEMPERATURE_1: %f degC',TEMP_1)

fprintf('\n ENTHALPY_1: %f KJ/kg',ENTHALPY_1)

fprintf('\n ENTOPRY_1: %f KJ/kgK',ENTOPRY_1)

% PRINTING THERMODYNAMIC PROPERTIES AT STATE 2

cprintf('Blue','\n\n AT STATE POINT 2 ')

fprintf('\n PRESSURE_2: %f BAR',PRESS_2)

fprintf('\n TEMPERATURE_2: %f degC',TEMP_2)

fprintf('\n ENTHALPY_2: %f KJ/kg',ENTHALPY_2)

fprintf('\n ENTOPRY_2: %f KJ/kgK',ENTOPRY_2)

fprintf('\n DRYNESS FRACTION AT STATE POINT 2 X_2: %f ',X2)

% PRINTING THERMODYNAMIC PROPERTIES AT STATE 3

cprintf('Blue','\n\n AT STATE POINT 3')

fprintf('\n PRESSURE_3: %f BAR',PRESS_3)

fprintf('\n TEMPERATURE_3: %f degC',TEMP_3)

fprintf('\n ENTHALPY_3: %f KJ/Kg',ENTHALPY_3)

fprintf('\n ENTROPY_3: %f KJ/KgK',ENTOPRY_3)

% PRINTING THERMODYNAMIC PROPERTIES AT STATE 4

cprintf('Blue','\n\n AT STATE POINT 4')

fprintf('\n PRESSURE_4: %f BAR',PRESS_4)

fprintf('\n TEMPERATURE_4: %f degC',TEMP_4)

fprintf('\n ENTHALPY_4: %f KJ/Kg',ENTHALPY_4)

fprintf('\n ENTROPY_4: %f KJ/KgK',ENTOPRY_4)

13. Using functions like ‘plot’, ‘text’, ‘title’, ‘xlabel’, ‘ylabel’, ‘grid on’, ‘hold on/off’, and ‘fig’ functions to temperature vs entropy graph by using all states. The below is the code.

figure(1)

hold on

plot([ENTOPRY_1 ENTOPRY_2],[TEMP_1 TEMP_2],'color','r','linewidth',2)

text(ENTOPRY_1,TEMP_1,'1')

text(ENTOPRY_2,TEMP_2,'2')

plot([ENTOPRY_2 ENTROPY_VAP_STATE_2],[TEMP_2 SAT_TEMP_P2],'color','g','linewidth',2)

text(ENTROPY_VAP_STATE_2,SAT_TEMP_P2,'2s')

plot([ENTROPY_VAP_STATE_2 ENTOPRY_3],[SAT_TEMP_P2 TEMP_3],'color','g','linewidth',2)

text(ENTOPRY_3,TEMP_3,'3')

plot([ENTOPRY_4 ENTOPRY_3],[TEMP_3 TEMP_4],'color','c','linewidth',2)

text(ENTOPRY_4,TEMP_4,'4')

plot([ENTOPRY_4 ENTROPY_LIQ_STATE_4],[TEMP_4 SAT_TEMP_P1],'color','m','linewidth',2)

text(ENTROPY_LIQ_STATE_4,SAT_TEMP_P1,'4s')

plot([ENTROPY_LIQ_STATE_4 ENTROPY_VAP_STATE_1],[SAT_TEMP_P1 SAT_TEMP_P1],'color','m','linewidth',2)

text(ENTROPY_VAP_STATE_1,SAT_TEMP_P1,'1s')

plot([ENTROPY_VAP_STATE_1 ENTOPRY_1],[SAT_TEMP_P1 TEMP_1],'color','m','linewidth',2)

plot(ENTROPY_LIQ_STATE,TEMP_RANGE,'color','g','linestyle','--','linewidth',2)

plot(ENTROPY_VAP_STATE,TEMP_RANGE,'color','r','linestyle','--','linewidth',2)

title('TEMPERATURE-ENTROPY (T-S) DIAGRAM FOR IDEAL RANKINE CYCLE')

xlabel('ENTROPY (KJ/Kg K)')

ylabel('TEMPERATURE (degC)')

text(3,310,'LIQUID CURVE','FontSize',8,'FontWeight','bold','Color','green','HorizontalAlignment','left')

text(8,74,'VAPOUR CURVE','FontSize',8,'FontWeight','bold','Color','red','HorizontalAlignment','left')

text(8,390,'TURBINE','FontSize',10,'FontWeight','bold','Color','red')

text(8,360,'CONDENSOR','FontSize',10,'FontWeight','bold','Color','green')

text(8,330,'PUMP','FontSize',10,'FontWeight','bold','Color','cyan')

text(8,300,'BOILER','FontSize',10,'FontWeight','bold','Color','magenta')

grid on

hold off

Similarly, the enthalpy vs entropy plots are printed for output the following is the code.

figure(2)

hold on

plot([ENTOPRY_1 ENTOPRY_2],[ENTHALPY_1 ENTHALPY_2],'color','r','linewidth',2)

text(ENTOPRY_1,ENTHALPY_1,'1')

text(ENTOPRY_2,ENTHALPY_2,'2')

plot([ENTOPRY_2 ENTROPY_VAP_STATE_2],[ENTHALPY_2 ENTHALPY_VAP_STATE_2],'color','g','linewidth',2)

text(ENTROPY_VAP_STATE_2,ENTHALPY_VAP_STATE_2,'2s')

plot([ENTROPY_VAP_STATE_2 ENTOPRY_3],[ENTHALPY_VAP_STATE_2 ENTHALPY_3],'color','g','linewidth',2)

text(ENTOPRY_3,ENTHALPY_3,'3')

plot([ENTOPRY_3 ENTOPRY_4],[ENTHALPY_3 ENTHALPY_4],'color','c','linewidth',2)

text(ENTOPRY_4,ENTHALPY_4,'4')

plot([ENTOPRY_4 ENTROPY_LIQ_STATE_4],[ENTHALPY_4 ENTHALPY_LIQ_STATE_4],'color','m','linewidth',2)

text(ENTROPY_LIQ_STATE_4,ENTHALPY_LIQ_STATE_4,'4s')

plot([ENTROPY_LIQ_STATE_4 ENTROPY_VAP_STATE_1],[ENTHALPY_LIQ_STATE_4 ENTHALPY_VAP_STATE_1],'color','m','linewidth',2)

text(ENTROPY_VAP_STATE_1,ENTHALPY_VAP_STATE_1,'1s')

plot([ENTROPY_VAP_STATE_1 ENTOPRY_1],[ENTHALPY_VAP_STATE_1 ENTHALPY_1],'color','m','linewidth',2)

plot(ENTROPY_LIQ_STATE,ENTHALPY_LIQ_STATE,'color','g','linestyle','--','linewidth',2)

plot(ENTROPY_VAP_STATE,ENTHALPY_VAP_STATE,'color','r','linestyle','--','linewidth',2)

title('ENTHALPY-ENTROPY (H-S) DIAGRAM FOR IDEAL RANKINE CYCLE')

xlabel('ENTROPY (KJ/Kg K)')

ylabel('ENTHALPY (KJ/Kg K)')

text(4,1815,'LIQUID CURVE','FontSize',8,'FontWeight','bold','Color','green','HorizontalAlignment','right')

text(7.5,2649,'VAPOUR CURVE','FontSize',8,'FontWeight','bold','Color','red','HorizontalAlignment','left')

text(1,3400,'TURBINE','FontSize',10,'FontWeight','bold','Color','red')

text(1,3200,'CONDENSOR','FontSize',10,'FontWeight','bold','Color','green')

text(1,3000,'PUMP','FontSize',10,'FontWeight','bold','Color','cyan')

text(1,2800,'BOILER','FontSize',10,'FontWeight','bold','Color','magenta')

grid on

hold off

14. The code for printing output for the work done on pump, work done by turbine, net output, thermal efficiency , back work ratio and specific heat consumption. The following is the code. Used ‘fprintf’, ‘cprintf’, and ‘disp’ functions.

cprintf('Blue','\n\n WORK DONE BY TURBINE: %f KJ/Kg',TURBINE_WORK)

cprintf('Blue','\n WORK DONE ON PUMP: %f KJ/Kg',WORK_PUMP)

cprintf('Blue','\n NET WORK DONE: %f KJ/Kg',NET_WORK)

cprintf('Blue','\n THERMAL EFFICIENCY: %f ',THERMAL_EFF)

disp('%')

cprintf('Blue','\n BACK_WORK_RATIO: %f\n',BACK_WORK_RATIO)

cprintf('Blue','\n SPECIFIC HEAT CONSUMPTION: %f Kg/kWh \n',SSC)

end

15. If user does not want to calculate the parameters for Rankine Cycle, the following code is executed. Finally, code say ‘thank you’ to user and breaks the loop to terminate the execution of the while loop.

else

cprintf('Green','\n THANK YOU')

% while loop breaks when user selects N or n

break

end

end

ERORS FACED AND STEPS TO OVERCOME

The following paragraphs will illustrate various errors encountered during programing and steps taken to resolve.

1. The following is error occurred because I did not close the parentheses while determining the steam dryness fraction X. MATLAB shown error in the command with specific line number 81 and it is identified. The below is screen shot of error.

The above issue is resolved with help of command window showing line number and then closing parentheses is placed. The below is screen shot:

2. In this MATLAB code, I have used ‘XSteam.m’ function from MATLAB, which is used for extracting the thermodynamic properties, while typing I used ‘Xsteam( ) which is wrong, I found the error through command window. The below is the screenshot of it.

The error is resolved by going through command window, I corrected by providing ‘XSteam( )’. The below is the screenshot of corrected.

3. while I am plotting the graphs for H-S and T-S graph repeatedly by taking user inputs ,I have issue: all the new plots are plotting in the same window. The below is the picture that describes.

To fix the above issue , I used ‘clf(figure(1))’ command to clear the graphs from the figure window but which is not correct, it is showing blank windows for figures. The below are the screenshots representing.

The above issue is fixed by using ‘close(figure(1))’ command to completely close previous plots, before the new plots are generated. The following is the fixed screenshots. The below screen shot shows no empty figure window before entering ‘y’ or “Y’ or ‘n’ or ‘N’ for user input to generate the Rankine cycle plots.

Finally, output is displayed.

OUTPUT

The MATLAB code is helpful in producing the all the parameters like temperature, pressure, entropy, enthalpy at state points, thermal efficiency, back work ratio, work done by turbine, work done on pump and specific heat consumption.

The following are output screens for providing input for calculations. Firstly, the below is the screenshot depicting process in the Rankine cycle.

When user provides ‘y’ or Y, then the following screenshot is observed and user inputs the parameters for calculations.

When enter is pressed on the computer keyboard, automatically, the output is generated . the below are the screen shots. All the state variables are determined are displayed in the command window for output.

The below window has work done by turbine, work done on pump, net work done, thermal efficiency, back work ratio and specific heat consumption.

The above screenshot also asks user to are you interested to calculate Rankine cycle details. Before that I would be showing the Temperature Vs Entropy and Enthalpy Vs Entropy.

The above, plot describes, 1-2: isentropic expansion, and it is represented with red line where turbine works produce mechanical output to produce electricity. There is point 2s, which is generated due to saturation temperature and saturation vapor entropy. The dry saturated vapor expands through a turbine generating power. This decreases the temperature and pressure of the vapor, and some condensation may occur.

Rankine cycle is never been ideal cycle. As a result of irreversibilities in various components such as fluid friction and heat loss to the surroundings, the actual cycle deviates from the ideal Rankine cycle. The deviations of actual pumps and turbines from the isentropic ones. That’s reason the point 2s comes and the line joining from point 1 to point 2s won’t be vertical line and not isentropic.

The process covering state point form 2s, 2 to 3 is constant pressure heat rejection, this happens in condenser. Here, the vapor is condensed to liquid phase. This is represented by green color line. The wet vapor then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid

The process between state points 3 to 4 is called isentropic compression where the entropy is constant, and the liquid phase is compressed to increase the pressure. As the fluid is a liquid at this stage, the working fluid is pumped from low to high pressure, so, it is done by pump or compressor, so some amount of energy is consumed by pump and it is loss in the process of work output produced at the end of turbine.

Once , the condensed fluid is pressurized is sent in to boiler, from state 4 to 4s and 1s, this process is called constant pressure heat addition, during which the heat addition takes places in steps to increase heat of the steam and it reached super-heated to produce good amount work and this is given input to the turbine. The high-pressure liquid enters a boiler, where it is heated at constant pressure by an external heat source to become a dry saturated vapor. The input energy required can be easily calculated graphically, using an entahlpy and entropy chart, or numerically, using steam table. This is represented by Magenta color. For this, I used ‘XSteam.m’ function.

The above picture has green dash ‘—’ line as liquid curve and red dash ‘—’ represents vapor curve. It is same in the enthalpy and entropy plot.

Correspondingly, enthalpy vs entropy plots are displayed. H-S diagram. The below is the screenshot of the plot.

An enthalpy–entropy chart, also known as the H–S chart or Mollier diagram, plots the total heat against entropy, describing the enthalpy of a thermodynamic system. A typical chart covers a pressure range of 0.01–1000 bar, and temperatures up to 800 degreesCelsius. It shows enthalpy H in terms of internal energy U and pressure p and Volume V.

The work done in the Rankine cycle is represented by line from state point 1 to state point 2 of H-S diagram. So, work done represented by length of ‘H’, so, the difference between enthalpies at state 1 to state 2.

In an Isobaric process, the pressure remains constant, so the heat interaction is the change in enthalpy. In an isenthalpic process, the enthalpy is constant. A horizontal line in the diagram represents an isenthalpic process. Similar to the T-S diagram, red lines for turbine, green line for condenser, cyan for pump work, which is isenthalpic process and magenta is for fluid heat work in the boiler.

Now, again I pressed ‘y’ or ‘Y’ for the input in the command window, the following is the screenshot

As soon as , I entered after pressing ‘y’ or ‘Y’, all the previous plots are closed. Then I provide new parameters for calculations

The following are the output screenshots. When enter is pressed on the computer keyboard, automatically, the output is generated . the below are the screen shots. All the state variables are determined are displayed in the command window for output.

The below window has work done by turbine, work done on pump, net work done, thermal efficiency, back work ratio and specific heat consumption.

The following is T-S and H-S Diagram:

Now I press ‘n’ or ‘N’ as I don’t wish to calculate further so I get the below screenshot.

Finally , all the All the state variables are calculated are displayed in the command window for output and Plots of T-S and H-S diagram generated, simultaneously work done by turbine, work done on pump, net work done, thermal efficiency, back work ratio and specific heat consumption are displayed in command window.

References:

1. https://www.sfu.ca/~mbahrami/ENSC%20461/Notes/Vapor%20Power%20Cycles.pdf

2. http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=th&chap_sec=10.1&page=theory#:~:text=The%20Rankine%20cycle%20is%20an,without%20irreversibilities%20and%20pressure%20drops.&text=2%2D3%3A%20Constant%20pressure%20heat,heat%20rejection%20in%20a%20condenser

3. http://www.larapedia.com/glossary_of_engineering_and_technical_terms/back_work_ratio_meaning_in_engineering_and_technical_terminology.html#:~:text=BACK%20WORK%20RATIO%20-%20Is%20the%20fraction%20of,used%20for%20medical%20and%20legal%20or%20special%20purposes.

4. https://drive.google.com/file/d/1RK_fvrOj38CIaQvmLT1S3daqHnxKCGU-/view
5. https://www.mathworks.com/help/matlab/ref/clf.html
6. https://www.mathworks.com/matlabcentral/answers/458086-how-to-specify-line-color-using-a-hexadecimal-color-code
7. https://www.toppr.com/ask/question/pressuretemperature-relationship-for-an-ideal-gas-undergoing-adiabatic-change-isgamma-c-p/
8. https://opentextbc.ca/chemistry/chapter/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law/#:~:text=of%20their%20properties.-,The%20pressure%20of%20a%20given%20amount%20of%20gas%20is%20directly,constant%20pressure%20(Charles's%20law).
9. http://www.mahalakshmiengineeringcollege.com/pdf/mec/IIIsem/ME2202/Unit%203%20-%2016%20Mark.pdf
10. https://www.tlv.com/global/TI/steam-theory/wet-steam-dry-steam.html
11. http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=session_blank&topic=th&chap_sec=06.5&page=theory
12. https://www.sfu.ca/~mbahrami/ENSC%20461/Notes/Vapor%20Power%20Cycles.pdf
13. https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/63586/versions/5/previews/cprintf.m/index.html
14. https://www.mathworks.com/matlabcentral/fileexchange/24093-cprintf-display-formatted-colored-text-in-the-command-wind
15. https://www.mathworks.com/matlabcentral/fileexchange/24093-cprintf-display-formatted-colored-text-in-the-command-wind
16. https://blogs.mathworks.com/community/2009/05/25/colorizing-text-output/
17. https://www.mathworks.com/matlabcentral/fileexchange/24093-cprintf-display-formatted-colored-text-in-the-command-wind
18. https://en.wikipedia.org/wiki/Rankine_cycle
19. https://energyeducation.ca/encyclopedia/Rankine_cycle
20. http://www.thermopedia.com/content/1072/
21. https://www.electrical4u.com/rankine-cycle/
22. https://www.thermal-engineering.org/what-is-rankine-cycle-steam-turbine-cycle-definition/
23. http://ww2.che.ufl.edu/ziegler/Problem%20set%20solutions.pdf
24. https://www.nuclear-power.net/nuclear-engineering/thermodynamics/thermodynamic-cycles/rankine-cycle-steam-turbine-cycle/example-of-rankine-cycle-problem-with-solution/
25. https://medium.com/@ashwinpalo/how-to-calculate-thermal-efficiency-of-rankine-cycle-37a7dbcadc12
26. https://www.grc.nasa.gov/www/k-12/airplane/compexp.html#:~:text=During%20the%20compression%20process%2C%20as,standard%20conditions%2C%20it%20is%201.4.&text=So%20if%20the%20pressure%20doubled%2C%20the%20temperature%20ratio%20is%201.219.
27. https://www.grc.nasa.gov/www/k-12/airplane/compexp.html#:~:text=During%20the%20compression%20process%2C%20as,standard%20conditions%2C%20it%20is%201.4.&text=So%20if%20the%20pressure%20doubled%2C%20the%20temperature%20ratio%20is%201.219.
28. https://www.tlv.com/global/TI/steam-theory/wet-steam-dry-steam.html
29. https://www.electrical4u.com/rankine-cycle/
30. http://www.erc.uct.ac.za/sites/default/files/image_tool/images/119/jesa/19-1jesa-kapooria.pdf
31. https://www.mathworks.com/help/matlab/ref/text.html#:~:text=text(%20x%20%2C%20y%20%2C%20txt%20)%20adds%20a%20text%20description,text%20in%203%2DD%20coordinates.
32. https://www.mathworks.com/help/matlab/creating_plots/add-text-to-specific-points-on-graph.html
33. https://www.mathworks.com/matlabcentral/fileexchange/9817-x-steam-thermodynamic-properties-of-water-and-steam
34. idoc.pub_a-textbook-of-thermal-engineering-rs-khurmi-and-jk-guptapdf.pdf

MAIN CODE

%% LEVEL 1
%{
THIS MATLAB CODE IS TO DETERMINE THE VARIOUS PARAMETERS FOR RANKINE CYCLE 
EFFICIENCY. INITIALLY, MATLAB CODE ASK USER TO INPUT HIS CHOICE TO 
CALCULATE EFFICIENCY OF RANKINE CYCLE OR NOT, THEN MATLAB CODE. 
TAKES INPUTS FROM THE USER TO DETERMINE PARAMETERS AT VARIOUS STATES IN 
THE RANKINE CYCLE, FURTHER, THE CODE WILL CALCULATE WORK DONE ON PUMP, 
TURBINE WORK, NET WORK, HEAT INPUT FOR HEATING CONDENSED WATER AND FINALLY
THERMAL EFFICIENCY AND SPECIFIC HEAT CONSUMPTION.
%}

%{
'clear all': THIS FUNCTION REMOVES ALL VARIABLES, FUNCTIONS AND 
MEX-FILES FROM-MEMORY AND LEAVING WORKSPACE EMPTY.
'close all': THIS FUNCTION WILL CLOSE ALL THE FIGURE HANDLES ARE VISIBLE 
AND HIDDEN FIGURE HANDLES
'clc': FUNCTION CLEARS TEXT FROM FUNCTION WINDOW
%}
clear all
close all
clc

%{
UNITS
T Temperature °C
p Pressure bar
h Enthalpy kJ/kg
v Specific volume m3/kg
rho Density kg/ m3
s Specific entropy kJ/(kg °C)
u Specific internal energy kJ/kg
Cp Specific isobaric heat capacity kJ/(kg °C)
Cv Specific isochoric heat capacity kJ/(kg °C)
%}
%% LEVEL 2
%{ 
I USED WHILE LOOP TO ASK THE USER TO PROVIDE HIS CHOICE OF INTEREST TO
CALCULATE THE PARAMETERS OF RANKINE CYCLE FOR THAT, I USED 'while' LOOP.
%}
while(1)
% SHOWING ALL THE PROCESSES IN THE RANKINE CYCLE

% I USED 'cprintf' FUNCTION TO PRINT THE PROCESS IN COLOR FONT

cprintf('Blue','\n RANKINE CYCLE SIMULATION \n\n')
cprintf('Red','1-2 ISENTROPIC EXPANSION IN THE TURBINE \n')
cprintf('Magenta','2-3 CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSOR \n')
cprintf('Red','3-2 ISENTROPIC COMPRESSION IN THE PUMP \n')
cprintf('Magenta','4-1 CONSTANT PRESSURE HEAT ADDITION INSIDE THE BOILER \n')


%% LEVEL 3
% PROVIDING INPUT PARAMETERS 
%{
HERE, USER IS ASKED USER OPINION OF CALCULATING RANKINE CYCLE EFFICIENCY OR
NOT.
%}
I_P=input('\n DO YOU WANT TO CALCULATE RANKINE CYCLE DETAILS ? Y or y/N or n:','s');
I_P_U=upper(I_P);

%IF USER PRESS "y" OR "Y", THE PROCESS BEGINS FOR THAT I USED 'if' and
%'else' FUNCTION.

if I_P_U=='Y'
% IF THERE ARE ANY EARLIER PLOT WINDOWS ARE PRESENT, THOSE PLOTS ARE CLOSED 
%{
THE close( fig ) CLOSES THE FIGURE SPECIFIED BY fig . CLOSE ALL CLOSES ALL 
FIGURES WHOSE HANDLES ARE VISIBLE. A FIGURE HANDLE IS HIDDEN IF THE HANDLE 
VISIBILITY PROPERTY IS SET TO 'CALLBACK' OR 'OFF' . ‘close all’ HIDDEN 
CLOSES ALL FIGURES, INCLUDING FIGURES WITH HIDDEN HANDLES.
%}

    close(figure(1),'reset')
    close(figure(2),'reset')
    
%{ 
HERE, USER PROVIDES INPUTS FOR THE CALCULATION TO BEGIN SUCH AS 
INLET PRESSURE, INLET TEMPERATURE FOR TURBINE AND INSIDE PRESSURE FOR 
CONDENSER
%}    

    PRESS_1=input(' ENTER THE TURBINE INLET PRESSURE (in bar):  ');
    TEMP_1=input('\n ENTER THE TURBINE INLET TEMPERATURE (in Degree Celsius):  ');
    PRESS_2=input('\n ENTER THE CONDENSOR INLET PRESSURE (in bar):  ');

%% LEVEL4
%{ 
DETERMINING THE Cp VALUES AT P1 AND P2 FOR SATURATED LIQUID & VAPOUR
USING 'XSteam' FUNCTION.
%}

%{
STEAM AND WATER PROPERTIES FOR MATLAB BASED ON THE "INTERNATIONAL 
ASSOCIATION FOR PROPERTIES OF WATER AND STEAM INDUSTRIAL FORMULATION 1997 
(IAPWS IF-97). A FULL IMPLEMENTATION OF THE IF-97 STANDARD THAT PROVIDES 
VERY ACCURATE STEAM AND WATER PROPERTIES IN RANGES FROM 0-1000 BAR AND 
0-2000°C. PROVIDED THERMODYNAMIC PROPERTIES ARE:
TEMPERATURE
PRESSURE
ENTHALPY
SPECIFIC VOLUME
DENSITY
SPECIFIC ENTROPY
SPECIFIC INTERNAL ENERGY
SPECIFIC ISOBARIC HEAT CAPACITY
SPECIFIC ISOCHORIC HEAT CAPACITY
SPEED OF SOUND
VISCOSITY
VAPOR FRACTION

%}
%CpV_p	SATURATED VAPOR HEAT CAPACITY 
%CpL_p	SATURATED LIQUID HEAT CAPACITY

    SPEC_HEAT_1_LIQUID=XSteam('CpL_p',PRESS_1);
    SPEC_HEAT_1_VAPOUR=XSteam('CpV_p',PRESS_1);

    SPEC_HEAT_2_LIQUID=XSteam('CpL_p',PRESS_2);
    SPEC_HEAT_2_VAPOUR=XSteam('CpV_p',PRESS_2);

%% LEVEL 5
% DETERMINING SATURATION TEMPERATURES AT P1 AND P2 USING 'XSteam' FUNCTION
%Tsat_p	SATURATION TEMPERATURE AT GIVEN PRESSURE

    SAT_TEMP_P1=XSteam('Tsat_p',PRESS_1);
    SAT_TEMP_P2=XSteam('Tsat_p',PRESS_2);
    
%{
HERE, I AM ASKING USER TO ENTER THE INLET TEMPERATURE TO BE MORE OR
EQUAL TO SATURATION TEMPERATURE WITH RESPECTIVE TO PRESSURE1.
%}
    if not (TEMP_1>=SAT_TEMP_P1)
    
        cprintf('_red','You entered Inlet Temperature less than Saturation Temperature\n')
        cprintf('_blue','\n Please enter the Inlet Temperature greater or equal to Saturation Temperature\n')
    else
%% LEVEL6
% DETERMINING ENTHALPY & ENTROPY AT SATURATION POINTS
%{
ENTHALPY	
hV_p	SATURATED VAPOR ENTHALPY
hL_p	SATURATED LIQUID ENTHALPY
hV_T	SATURATED VAPOR ENTHALPY
hL_T	SATURATED LIQUID ENTHALPY
h_pT	ENTHALPY AS A FUNCTION OF PRESSURE AND TEMPERATURE
h_px	ENTHALPY AS A FUNCTION OF PRESSURE AND VAPOR FRACTION
%}
%{
SPECIFIC ENTROPY 	
sV_p	SATURATED VAPOR ENTROPY
sL_p	SATURATED LIQUID ENTROPY
sV_T	SATURATED VAPOR ENTROPY
sL_T	SATURATED LIQUID ENTROPY
s_pT	SPECIFIC ENTROPY AS A FUNCTION OF PRESSURE AND TEMPERATURE
(RETURNS SATURATED VAPOR ENTHALPY IF MIXTURE.)
%}

%{
BASED ON RANKINE CYCLE, CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSOR
CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSOR, SO PRESSURE AT STATE-1 
IS EQUAL TO PRESSURE AT STATE-4 AND PRESSURE AT STATE-2 IS EQUAL TO 
PRESSURE AT STATE-3.
%}

% SATURATION PROPERTIES AT STATE1
        ENTHALPY_VAP_STATE_1=XSteam('hV_p',PRESS_1);
        ENTROPY_VAP_STATE_1=XSteam('sV_p',PRESS_1);

        ENTHALPY_LIQ_STATE_1=XSteam('hL_p',PRESS_1);
        ENTROPY_LIQ_STATE_1=XSteam('sL_p',PRESS_1);

% SATURATION PROPERTIES AT STATE2
        ENTHALPY_VAP_STATE_2=XSteam('hV_p',PRESS_2);
        ENTROPY_VAP_STATE_2=XSteam('sV_p',PRESS_2);

% SATURATION PROPERTIES AT STATE3
        ENTHALPY_LIQ_STATE_3=XSteam('hL_p',PRESS_2);
        ENTROPY_LIQ_STATE_3=XSteam('sL_p',PRESS_2);

% SATURATION PROPERTIES AT STATE4
        ENTHALPY_LIQ_STATE_4=XSteam('hL_p',PRESS_1);
        ENTROPY_LIQ_STATE_4=XSteam('sL_p',PRESS_1);


%% LEVEL7
%DETERMINING PROPERTIES
%{
I USED XSTEAM FUNCTION TO EXTRACT ENTHALPY, ENTROPY AT STATE 1 
WITH RESPECT TO PRESSURE AND TEMPERATURE.
%}

        ENTHALPY_1=XSteam('h_pT',PRESS_1,TEMP_1);

        ENTOPRY_1=XSteam('s_pT',PRESS_1,TEMP_1);
%{
BASED ON RANKINE CYCLE, CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSER
CONSTANT PRESSURE HEAT ADDITION IN THE BOILER
%}
        PRESS_4=PRESS_1;
        PRESS_3=PRESS_2;

%{
I USED XSteam FUNCTION TO EXTRACT ENTHALPY, ENTROPY AT STATE 3 AND 
SATURATION TEMPERATURE.
%}        
        ENTHALPY_LIQ_STATE_3=XSteam('hL_p',PRESS_3);
        ENTHALPY_3=ENTHALPY_LIQ_STATE_3;

        ENTROPY_LIQ_STATE_3=XSteam('sL_p',PRESS_3);
        ENTOPRY_3=ENTROPY_LIQ_STATE_3;

        SAT_TEMP_P3=XSteam('Tsat_p',PRESS_3);
        TEMP_3=SAT_TEMP_P3;
%{
AS IT IS ISENTROPIC EXAPNSION, SO ENTROPY at STATE 1 is same AS STATE 2 
%}         

        ENTOPRY_2=ENTOPRY_1;
%{
AS IT IS CONSTANT PRESSURE HEAT REJECTION BY THE CONDENSOR, 
SO TEMPERATURE at STATE 2 is same AS STATE 3 
%}
        TEMP_2=TEMP_3;

        ENTROPY_LIQ_STATE_2=XSteam('sL_p',PRESS_2);
        ENTROPY_VAP_STATE_2=XSteam('sV_p',PRESS_2);
        
% CALCULATING DRYNESS FACTOR
        X2=(ENTOPRY_2-ENTROPY_LIQ_STATE_2)/(ENTROPY_VAP_STATE_2-ENTROPY_LIQ_STATE_2);

        ENTHALPY_VAP_STATE_2=XSteam('hV_p',PRESS_2);
        ENTHALPY_LIQ_STATE_2=XSteam('hL_p',PRESS_2);
        
% CALCULATING ENTHALPY AT STATE-2
        ENTHALPY_2=ENTHALPY_LIQ_STATE_2+X2*(ENTHALPY_VAP_STATE_2-ENTHALPY_LIQ_STATE_2);

% AS IT IS ISENTROPIC COMPRESSION, SO ENTROPY at STATE 2 is same AS STATE 4
        ENTOPRY_4=ENTOPRY_3;

   
%{
        
Cp_ps-SPECIFIC ISOBARIC HEAT CAPACITY AS A FUNCTION OF PRESSURE AND ENTROPY.
Cv_ps-SPECIFIC ISOCHORIC HEAT CAPACITY AS A FUNCTION OF PRESSURE AND ENTROPY.

SPECIFIC ISOCHORIC HEAT CAPACITY 
SPECIFIC ISOBARIC HEAT CAPACITY
%}        

        SPEC_ISO_CHO_CAPACITY_4=XSteam('Cv_ps',PRESS_4,ENTOPRY_4);

        SPEC_ISO_BAR_CAPACITY_4=XSteam('Cp_ps',PRESS_4,ENTOPRY_4);

        GAMA_4=SPEC_ISO_BAR_CAPACITY_4/SPEC_ISO_CHO_CAPACITY_4;

        TEMP_4=TEMP_3*((PRESS_4/PRESS_3)^((GAMA_4-1)/(GAMA_4)));
        
%CONVERSION of BAR to Mpa
        PRESS_4_mpa=PRESS_4*0.1;
        PRESS_3_mpa=PRESS_3*0.1;
        
%{
I USED XSteam FUNCTION TO EXTRACT VOLUME at PRESSURE_3
%}        
        VOLUME_3=XSteam('vL_p',PRESS_3);
        
% BASICALLY WORK on PUMP IS CALCULATED=ENTHALPY_3-ENTHALPY_4
        WORK_PUMP=VOLUME_3*(PRESS_4_mpa-PRESS_3_mpa)*1000;
        
        ENTHALPY_4=ENTHALPY_3-WORK_PUMP;
        
        INLET_HEAT=ENTHALPY_1-ENTHALPY_4;
        
% DETERMINATION OF WORKDONE, HEAT, SSC(SPECIFIC HEAT CONSUMPTION) AND EFFICIENCY         
        TURBINE_WORK=ENTHALPY_1-ENTHALPY_2;
        NET_WORK=TURBINE_WORK-WORK_PUMP;
        THERMAL_EFF=(NET_WORK*100)/INLET_HEAT;
        BACK_WORK_RATIO=WORK_PUMP/TURBINE_WORK;
        SSC=3600/TURBINE_WORK;
  
 %% LEVEL8
% DETERMINING SATURATION AND LIQUID LINES

% CREATING 'TEMP_RANGE' BY USING 'linspace' FUNCTION.

%{
THE ‘linspace’ FUNCTION GENERATES LINEARLY SPACED VECTORS. IT IS SIMILAR 
TO THE COLON OPERATOR ":", BUT GIVES DIRECT CONTROL OVER THE NUMBER OF 
POINTS. Y = linspace(A,B) GENERATES A ROW VECTOR Y OF 100 POINTS LINEARLY
SPACED BETWEEN AND INCLUDING A AND B.
%}
        TEMP_RANGE=linspace(1,TEMP_1,1000);
        for i=1:length(TEMP_RANGE)
            ENTHALPY_LIQ_STATE(i)=XSteam('hL_T',TEMP_RANGE(i));
            ENTHALPY_VAP_STATE(i)=XSteam('hV_T',TEMP_RANGE(i));
     
            ENTROPY_LIQ_STATE(i)=XSteam('sL_T',TEMP_RANGE(i));
            ENTROPY_VAP_STATE(i)=XSteam('sV_T',TEMP_RANGE(i));
        end
 
%% LEVEL9

% PRINTING THERMODYNAMIC PROPERTIES AT STATE 1
        cprintf('Blue','\n\n THE OUPUTS OF THE RANKINE CYCLE')
        cprintf('Blue','\n\n AT STATE POINT 1')
        fprintf('\n PRESSURE_1: %f BAR',PRESS_1)
        fprintf('\n TEMPERATURE_1: %f degC',TEMP_1)
        fprintf('\n ENTHALPY_1: %f KJ/kg',ENTHALPY_1)
        fprintf('\n ENTOPRY_1: %f KJ/kgK',ENTOPRY_1)
        
% PRINTING THERMODYNAMIC PROPERTIES AT STATE 2

        cprintf('Blue','\n\n AT STATE POINT 2 ')
        fprintf('\n PRESSURE_2: %f BAR',PRESS_2)
        fprintf('\n TEMPERATURE_2: %f degC',TEMP_2)
        fprintf('\n ENTHALPY_2: %f KJ/kg',ENTHALPY_2)
        fprintf('\n ENTOPRY_2: %f KJ/kgK',ENTOPRY_2)
        fprintf('\n DRYNESS FRACTION AT STATE POINT 2 X_2: %f ',X2)
        
% PRINTING THERMODYNAMIC PROPERTIES AT STATE 3
 
        cprintf('Blue','\n\n AT STATE POINT 3')
        fprintf('\n PRESSURE_3: %f BAR',PRESS_3)
        fprintf('\n TEMPERATURE_3: %f degC',TEMP_3)
        fprintf('\n ENTHALPY_3: %f KJ/Kg',ENTHALPY_3)
        fprintf('\n ENTROPY_3: %f KJ/KgK',ENTOPRY_3)
 
% PRINTING THERMODYNAMIC PROPERTIES AT STATE 4

        cprintf('Blue','\n\n AT STATE POINT 4')
        fprintf('\n PRESSURE_4: %f BAR',PRESS_4)
        fprintf('\n TEMPERATURE_4: %f degC',TEMP_4)
        fprintf('\n ENTHALPY_4: %f KJ/Kg',ENTHALPY_4)
        fprintf('\n ENTROPY_4: %f KJ/KgK',ENTOPRY_4)
 
%% LEVEL10
% PLOTTING TEMPERATURE-ENTROPY (T-S) DIAGRAM

%{
    xlabel(TXT) LABELS THE X-AXIS OF THE CURRENT AXES OR STANDALONE 
    VISUALIZATION. XLABEL COMMAND REPLACES THE OLD LABEL WITH THE NEW LABEL
 
    ylabel(TXT) LABELS THE Y-AXIS OF THE CURRENT AXES OR STANDALONE 
    VISUALIZATION. XLABEL COMMAND REPLACES THE OLD LABEL WITH THE NEW LABEL
 
    zlabel(TXT) LABELS THE Z-AXIS OF THE CURRENT AXES OR STANDALONE 
    VISUALIZATION. XLABEL COMMAND REPLACES THE OLD LABEL WITH THE NEW LABEL
%}
    
%{
    THE TITLE IS LOCATED AT THE TOP AND IN THE CENTER OF THE AXES. 
    title(' STRING ') OUTPUTS THE STRING AT THE TOP AND IN THE CENTER OF 
    THE CURRENT AXES. title(FNAME) EVALUATES THE FUNCTION THAT RETURNS A 
    STRING AND DISPLAYS THE STRING AT THE TOP AND IN THE CENTER OF THE 
    CURRENT AXES
 %}
%{
    figure: THESE OBJECTS ARE THE INDIVIDUAL WINDOWS ON THE SCREEN IN WHICH 
    MATLAB DISPLAYS GRAPHICAL OUTPUT. figure CREATES A NEW FIGURE OBJECT 
    USING DEFAULT PROPERTY VALUES. 
%}
%{
    HERE USING THE ' plot' FUNCTION TO PLOT GRAPHS FOR TEMPERATURES VS 
    ENTROPY AND ENTHALPY VS ENTROPY. I USED OTHER FEATURES OF 'plot'
    FUNCTION LIKE 'color','linestyle','linewidth.
%}
%{
The ‘text’ FUNCTION IS THE LOW-LEVEL FUNCTION FOR CREATING TEXT GRAPHICS 
OBJECTS. USE TEXT TO PLACE CHARACTER STRINGS AT SPECIFIED LOCATIONS. 
text(X,Y,'STRING') ADDS THE STRING IN QUOTES TO THE LOCATION SPECIFIED BY 
THE POINT (X,Y) . ... H = text(..) RETURNS A COLUMN VECTOR OF HANDLES TO 
TEXT OBJECTS, ONE HANDLE PER OBJECT.

I USED THIS FUNCTION FOR NAMING STATE POINTS, NAMING PROCESS AND
THERMODYNAMIC CURVES.I USED OTHER FEATURES OF 'text' FUNCTION LIKE 
'FontSize','FontWeight','Color','HorizontalAlignment'.

%}

        figure(1)
        hold on
        plot([ENTOPRY_1 ENTOPRY_2],[TEMP_1 TEMP_2],'color','r','linewidth',2)
        text(ENTOPRY_1,TEMP_1,'1')
        text(ENTOPRY_2,TEMP_2,'2')
        
        plot([ENTOPRY_2 ENTROPY_VAP_STATE_2],[TEMP_2 SAT_TEMP_P2],'color','g','linewidth',2)
        text(ENTROPY_VAP_STATE_2,SAT_TEMP_P2,'2s')

        plot([ENTROPY_VAP_STATE_2 ENTOPRY_3],[SAT_TEMP_P2 TEMP_3],'color','g','linewidth',2)
        text(ENTOPRY_3,TEMP_3,'3')

        plot([ENTOPRY_4 ENTOPRY_3],[TEMP_3 TEMP_4],'color','c','linewidth',2)
        text(ENTOPRY_4,TEMP_4,'4')

        plot([ENTOPRY_4 ENTROPY_LIQ_STATE_4],[TEMP_4 SAT_TEMP_P1],'color','m','linewidth',2)
        text(ENTROPY_LIQ_STATE_4,SAT_TEMP_P1,'4s')

        plot([ENTROPY_LIQ_STATE_4 ENTROPY_VAP_STATE_1],[SAT_TEMP_P1 SAT_TEMP_P1],'color','m','linewidth',2)
        text(ENTROPY_VAP_STATE_1,SAT_TEMP_P1,'1s')

        plot([ENTROPY_VAP_STATE_1 ENTOPRY_1],[SAT_TEMP_P1 TEMP_1],'color','m','linewidth',2)

        plot(ENTROPY_LIQ_STATE,TEMP_RANGE,'color','g','linestyle','--','linewidth',2)
        plot(ENTROPY_VAP_STATE,TEMP_RANGE,'color','r','linestyle','--','linewidth',2)

        title('TEMPERATURE-ENTROPY (T-S) DIAGRAM FOR IDEAL RANKINE CYCLE')
        xlabel('ENTROPY (KJ/Kg K)')
        ylabel('TEMPERATURE (degC)')
        
        text(3,310,'LIQUID CURVE','FontSize',8,'FontWeight','bold','Color','green','HorizontalAlignment','left')
        text(8,74,'VAPOUR CURVE','FontSize',8,'FontWeight','bold','Color','red','HorizontalAlignment','left')
        
        text(8,390,'TURBINE','FontSize',10,'FontWeight','bold','Color','red')
        text(8,360,'CONDENSER','FontSize',10,'FontWeight','bold','Color','green')
        text(8,330,'PUMP','FontSize',10,'FontWeight','bold','Color','cyan')
        text(8,300,'BOILER','FontSize',10,'FontWeight','bold','Color','magenta') 
        
        grid on
        
        hold off
%% LEVEL 11

%PLOTTING ENTHALPY-ENTROPY (H-S) DIAGRAM
        figure(2)
        hold on
        plot([ENTOPRY_1 ENTOPRY_2],[ENTHALPY_1 ENTHALPY_2],'color','r','linewidth',2)
        text(ENTOPRY_1,ENTHALPY_1,'1')
        text(ENTOPRY_2,ENTHALPY_2,'2')
        
        plot([ENTOPRY_2 ENTROPY_VAP_STATE_2],[ENTHALPY_2 ENTHALPY_VAP_STATE_2],'color','g','linewidth',2)
        text(ENTROPY_VAP_STATE_2,ENTHALPY_VAP_STATE_2,'2s')

        plot([ENTROPY_VAP_STATE_2 ENTOPRY_3],[ENTHALPY_VAP_STATE_2 ENTHALPY_3],'color','g','linewidth',2)
        text(ENTOPRY_3,ENTHALPY_3,'3')

        plot([ENTOPRY_3 ENTOPRY_4],[ENTHALPY_3 ENTHALPY_4],'color','c','linewidth',2)
        text(ENTOPRY_4,ENTHALPY_4,'4')

        plot([ENTOPRY_4 ENTROPY_LIQ_STATE_4],[ENTHALPY_4 ENTHALPY_LIQ_STATE_4],'color','m','linewidth',2)
        text(ENTROPY_LIQ_STATE_4,ENTHALPY_LIQ_STATE_4,'4s')

        plot([ENTROPY_LIQ_STATE_4 ENTROPY_VAP_STATE_1],[ENTHALPY_LIQ_STATE_4 ENTHALPY_VAP_STATE_1],'color','m','linewidth',2)
        text(ENTROPY_VAP_STATE_1,ENTHALPY_VAP_STATE_1,'1s')

        plot([ENTROPY_VAP_STATE_1 ENTOPRY_1],[ENTHALPY_VAP_STATE_1 ENTHALPY_1],'color','m','linewidth',2)

        plot(ENTROPY_LIQ_STATE,ENTHALPY_LIQ_STATE,'color','g','linestyle','--','linewidth',2)
        plot(ENTROPY_VAP_STATE,ENTHALPY_VAP_STATE,'color','r','linestyle','--','linewidth',2)

        title('ENTHALPY-ENTROPY (H-S) DIAGRAM FOR IDEAL RANKINE CYCLE')
        xlabel('ENTROPY (KJ/Kg K)')
        ylabel('ENTHALPY (KJ/Kg K)')
        
        text(4,1815,'LIQUID CURVE','FontSize',8,'FontWeight','bold','Color','green','HorizontalAlignment','right')
        text(7.5,2649,'VAPOUR CURVE','FontSize',8,'FontWeight','bold','Color','red','HorizontalAlignment','left')
        
        text(1,3400,'TURBINE','FontSize',10,'FontWeight','bold','Color','red')
        text(1,3200,'CONDENSER','FontSize',10,'FontWeight','bold','Color','green')
        text(1,3000,'PUMP','FontSize',10,'FontWeight','bold','Color','cyan')
        text(1,2800,'BOILER','FontSize',10,'FontWeight','bold','Color','magenta') 
        
        grid on
        
        hold off
%% LEVEL12
% PRINTING WORKDONE, HEAT, SSC(SPECIFIC HEAT CONSUMPTION) AND EFFICIENCY 
% I USED 'cprintf' FUNCTION TO PRINT THE PROCESS IN COLOR FONT
 
        cprintf('Blue','\n\n WORK DONE BY TURBINE: %f KJ/Kg',TURBINE_WORK)
        cprintf('Blue','\n WORK DONE ON PUMP: %f KJ/Kg',WORK_PUMP)
 
        cprintf('Blue','\n NET WORK DONE: %f KJ/Kg',NET_WORK)

        cprintf('Blue','\n THERMAL EFFICIENCY: %f ',THERMAL_EFF)
        disp('%')
        
        cprintf('Blue','\n BACK_WORK_RATIO: %f\n',BACK_WORK_RATIO)

        cprintf('Blue','\n SPECIFIC HEAT CONSUMPTION: %f Kg/kWh \n',SSC)
        
        
        
    end
 
    else
        cprintf('Green','\n THANK YOU')
    % while loop breaks when user selects N or n
   break
end

end




%XSteam.m function


%h_prho behöver T_prho för samtliga regioner!!!!

%***********************************************************************************************************
%* Water and steam properties according to IAPWS IF-97                                                     *
%* By Magnus Holmgren, www.x-eng.com                                                                       *
%* The steam tables are free and provided as is.                                                           *
%* We take no responsibilities for any errors in the code or damage thereby.                               *
%* You are free to use, modify and distribute the code as long as authorship is properly acknowledged.     *
%* Please notify me at [email protected] if the code is used in commercial applications                     *
%***********************************************************************************************************
%
% XSteam provides accurate steam and water properties from 0 - 1000 bar and from 0 - 2000 deg C according to
% the standard IAPWS IF-97. For accuracy of the functions in different regions see IF-97 (www.iapws.org)
%
% *** Using XSteam *****************************************************************************************
%XSteam take 2 or 3 arguments. The first argument must always be the steam table function you want to use.
%The other arguments are the inputs to that function.
%Example: XSteam('h_pt',1,20)  Returns the enthalpy of water at 1 bar and 20 degC
%Example: XSteam('TSat_p',1)  Returns the saturation temperature of water at 1 bar.
%For a list of valid Steam Table functions se bellow or the XSteam macros for MS Excel.
%
%*** Nomenclature ******************************************************************************************
% First the wanted property then a _ then the wanted input properties. 
% Example. T_ph is temperature as a function of pressure and enthalpy. 
% For a list of valid functions se bellow or XSteam for MS Excel.
% T     Temperature (deg C)
% p	    Pressure    (bar)
% h	    Enthalpy    (kJ/kg)
% v	    Specific volume (m3/kg)
% rho	Density
% s	    Specific entropy 
% u	    Specific internal energy 
% Cp	Specific isobaric heat capacity 
% Cv	Specific isochoric heat capacity 
% w	    Speed of sound 
% my	Viscosity
% tc	Thermal Conductivity
% st	Surface Tension
% x	    Vapour fraction
% vx	Vapour Volume Fraction
%
%*** Valid Steam table functions. ****************************************************************************
%
%Temperature	
%Tsat_p	Saturation temperature
%T_ph	Temperture as a function of pressure and enthalpy
%T_ps	Temperture as a function of pressure and entropy
%T_hs	Temperture as a function of enthalpy and entropy
%
%Pressure	
%psat_T	Saturation pressure
%p_hs	Pressure as a function of h and s. 
%p_hrho Pressure as a function of h and rho. Very unaccurate for solid water region since it's almost incompressible!
%
%Enthalpy	
%hV_p	Saturated vapour enthalpy
%hL_p	Saturated liquid enthalpy
%hV_T	Saturated vapour enthalpy
%hL_T	Saturated liquid enthalpy
%h_pT	Entalpy as a function of pressure and temperature.
%h_ps	Entalpy as a function of pressure and entropy.
%h_px	Entalpy as a function of pressure and vapour fraction
%h_prho	Entalpy as a function of pressure and density. Observe for low temperatures (liquid) this equation has 2 solutions. 
%h_Tx	Entalpy as a function of temperature and vapour fraction
%
%Specific volume	
%vV_p	Saturated vapour volume
%vL_p	Saturated liquid volume
%vV_T	Saturated vapour volume
%vL_T	Saturated liquid volume
%v_pT	Specific volume as a function of pressure and temperature.
%v_ph	Specific volume as a function of pressure and enthalpy
%v_ps	Specific volume as a function of pressure and entropy.
%
%Density	
%rhoV_p	Saturated vapour density
%rhoL_p	Saturated liquid density
%rhoV_T	Saturated vapour density
%rhoL_T	Saturated liquid density
%rho_pT	Density as a function of pressure and temperature.
%rho_ph	Density as a function of pressure and enthalpy
%rho_ps	Density as a function of pressure and entropy.
%
%Specific entropy 	
%sV_p	Saturated vapour entropy
%sL_p	Saturated liquid entropy
%sV_T	Saturated vapour entropy
%sL_T	Saturated liquid entropy
%s_pT	Specific entropy as a function of pressure and temperature (Returns saturated vapour entalpy if mixture.)
%s_ph	Specific entropy as a function of pressure and enthalpy
%
%Specific internal energy 	
%uV_p	Saturated vapour internal energy
%uL_p	Saturated liquid internal energy
%uV_T	Saturated vapour internal energy
%uL_T	Saturated liquid internal energy
%u_pT	Specific internal energy as a function of pressure and temperature.
%u_ph	Specific internal energy as a function of pressure and enthalpy
%u_ps	Specific internal energy as a function of pressure and entropy.
%
%Specific isobaric heat capacity 	
%CpV_p	Saturated vapour heat capacity 
%CpL_p	Saturated liquid heat capacity 
%CpV_T	Saturated vapour heat capacity 
%CpL_T	Saturated liquid heat capacity 
%Cp_pT	Specific isobaric heat capacity as a function of pressure and temperature.
%Cp_ph	Specific isobaric heat capacity as a function of pressure and enthalpy
%Cp_ps	Specific isobaric heat capacity as a function of pressure and entropy.
%
%Specific isochoric heat capacity 	
%CvV_p	Saturated vapour isochoric heat capacity
%CvL_p	Saturated liquid isochoric heat capacity
%CvV_T	Saturated vapour isochoric heat capacity
%CvL_T	Saturated liquid isochoric heat capacity
%Cv_pT	Specific isochoric heat capacity as a function of pressure and temperature.
%Cv_ph	Specific isochoric heat capacity as a function of pressure and enthalpy
%Cv_ps	Specific isochoric heat capacity as a function of pressure and entropy.
%
%Speed of sound 	
%wV_p	Saturated vapour speed of sound
%wL_p	Saturated liquid speed of sound
%wV_T	Saturated vapour speed of sound
%wL_T	Saturated liquid speed of sound
%w_pT	Speed of sound as a function of pressure and temperature.
%w_ph	Speed of sound as a function of pressure and enthalpy
%w_ps	Speed of sound as a function of pressure and entropy.
%
%Viscosity	
%Viscosity is not part of IAPWS Steam IF97. Equations from 
%"Revised Release on the IAPWS Formulation 1985 for the Viscosity of Ordinary Water Substance", 2003 are used.	
%Viscosity in the mixed region (4) is interpolated according to the density. This is not true since it will be two fases.	
%my_pT	Viscosity as a function of pressure and temperature.
%my_ph	Viscosity as a function of pressure and enthalpy
%my_ps	Viscosity as a function of pressure and entropy.
%
%Thermal Conductivity	
%Revised release on the IAPS Formulation 1985 for the Thermal Conductivity of ordinary water substance (IAPWS 1998)	
%tcL_p	Saturated vapour thermal conductivity
%tcV_p	Saturated liquid thermal conductivity
%tcL_T	Saturated vapour thermal conductivity
%tcV_T	Saturated liquid thermal conductivity
%tc_pT	Thermal conductivity as a function of pressure and temperature.
%tc_ph	Thermal conductivity as a function of pressure and enthalpy
%tc_hs	Thermal conductivity as a function of enthalpy and entropy
%
%Surface tension
%st_T	Surface tension for two phase water/steam as a function of T
%st_p	Surface tension for two phase water/steam as a function of T
%Vapour fraction
%x_ph	Vapour fraction as a function of pressure and enthalpy
%x_ps	Vapour fraction as a function of pressure and entropy.
%
%Vapour volume fraction
%vx_ph	Vapour volume fraction as a function of pressure and enthalpy
%vx_ps	Vapour volume fraction as a function of pressure and entropy.


function Out=XSteam(fun,In1,In2)
%*Contents.
%*1 Calling functions
%*1.1
%*1.2 Temperature (T)
%*1.3 Pressure (p)
%*1.4 Enthalpy (h)
%*1.5 Specific Volume (v)
%*1.6 Density (rho)
%*1.7 Specific entropy (s)
%*1.8 Specific internal energy (u)
%*1.9 Specific isobaric heat capacity (Cp)
%*1.10 Specific isochoric heat capacity (Cv)
%*1.11 Speed of sound
%*1.12 Viscosity
%*1.13 Prandtl
%*1.14 Kappa
%*1.15 Surface tension
%*1.16 Heat conductivity
%*1.17 Vapour fraction
%*1.18 Vapour Volume Fraction
%
%*2 IAPWS IF 97 Calling functions
%*2.1 Functions for region 1
%*2.2 Functions for region 2
%*2.3 Functions for region 3
%*2.4 Functions for region 4
%*2.5 Functions for region 5
%
%*3 Region Selection
%*3.1 Regions as a function of pT
%*3.2 Regions as a function of ph
%*3.3 Regions as a function of ps
%*3.4 Regions as a function of hs
%
%4 Region Borders
%4.1 Boundary between region 1 and 3.
%4.2 Region 3. pSat_h and pSat_s
%4.3 Region boundary 1to3 and 3to2 as a functions of s
%
%5 Transport properties
%5.1 Viscosity (IAPWS formulation 1985)
%5.2 Thermal Conductivity (IAPWS formulation 1985)
%5.3 Surface Tension
%
%6 Units
%
%7 Verification
%7.1 Verifiy region 1
%7.2 Verifiy region 2
%7.3 Verifiy region 3
%7.4 Verifiy region 4
%7.5 Verifiy region 5

%***********************************************************************************************************
%*1 Calling functions                                                                                      *
%***********************************************************************************************************

%***********************************************************************************************************
%*1.1


fun=lower(fun);

switch fun
    %***********************************************************************************************************
    %*1.2 Temperature
case 'tsat_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        Out = fromSIunit_T(T4_p(p));
    else
        Out = NaN;
    end
case 'tsat_s'
    s = toSIunit_s(In1);
    if s > -0.0001545495919  && s < 9.155759395 
        ps = p4_s(s);
        Out = fromSIunit_T(T4_p(ps));
    else
        Out = NaN;
    end
case 't_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Out = fromSIunit_T(T1_ph(p, h));
    case 2
        Out = fromSIunit_T(T2_ph(p, h));
    case 3
        Out = fromSIunit_T(T3_ph(p, h));
    case 4
        Out = fromSIunit_T(T4_p(p));
    case 5
        Out = fromSIunit_T(T5_ph(p, h));
    otherwise
        Out = NaN;
    end
case 't_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Out = fromSIunit_T(T1_ps(p, s));
    case 2
        Out = fromSIunit_T(T2_ps(p, s));
    case 3
        Out = fromSIunit_T(T3_ps(p, s));
    case 4
        Out = fromSIunit_T(T4_p(p));
    case 5
        Out = fromSIunit_T(T5_ps(p, s));
    otherwise
        Out = NaN;
    end 
    
case 't_hs'
    h = toSIunit_h(In1);
    s = toSIunit_s(In2);
    Region = region_hs(h, s);
    switch Region
    case 1
        p1 = p1_hs(h, s);
        Out = fromSIunit_T(T1_ph(p1, h));
    case 2
        p2 = p2_hs(h, s);
        Out = fromSIunit_T(T2_ph(p2, h));
    case 3
        p3 = p3_hs(h, s);
        Out = fromSIunit_T(T3_ph(p3, h));
    case 4
        Out = fromSIunit_T(T4_hs(h, s));
    case 5
        error('functions of hs is not avlaible in region 5');
    otherwise
        Out = NaN;
    end
    %***********************************************************************************************************
    %*1.3 Pressure (p)
case 'psat_t'
    T = toSIunit_T(In1);
    if T < 647.096  && T > 273.15 
        Out = fromSIunit_p(p4_T(T));
    else
        Out = NaN;
    end
    
case 'psat_s'
    s = toSIunit_s(In1);
    if s > -0.0001545495919  && s < 9.155759395 
        Out = fromSIunit_p(p4_s(s));
    else
        Out = NaN;
    end
    
case 'p_hs'
    h = toSIunit_h(In1);
    s = toSIunit_s(In2);
    Region = region_hs(h, s);
    switch Region
    case 1
        Out = fromSIunit_p(p1_hs(h, s));
    case 2
        Out = fromSIunit_p(p2_hs(h, s));
    case 3
        Out = fromSIunit_p(p3_hs(h, s));
    case 4
        tSat = T4_hs(h, s);
        Out = fromSIunit_p(p4_T(tSat));
    case 5
        error('functions of hs is not avlaible in region 5');
    otherwise
        Out = NaN;
    end
    
    case 'p_hrho'
    h=In1;
    rho=In2;
%Not valid for water or sumpercritical since water rho does not change very much with p.
%Uses iteration to find p.
  High_Bound = fromSIunit_p(100);
  Low_Bound = fromSIunit_p(0.000611657);
  ps = fromSIunit_p(10);
  rhos = 1 / XSteam('v_ph',ps, h);
  while abs(rho - rhos) > 0.0000001
    rhos = 1 / XSteam('v_ph',ps, h);
    if rhos >= rho
      High_Bound = ps;
    else
      Low_Bound = ps;
    end
    ps = (Low_Bound + High_Bound) / 2;
  end
    Out = ps;

    %***********************************************************************************************************
    %*1.4 Enthalpy (h)
case 'hv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657 && p < 22.06395 
        Out = fromSIunit_h(h4V_p(p));
    else
        Out = NaN;
    end
    
case 'hl_p'
    p = toSIunit_p(In1);
    if p > 0.000611657 && p < 22.06395 
        Out = fromSIunit_h(h4L_p(p));
    else
        Out = NaN;
    end
    
case 'hv_t'
    T = toSIunit_T(In1);
    if T > 273.15 && T < 647.096 
        p = p4_T(T);
        Out = fromSIunit_h(h4V_p(p));
    else
        Out = NaN;
    end
    
case 'hl_t'
    T = toSIunit_T(In1);
    if T > 273.15 && T < 647.096 
        p = p4_T(T);
        Out = fromSIunit_h(h4L_p(p));
    else
        Out = NaN;
    end
    
    
case 'h_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_h(h1_pT(p, T));
    case 2
        Out = fromSIunit_h(h2_pT(p, T));
    case 3
        Out = fromSIunit_h(h3_pT(p, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_h(h5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case 'h_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Out = fromSIunit_h(h1_pT(p, T1_ps(p, s)));
    case 2
        Out = fromSIunit_h(h2_pT(p, T2_ps(p, s)));
    case 3
        Out = fromSIunit_h(h3_rhoT(1 / v3_ps(p, s), T3_ps(p, s)));
    case 4
        xs = x4_ps(p, s);
        Out = fromSIunit_h(xs * h4V_p(p) + (1 - xs) * h4L_p(p));
    case 5
        Out = fromSIunit_h(h5_pT(p, T5_ps(p, s)));
    otherwise
        Out = NaN;
    end
    
case 'h_px'
    p = toSIunit_p(In1);
    x = toSIunit_x(In2);
    if x > 1 || x < 0 || p >= 22.064 
        Out = NaN;
        return
    end
    hL = h4L_p(p);
    hV = h4V_p(p);
    Out = hL + x * (hV - hL);
    
case 'h_prho'
    p = toSIunit_p(In1);
    rho = 1 / toSIunit_v(1 / In2);
    Region = Region_prho(p, rho);
    switch Region
        case 1
            Out = fromSIunit_h(h1_pT(p, T1_prho(p, rho)));
        case 2
            Out = fromSIunit_h(h2_pT(p, T2_prho(p, rho)));
        case 3
            Out = fromSIunit_h(h3_rhoT(rho, T3_prho(p, rho)));
        case 4
            if p < 16.529
                vV = v2_pT(p, T4_p(p));
                vL = v1_pT(p, T4_p(p));
            else
                vV = v3_ph(p, h4V_p(p));
                vL = v3_ph(p, h4L_p(p));
            end
            hV = h4V_p(p);
            hL = h4L_p(p);
            x = (1 / rho - vL) / (vV - vL);
            Out = fromSIunit_h((1 - x) * hL + x * hV);
        case 5
            Out = fromSIunit_h(h5_pT(p, T5_prho(p, rho)));
        otherwise
            Out = NaN;
    end

case 'h_tx'
    T = toSIunit_T(In1);
    x = toSIunit_x(In2);
    if x > 1 || x < 0 || T >= 647.096 
        Out = NaN;
        return
    end
    p = p4_T(T);
    hL = h4L_p(p);
    hV = h4V_p(p);
    Out = hL + x * (hV - hL);
    
    %***********************************************************************************************************
    %*1.5 Specific Volume (v)
case {'vv_p','rhov_p'}
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_v(v2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_v(v3_ph(p, h4V_p(p)));
        end
    else
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
    
case {'vl_p','rhol_p'}
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_v(v1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_v(v3_ph(p, h4L_p(p)));
        end
    else
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
case {'vv_t','rhov_t'}
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_v(v2_pT(p4_T(T), T));
        else
            Out = fromSIunit_v(v3_ph(p4_T(T), h4V_p(p4_T(T))));
        end
    else
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
case {'vl_t','rhol_t'}
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_v(v1_pT(p4_T(T), T));
        else
            Out = fromSIunit_v(v3_ph(p4_T(T), h4L_p(p4_T(T))));
        end
    else
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
case {'v_pt','rho_pt'}
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_v(v1_pT(p, T));
    case 2
        Out = fromSIunit_v(v2_pT(p, T));
    case 3
        Out = fromSIunit_v(v3_ph(p, h3_pT(p, T)));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_v(v5_pT(p, T));
    otherwise
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
    
case {'v_ph','rho_ph'}
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Out = fromSIunit_v(v1_pT(p, T1_ph(p, h)));
    case 2
        Out = fromSIunit_v(v2_pT(p, T2_ph(p, h)));
    case 3
        Out = fromSIunit_v(v3_ph(p, h));
    case 4
        xs = x4_ph(p, h);
        if p < 16.529 
            v4v = v2_pT(p, T4_p(p));
            v4L = v1_pT(p, T4_p(p));
        else
            v4v = v3_ph(p, h4V_p(p));
            v4L = v3_ph(p, h4L_p(p));
        end
        Out = fromSIunit_v((xs * v4v + (1 - xs) * v4L));
    case 5
        Ts = T5_ph(p, h);
        Out = fromSIunit_v(v5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
case {'v_ps','rho_ps'}
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Out = fromSIunit_v(v1_pT(p, T1_ps(p, s)));
    case 2
        Out = fromSIunit_v(v2_pT(p, T2_ps(p, s)));
    case 3
        Out = fromSIunit_v(v3_ps(p, s));
    case 4
        xs = x4_ps(p, s);
        if p < 16.529 
            v4v = v2_pT(p, T4_p(p));
            v4L = v1_pT(p, T4_p(p));
        else
            v4v = v3_ph(p, h4V_p(p));
            v4L = v3_ph(p, h4L_p(p));
        end
        Out = fromSIunit_v((xs * v4v + (1 - xs) * v4L));
    case 5
        Ts = T5_ps(p, s);
        Out = fromSIunit_v(v5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    if fun(1)=='r' 
        Out=1/Out;
    end
    
    %***********************************************************************************************************
    %*1.6 Density (rho)
    % Density is calculated as 1/v. Se section 1.5 Volume
    %***********************************************************************************************************
    %*1.7 Specific entropy (s)
case 'sv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_s(s2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_s(s3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'sl_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_s(s1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_s(s3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'sv_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_s(s2_pT(p4_T(T), T));
        else
            Out = fromSIunit_s(s3_rhoT(1 / (v3_ph(p4_T(T), h4V_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'sl_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_s(s1_pT(p4_T(T), T));
        else
            Out = fromSIunit_s(s3_rhoT(1 / (v3_ph(p4_T(T), h4L_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 's_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_s(s1_pT(p, T));
    case 2
        Out = fromSIunit_s(s2_pT(p, T));
    case 3
        hs = h3_pT(p, T);
        rhos = 1 / v3_ph(p, hs);
        Out = fromSIunit_s(s3_rhoT(rhos, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_s(s5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case 's_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        T = T1_ph(p, h);
        Out = fromSIunit_s(s1_pT(p, T));
    case 2
        T = T2_ph(p, h);
        Out = fromSIunit_s(s2_pT(p, T));
    case 3
        rhos = 1 / v3_ph(p, h);
        Ts = T3_ph(p, h);
        Out = fromSIunit_s(s3_rhoT(rhos, Ts));
    case 4
        Ts = T4_p(p);
        xs = x4_ph(p, h);
        if p < 16.529 
            s4v = s2_pT(p, Ts);
            s4L = s1_pT(p, Ts);
        else
            v4v = v3_ph(p, h4V_p(p));
            s4v = s3_rhoT(1 / v4v, Ts);
            v4L = v3_ph(p, h4L_p(p));
            s4L = s3_rhoT(1 / v4L, Ts);
        end
        Out = fromSIunit_s((xs * s4v + (1 - xs) * s4L));
    case 5
        T = T5_ph(p, h);
        Out = fromSIunit_s(s5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
    
    %***********************************************************************************************************
    %*1.8 Specific internal energy (u)
case 'uv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_u(u2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_u(u3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'ul_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_u(u1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_u(u3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'uv_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_u(u2_pT(p4_T(T), T));
        else
            Out = fromSIunit_u(u3_rhoT(1 / (v3_ph(p4_T(T), h4V_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'ul_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_u(u1_pT(p4_T(T), T));
        else
            Out = fromSIunit_u(u3_rhoT(1 / (v3_ph(p4_T(T), h4L_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'u_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_u(u1_pT(p, T));
    case 2
        Out = fromSIunit_u(u2_pT(p, T));
    case 3
        hs = h3_pT(p, T);
        rhos = 1 / v3_ph(p, hs);
        Out = fromSIunit_u(u3_rhoT(rhos, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_u(u5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case 'u_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Ts = T1_ph(p, h);
        Out = fromSIunit_u(u1_pT(p, Ts));
    case 2
        Ts = T2_ph(p, h);
        Out = fromSIunit_u(u2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ph(p, h);
        Ts = T3_ph(p, h);
        Out = fromSIunit_u(u3_rhoT(rhos, Ts));
    case 4
        Ts = T4_p(p);
        xs = x4_ph(p, h);
        if p < 16.529 
            u4v = u2_pT(p, Ts);
            u4L = u1_pT(p, Ts);
        else
            v4v = v3_ph(p, h4V_p(p));
            u4v = u3_rhoT(1 / v4v, Ts);
            v4L = v3_ph(p, h4L_p(p));
            u4L = u3_rhoT(1 / v4L, Ts);
        end
        Out = fromSIunit_u((xs * u4v + (1 - xs) * u4L));
    case 5
        Ts = T5_ph(p, h);
        Out = fromSIunit_u(u5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    
case 'u_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Ts = T1_ps(p, s);
        Out = fromSIunit_u(u1_pT(p, Ts));
    case 2
        Ts = T2_ps(p, s);
        Out = fromSIunit_u(u2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ps(p, s);
        Ts = T3_ps(p, s);
        Out = fromSIunit_u(u3_rhoT(rhos, Ts));
    case 4
        if p < 16.529 
            uLp = u1_pT(p, T4_p(p));
            uVp = u2_pT(p, T4_p(p));
        else
            uLp = u3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p));
            uVp = u3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p));
        end
        xs = x4_ps(p, s);
        Out = fromSIunit_u((xs * uVp + (1 - xs) * uLp));
    case 5
        Ts = T5_ps(p, s);
        Out = fromSIunit_u(u5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    %***********************************************************************************************************
    %*1.9 Specific isobaric heat capacity (Cp)
case 'cpv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_Cp(Cp2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_Cp(Cp3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'cpl_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_Cp(Cp1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_Cp(Cp3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'cpv_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_Cp(Cp2_pT(p4_T(T), T));
        else
            Out = fromSIunit_Cp(Cp3_rhoT(1 / (v3_ph(p4_T(T), h4V_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'cpl_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_Cp(Cp1_pT(p4_T(T), T));
        else
            Out = fromSIunit_Cp(Cp3_rhoT(1 / (v3_ph(p4_T(T), h4L_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'cp_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_Cp(Cp1_pT(p, T));
    case 2
        Out = fromSIunit_Cp(Cp2_pT(p, T));
    case 3
        hs = h3_pT(p, T);
        rhos = 1 / v3_ph(p, hs);
        Out = fromSIunit_Cp(Cp3_rhoT(rhos, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_Cp(Cp5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case 'cp_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Ts = T1_ph(p, h);
        Out = fromSIunit_Cp(Cp1_pT(p, Ts));
    case 2
        Ts = T2_ph(p, h);
        Out = fromSIunit_Cp(Cp2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ph(p, h);
        Ts = T3_ph(p, h);
        Out = fromSIunit_Cp(Cp3_rhoT(rhos, Ts));
    case 4
        Out = NaN;
    case 5
        Ts = T5_ph(p, h);
        Out = fromSIunit_Cp(Cp5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    
case 'cp_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Ts = T1_ps(p, s);
        Out = fromSIunit_Cp(Cp1_pT(p, Ts));
    case 2
        Ts = T2_ps(p, s);
        Out = fromSIunit_Cp(Cp2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ps(p, s);
        Ts = T3_ps(p, s);
        Out = fromSIunit_Cp(Cp3_rhoT(rhos, Ts));
    case 4
        Out = NaN;
    case 5
        Ts = T5_ps(p, s);
        Out = fromSIunit_Cp(Cp5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    
    %***********************************************************************************************************
    %*1.10 Specific isochoric heat capacity (Cv)
case 'cvv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_Cv(Cv2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_Cv(Cv3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'cvl_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_Cv(Cv1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_Cv(Cv3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'cvv_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_Cv(Cv2_pT(p4_T(T), T));
        else
            Out = fromSIunit_Cv(Cv3_rhoT(1 / (v3_ph(p4_T(T), h4V_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'cvl_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_Cv(Cv1_pT(p4_T(T), T));
        else
            Out = fromSIunit_Cv(Cv3_rhoT(1 / (v3_ph(p4_T(T), h4L_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'cv_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_Cv(Cv1_pT(p, T));
    case 2
        Out = fromSIunit_Cv(Cv2_pT(p, T));
    case 3
        hs = h3_pT(p, T);
        rhos = 1 / v3_ph(p, hs);
        Out = fromSIunit_Cv(Cv3_rhoT(rhos, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_Cv(Cv5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case 'cv_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Ts = T1_ph(p, h);
        Out = fromSIunit_Cv(Cv1_pT(p, Ts));
    case 2
        Ts = T2_ph(p, h);
        Out = fromSIunit_Cv(Cv2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ph(p, h);
        Ts = T3_ph(p, h);
        Out = fromSIunit_Cv(Cv3_rhoT(rhos, Ts));
    case 4
        Out = NaN;
    case 5
        Ts = T5_ph(p, h);
        Out = fromSIunit_Cv(Cv5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    
    
case 'cv_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Ts = T1_ps(p, s);
        Out = fromSIunit_Cv(Cv1_pT(p, Ts));
    case 2
        Ts = T2_ps(p, s);
        Out = fromSIunit_Cv(Cv2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ps(p, s);
        Ts = T3_ps(p, s);
        Out = fromSIunit_Cv(Cv3_rhoT(rhos, Ts));
    case 4
        Out = NaN;  %(xs * CvVp + (1 - xs) * CvLp) / Cv_scale - Cv_offset
    case 5
        Ts = T5_ps(p, s);
        Out = fromSIunit_Cv(Cv5_pT(p, Ts));
    otherwise
        Out = CVErr(xlErrValue);
    end
    
    
    %***********************************************************************************************************
    %*1.11 Speed of sound
case 'wv_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_w(w2_pT(p, T4_p(p)));
        else
            Out = fromSIunit_w(w3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'wl_p'
    p = toSIunit_p(In1);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            Out = fromSIunit_w(w1_pT(p, T4_p(p)));
        else
            Out = fromSIunit_w(w3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p)));
        end
    else
        Out = NaN;
    end
    
case 'wv_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_w(w2_pT(p4_T(T), T));
        else
            Out = fromSIunit_w(w3_rhoT(1 / (v3_ph(p4_T(T), h4V_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'wl_t'
    T = toSIunit_T(In1);
    if T > 273.15  && T < 647.096 
        if T <= 623.15 
            Out = fromSIunit_w(w1_pT(p4_T(T), T));
        else
            Out = fromSIunit_w(w3_rhoT(1 / (v3_ph(p4_T(T), h4L_p(p4_T(T)))), T));
        end
    else
        Out = NaN;
    end
    
case 'w_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 1
        Out = fromSIunit_w(w1_pT(p, T));
    case 2
        Out = fromSIunit_w(w2_pT(p, T));
    case 3
        hs = h3_pT(p, T);
        rhos = 1 / v3_ph(p, hs);
        Out = fromSIunit_w(w3_rhoT(rhos, T));
    case 4
        Out = NaN;
    case 5
        Out = fromSIunit_w(w5_pT(p, T));
    otherwise
        Out = NaN;
    end
    
    
case 'w_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case 1
        Ts = T1_ph(p, h);
        Out = fromSIunit_w(w1_pT(p, Ts));
    case 2
        Ts = T2_ph(p, h);
        Out = fromSIunit_w(w2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ph(p, h);
        Ts = T3_ph(p, h);
        Out = fromSIunit_w(w3_rhoT(rhos, Ts));
    case 4
        Out = NaN;
    case 5
        Ts = T5_ph(p, h);
        Out = fromSIunit_w(w5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    
case 'w_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    Region = region_ps(p, s);
    switch Region
    case 1
        Ts = T1_ps(p, s);
        Out = fromSIunit_w(w1_pT(p, Ts));
    case 2
        Ts = T2_ps(p, s);
        Out = fromSIunit_w(w2_pT(p, Ts));
    case 3
        rhos = 1 / v3_ps(p, s);
        Ts = T3_ps(p, s);
        Out = fromSIunit_w(w3_rhoT(rhos, Ts));
    case 4
        Out = NaN; %(xs * wVp + (1 - xs) * wLp) / w_scale - w_offset
    case 5
        Ts = T5_ps(p, s);
        Out = fromSIunit_w(w5_pT(p, Ts));
    otherwise
        Out = NaN;
    end
    %***********************************************************************************************************
    %*1.12 Viscosity
case 'my_pt'
    p = toSIunit_p(In1);
    T = toSIunit_T(In2);
    Region = region_pT(p, T);
    switch Region
    case 4
        Out = NaN;
    case {1, 2, 3, 5}
        Out = fromSIunit_my(my_AllRegions_pT(p, T));
    otherwise
        Out = NaN;
    end
    
case {'my_ph'}
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    Region = region_ph(p, h);
    switch Region
    case {1, 2, 3, 5}
        Out = fromSIunit_my(my_AllRegions_ph(p, h));
    case {4}
        Out = NaN;  
    otherwise
        Out = NaN;
    end
    
case 'my_ps'
    h = XSteam('h_ps',In1, In2);
    Out = XSteam('my_ph',In1, h);
    
    %***********************************************************************************************************
    %*1.13 Prandtl
    case 'pr_pt'
  Cp = toSIunit_Cp(XSteam('Cp_pT',In1, In2));
  my = toSIunit_my(XSteam('my_pT',In1,In2));
  tc = toSIunit_tc(XSteam('tc_pT',In1,In2));
  Out = Cp * 1000 * my / tc;

    case 'pr_ph'
  Cp = toSIunit_Cp(XSteam('Cp_ph',In1, In2));
  my = toSIunit_my(XSteam('my_ph',In1,In2));
  tc = toSIunit_tc(XSteam('tc_ph',In1,In2));
  Out = Cp * 1000 * my / tc;

    %***********************************************************************************************************
    %*1.14 Kappa
    %***********************************************************************************************************
    %***********************************************************************************************************
    %*1.15 Surface tension
case 'st_t'
    T = toSIunit_T(In1);
    Out = fromSIunit_st(Surface_Tension_T(T));
    
case 'st_p'
    T = XSteam('Tsat_p',In1);
    T = toSIunit_T(T);
    Out = fromSIunit_st(Surface_Tension_T(T));
    
    %***********************************************************************************************************
    %*1.16 Thermal conductivity
case 'tcl_p'
    T = XSteam('Tsat_p',In1);
    v = XSteam('vL_p',In1);
    p = toSIunit_p(In1);
    T = toSIunit_T(T);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
    
case 'tcv_p'
    ps = In1;
    T = XSteam('Tsat_p',ps);
    v = XSteam('vV_p',ps);
    p = toSIunit_p(In1);
    T = toSIunit_T(T);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
case 'tcl_t'
    Ts = In1;
    p = XSteam('psat_T',Ts);
    v = XSteam('vL_T',Ts);
    p = toSIunit_p(p);
    T = toSIunit_T(Ts);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
case 'tcv_t'
    Ts = In1;
    p = XSteam('psat_T',Ts);
    v = XSteam('vV_T',Ts);
    p = toSIunit_p(p);
    T = toSIunit_T(Ts);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
case 'tc_pt'
    Ts = In2;
    ps = In1;
    v = XSteam('v_pT',ps, Ts);
    p = toSIunit_p(ps);
    T = toSIunit_T(Ts);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
case 'tc_ph'
    hs = In2;
    ps = In1;
    v = XSteam('v_ph',ps, hs);
    T = XSteam('T_ph',ps, hs);
    p = toSIunit_p(ps);
    T = toSIunit_T(T);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    
case 'tc_hs'
    hs = In1;
    p = XSteam('p_hs',hs, In2);
    ps = p;
    v = XSteam('v_ph',ps, hs);
    T = XSteam('T_ph',ps, hs);
    p = toSIunit_p(p);
    T = toSIunit_T(T);
    v = toSIunit_v(v);
    rho = 1 / v;
    Out = fromSIunit_tc(tc_ptrho(p, T, rho));
    %***********************************************************************************************************
    %*1.17 Vapour fraction
case 'x_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    if p > 0.000611657  && p < 22.06395 
        Out = fromSIunit_x(x4_ph(p, h));
    else
        Out = NaN;
    end
    
case 'x_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    if p > 0.000611657  && p < 22.06395 
        Out = fromSIunit_x(x4_ps(p, s));
    else
        Out = NaN;
    end
    
    %***********************************************************************************************************
    %*1.18 Vapour Volume Fraction
case 'vx_ph'
    p = toSIunit_p(In1);
    h = toSIunit_h(In2);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            vL = v1_pT(p, T4_p(p));
            vV = v2_pT(p, T4_p(p));
        else
            vL = v3_ph(p, h4L_p(p));
            vV = v3_ph(p, h4V_p(p));
        end
        xs = x4_ph(p, h);
        Out = fromSIunit_vx((xs * vV / (xs * vV + (1 - xs) * vL)));
    else
        Out = NaN;
    end
    
case 'vx_ps'
    p = toSIunit_p(In1);
    s = toSIunit_s(In2);
    if p > 0.000611657  && p < 22.06395 
        if p < 16.529 
            vL = v1_pT(p, T4_p(p));
            vV = v2_pT(p, T4_p(p));
        else
            vL = v3_ph(p, h4L_p(p));
            vV = v3_ph(p, h4V_p(p));
        end
        xs = x4_ps(p, s);
        Out = fromSIunit_vx((xs * vV / (xs * vV + (1 - xs) * vL)));
    else
        Out = NaN;
    end
 
 case 'check'
   err=check();
    
otherwise
    error(['Unknown calling function to XSteam, ',fun, ' See help XSteam for valid calling functions']);
end
%***********************************************************************************************************
%*2 IAPWS IF 97 Calling functions                                                                          *
%***********************************************************************************************************
%
%***********************************************************************************************************
%*2.1 Functions for region 1
function v1_pT = v1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_pi = 0;
for i = 1 : 34
    gamma_der_pi = gamma_der_pi - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * (tau - 1.222) ^ J1(i);
end
v1_pT = R * T / p * Pi * gamma_der_pi / 1000;

function h1_pT = h1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_tau = 0;
for i = 1 : 34
    gamma_der_tau = gamma_der_tau + (n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (tau - 1.222) ^ (J1(i) - 1));
end
h1_pT = R * T * tau * gamma_der_tau;

function u1_pT = u1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_tau = 0;
gamma_der_pi = 0;
for i = 1 : 34
    gamma_der_pi = gamma_der_pi - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * (tau - 1.222) ^ J1(i);
    gamma_der_tau = gamma_der_tau + (n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (tau - 1.222) ^ (J1(i) - 1));
end
u1_pT = R * T * (tau * gamma_der_tau - Pi * gamma_der_pi);

function s1_pT = s1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma = 0;
gamma_der_tau = 0;
for i = 1 : 34
    gamma_der_tau = gamma_der_tau + (n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (tau - 1.222) ^ (J1(i) - 1));
    gamma = gamma + n1(i) * (7.1 - Pi) ^ I1(i) * (tau - 1.222) ^ J1(i);
end
s1_pT = R * tau * gamma_der_tau - R * gamma;

function Cp1_pT = Cp1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_tautau = 0;
for i = 1 :34
    gamma_der_tautau = gamma_der_tautau + (n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (J1(i) - 1) * (tau - 1.222) ^ (J1(i) - 2));
end
Cp1_pT = -R * tau ^ 2 * gamma_der_tautau;

function Cv1_pT = Cv1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_pi = 0;
gamma_der_pipi = 0;
gamma_der_pitau = 0;
gamma_der_tautau = 0;
for i = 1 : 34
    gamma_der_pi = gamma_der_pi - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * (tau - 1.222) ^ J1(i);
    gamma_der_pipi = gamma_der_pipi + n1(i) * I1(i) * (I1(i) - 1) * (7.1 - Pi) ^ (I1(i) - 2) * (tau - 1.222) ^ J1(i);
    gamma_der_pitau = gamma_der_pitau - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * J1(i) * (tau - 1.222) ^ (J1(i) - 1);
    gamma_der_tautau = gamma_der_tautau + n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (J1(i) - 1) * (tau - 1.222) ^ (J1(i) - 2);
end
Cv1_pT = R * (-tau ^ 2 * gamma_der_tautau + (gamma_der_pi - tau * gamma_der_pitau) ^ 2 / gamma_der_pipi);

function w1_pT = w1_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation
%Eqution 7, Table 3, Page 6
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32];
J1 = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41];
n1 = [0.14632971213167, -0.84548187169114, -3.756360367204, 3.3855169168385, -0.95791963387872, 0.15772038513228, -0.016616417199501, 8.1214629983568E-04, 2.8319080123804E-04, -6.0706301565874E-04, -0.018990068218419, -0.032529748770505, -0.021841717175414, -5.283835796993E-05, -4.7184321073267E-04, -3.0001780793026E-04, 4.7661393906987E-05, -4.4141845330846E-06, -7.2694996297594E-16, -3.1679644845054E-05, -2.8270797985312E-06, -8.5205128120103E-10, -2.2425281908E-06, -6.5171222895601E-07, -1.4341729937924E-13, -4.0516996860117E-07, -1.2734301741641E-09, -1.7424871230634E-10, -6.8762131295531E-19, 1.4478307828521E-20, 2.6335781662795E-23, -1.1947622640071E-23, 1.8228094581404E-24, -9.3537087292458E-26];
R = 0.461526; %kJ/(kg K)
Pi = p / 16.53;
tau = 1386 / T;
gamma_der_pi = 0;
gamma_der_pipi = 0;
gamma_der_pitau = 0;
gamma_der_tautau = 0;
for i = 1 : 34
    gamma_der_pi = gamma_der_pi - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * (tau - 1.222) ^ J1(i);
    gamma_der_pipi = gamma_der_pipi + n1(i) * I1(i) * (I1(i) - 1) * (7.1 - Pi) ^ (I1(i) - 2) * (tau - 1.222) ^ J1(i);
    gamma_der_pitau = gamma_der_pitau - n1(i) * I1(i) * (7.1 - Pi) ^ (I1(i) - 1) * J1(i) * (tau - 1.222) ^ (J1(i) - 1);
    gamma_der_tautau = gamma_der_tautau + n1(i) * (7.1 - Pi) ^ I1(i) * J1(i) * (J1(i) - 1) * (tau - 1.222) ^ (J1(i) - 2);
end
w1_pT = (1000 * R * T * gamma_der_pi ^ 2 / ((gamma_der_pi - tau * gamma_der_pitau) ^ 2 / (tau ^ 2 * gamma_der_tautau) - gamma_der_pipi)) ^ 0.5;

function T1_ph = T1_ph(p, h)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation, 5.2.1 The Backward Equation T ( p,h )
%Eqution 11, Table 6, Page 10
I1 = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6];
J1 = [0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32];
n1 = [-238.72489924521, 404.21188637945, 113.49746881718, -5.8457616048039, -1.528548241314E-04, -1.0866707695377E-06, -13.391744872602, 43.211039183559, -54.010067170506, 30.535892203916, -6.5964749423638, 9.3965400878363E-03, 1.157364750534E-07, -2.5858641282073E-05, -4.0644363084799E-09, 6.6456186191635E-08, 8.0670734103027E-11, -9.3477771213947E-13, 5.8265442020601E-15, -1.5020185953503E-17];
Pi = p / 1;
eta = h / 2500;
T = 0;
for i = 1 : 20
    T = T + n1(i) * Pi ^ I1(i) * (eta + 1) ^ J1(i);
end
T1_ph = T;

function T1_ps = T1_ps(p, s)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%5 Equations for Region 1, Section. 5.1 Basic Equation, 5.2.2 The Backward Equation T ( p, s )
%Eqution 13, Table 8, Page 11
I1 = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4];
J1 = [0, 1, 2, 3, 11, 31, 0, 1, 2, 3, 12, 31, 0, 1, 2, 9, 31, 10, 32, 32];
n1 = [174.78268058307, 34.806930892873, 6.5292584978455, 0.33039981775489, -1.9281382923196E-07, -2.4909197244573E-23, -0.26107636489332, 0.22592965981586, -0.064256463395226, 7.8876289270526E-03, 3.5672110607366E-10, 1.7332496994895E-24, 5.6608900654837E-04, -3.2635483139717E-04, 4.4778286690632E-05, -5.1322156908507E-10, -4.2522657042207E-26, 2.6400441360689E-13, 7.8124600459723E-29, -3.0732199903668E-31];
Pi = p / 1;
Sigma = s / 1;
T = 0;
for i = 1 : 20
    T = T + n1(i) * Pi ^ I1(i) * (Sigma + 2) ^ J1(i);
end
T1_ps = T;

function p1_hs = p1_hs(h, s)
%Supplementary Release on Backward Equations for Pressure as a Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%5 Backward Equation p(h,s) for Region 1
%Eqution 1, Table 2, Page 5
I1 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5];
J1 = [0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0];
n1 = [-0.691997014660582, -18.361254878756, -9.28332409297335, 65.9639569909906, -16.2060388912024, 450.620017338667, 854.68067822417, 6075.23214001162, 32.6487682621856, -26.9408844582931, -319.9478483343, -928.35430704332, 30.3634537455249, -65.0540422444146, -4309.9131651613, -747.512324096068, 730.000345529245, 1142.84032569021, -436.407041874559];
eta = h / 3400;
Sigma = s / 7.6;
p = 0;
for i = 1 : 19
    p = p + n1(i) * (eta + 0.05) ^ I1(i) * (Sigma + 0.05) ^ J1(i);
end
p1_hs = p * 100;

function T1_prho = T1_prho(p ,rho)
  %Solve by iteration. Observe that for low temperatures this equation has 2 solutions.
  %Solve with half interval method
  Low_Bound = 273.15;
  High_Bound = T4_p(p);
  rhos=-1000;
  while abs(rho - rhos) > 0.00001
    Ts = (Low_Bound + High_Bound) / 2;
    rhos = 1 / v1_pT(p, Ts);
    if rhos < rho
      High_Bound = Ts;
    else
      Low_Bound = Ts;
    end
  end
  T1_prho = Ts;

%***********************************************************************************************************
%*2.2 functions for region 2

function v2_pT = v2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_pi = 1 / Pi;
gr_pi = 0;
for i = 1 : 43
    gr_pi = gr_pi + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * (tau - 0.5) ^ Jr(i);
end
v2_pT = R * T / p * Pi * (g0_pi + gr_pi) / 1000;

function h2_pT = h2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_tau = 0;
for i = 1 : 9
    g0_tau = g0_tau + n0(i) * J0(i) * tau ^ (J0(i) - 1);
end
gr_tau = 0;
for i = 1 : 43
    gr_tau = gr_tau + nr(i) * Pi ^ Ir(i) * Jr(i) * (tau - 0.5) ^ (Jr(i) - 1);
end
h2_pT = R * T * tau * (g0_tau + gr_tau);

function u2_pT = u2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_pi = 1 / Pi;
g0_tau = 0;
for i = 1 : 9
    g0_tau = g0_tau + n0(i) * J0(i) * tau ^ (J0(i) - 1);
end
gr_pi = 0;
gr_tau = 0;
for i = 1 : 43
    gr_pi = gr_pi + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * (tau - 0.5) ^ Jr(i);
    gr_tau = gr_tau + nr(i) * Pi ^ Ir(i) * Jr(i) * (tau - 0.5) ^ (Jr(i) - 1);
end
u2_pT = R * T * (tau * (g0_tau + gr_tau) - Pi * (g0_pi + gr_pi));


function s2_pT = s2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0 = log(Pi);
g0_tau = 0;
for i = 1 : 9
    g0 = g0 + n0(i) * tau ^ J0(i);
    g0_tau = g0_tau + n0(i) * J0(i) * tau ^ (J0(i) - 1);
end
gr = 0;
gr_tau = 0;
for i = 1 : 43
    gr = gr + nr(i) * Pi ^ Ir(i) * (tau - 0.5) ^ Jr(i);
    gr_tau = gr_tau + nr(i) * Pi ^ Ir(i) * Jr(i) * (tau - 0.5) ^ (Jr(i) - 1);
end
s2_pT = R * (tau * (g0_tau + gr_tau) - (g0 + gr));

function Cp2_pT = Cp2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_tautau = 0;
for i = 1 : 9
    g0_tautau = g0_tautau + n0(i) * J0(i) * (J0(i) - 1) * tau ^ (J0(i) - 2);
end
gr_tautau = 0;
for i = 1 : 43
    gr_tautau = gr_tautau + nr(i) * Pi ^ Ir(i) * Jr(i) * (Jr(i) - 1) * (tau - 0.5) ^ (Jr(i) - 2);
end
Cp2_pT = -R * tau ^ 2 * (g0_tautau + gr_tautau);

function Cv2_pT = Cv2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_tautau = 0;
for i =  1 : 9
    g0_tautau = g0_tautau + n0(i) * J0(i) * (J0(i) - 1) * tau ^ (J0(i) - 2);
end
gr_pi = 0;
gr_pitau = 0;
gr_pipi = 0;
gr_tautau = 0;
for i = 1 : 43
    gr_pi = gr_pi + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * (tau - 0.5) ^ Jr(i);
    gr_pipi = gr_pipi + nr(i) * Ir(i) * (Ir(i) - 1) * Pi ^ (Ir(i) - 2) * (tau - 0.5) ^ Jr(i);
    gr_pitau = gr_pitau + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * Jr(i) * (tau - 0.5) ^ (Jr(i) - 1);
    gr_tautau = gr_tautau + nr(i) * Pi ^ Ir(i) * Jr(i) * (Jr(i) - 1) * (tau - 0.5) ^ (Jr(i) - 2);
end
Cv2_pT = R * (-tau ^ 2 * (g0_tautau + gr_tautau) - (1 + Pi * gr_pi - tau * Pi * gr_pitau) ^ 2 / (1 - Pi ^ 2 * gr_pipi));

function w2_pT = w2_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2, Section. 6.1 Basic Equation
%Table 11 and 12, Page 14 and 15
J0 = [0, 1, -5, -4, -3, -2, -1, 2, 3];
n0 = [-9.6927686500217, 10.086655968018, -0.005608791128302, 0.071452738081455, -0.40710498223928, 1.4240819171444, -4.383951131945, -0.28408632460772, 0.021268463753307];
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24];
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58];
nr = [-1.7731742473213E-03, -0.017834862292358, -0.045996013696365, -0.057581259083432, -0.05032527872793, -3.3032641670203E-05, -1.8948987516315E-04, -3.9392777243355E-03, -0.043797295650573, -2.6674547914087E-05, 2.0481737692309E-08, 4.3870667284435E-07, -3.227767723857E-05, -1.5033924542148E-03, -0.040668253562649, -7.8847309559367E-10, 1.2790717852285E-08, 4.8225372718507E-07, 2.2922076337661E-06, -1.6714766451061E-11, -2.1171472321355E-03, -23.895741934104, -5.905956432427E-18, -1.2621808899101E-06, -0.038946842435739, 1.1256211360459E-11, -8.2311340897998, 1.9809712802088E-08, 1.0406965210174E-19, -1.0234747095929E-13, -1.0018179379511E-09, -8.0882908646985E-11, 0.10693031879409, -0.33662250574171, 8.9185845355421E-25, 3.0629316876232E-13, -4.2002467698208E-06, -5.9056029685639E-26, 3.7826947613457E-06, -1.2768608934681E-15, 7.3087610595061E-29, 5.5414715350778E-17, -9.436970724121E-07];
R = 0.461526; %kJ/(kg K)
Pi = p;
tau = 540 / T;
g0_tautau = 0;
for i =  1 : 9
    g0_tautau = g0_tautau + n0(i) * J0(i) * (J0(i) - 1) * tau ^ (J0(i) - 2);
end
gr_pi = 0;
gr_pitau = 0;
gr_pipi = 0;
gr_tautau = 0;
for i = 1 : 43
    gr_pi = gr_pi + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * (tau - 0.5) ^ Jr(i);
    gr_pipi = gr_pipi + nr(i) * Ir(i) * (Ir(i) - 1) * Pi ^ (Ir(i) - 2) * (tau - 0.5) ^ Jr(i);
    gr_pitau = gr_pitau + nr(i) * Ir(i) * Pi ^ (Ir(i) - 1) * Jr(i) * (tau - 0.5) ^ (Jr(i) - 1);
    gr_tautau = gr_tautau + nr(i) * Pi ^ Ir(i) * Jr(i) * (Jr(i) - 1) * (tau - 0.5) ^ (Jr(i) - 2);
end
w2_pT = (1000 * R * T * (1 + 2 * Pi * gr_pi + Pi ^ 2 * gr_pi ^ 2) / ((1 - Pi ^ 2 * gr_pipi) + (1 + Pi * gr_pi - tau * Pi * gr_pitau) ^ 2 / (tau ^ 2 * (g0_tautau + gr_tautau)))) ^ 0.5;

function T2_ph = T2_ph(p, h)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2,6.3.1 The Backward Equations T( p, h ) for Subregions 2a, 2b, and 2c
if p < 4 
    sub_reg = 1;
else
    if p < (905.84278514723 - 0.67955786399241 * h + 1.2809002730136E-04 * h ^ 2) 
        sub_reg = 2;
    else
        sub_reg = 3;
    end
end

switch sub_reg
case 1
    %Subregion A
    %Table 20, Eq 22, page 22
    Ji = [0, 1, 2, 3, 7, 20, 0, 1, 2, 3, 7, 9, 11, 18, 44, 0, 2, 7, 36, 38, 40, 42, 44, 24, 44, 12, 32, 44, 32, 36, 42, 34, 44, 28];
    Ii = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7];
    ni = [1089.8952318288, 849.51654495535, -107.81748091826, 33.153654801263, -7.4232016790248, 11.765048724356, 1.844574935579, -4.1792700549624, 6.2478196935812, -17.344563108114, -200.58176862096, 271.96065473796, -455.11318285818, 3091.9688604755, 252266.40357872, -6.1707422868339E-03, -0.31078046629583, 11.670873077107, 128127984.04046, -985549096.23276, 2822454697.3002, -3594897141.0703, 1722734991.3197, -13551.334240775, 12848734.66465, 1.3865724283226, 235988.32556514, -13105236.545054, 7399.9835474766, -551966.9703006, 3715408.5996233, 19127.72923966, -415351.64835634, -62.459855192507];
    Ts = 0;
    hs = h / 2000;
    for i = 1 : 34
        Ts = Ts + ni(i) * p ^ (Ii(i)) * (hs - 2.1) ^ Ji(i);
    end
    T2_ph = Ts;
case 2
    %Subregion B
    %Table 21, Eq 23, page 23
    Ji = [0, 1, 2, 12, 18, 24, 28, 40, 0, 2, 6, 12, 18, 24, 28, 40, 2, 8, 18, 40, 1, 2, 12, 24, 2, 12, 18, 24, 28, 40, 18, 24, 40, 28, 2, 28, 1, 40];
    Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 9, 9];
    ni = [1489.5041079516, 743.07798314034, -97.708318797837, 2.4742464705674, -0.63281320016026, 1.1385952129658, -0.47811863648625, 8.5208123431544E-03, 0.93747147377932, 3.3593118604916, 3.3809355601454, 0.16844539671904, 0.73875745236695, -0.47128737436186, 0.15020273139707, -0.002176411421975, -0.021810755324761, -0.10829784403677, -0.046333324635812, 7.1280351959551E-05, 1.1032831789999E-04, 1.8955248387902E-04, 3.0891541160537E-03, 1.3555504554949E-03, 2.8640237477456E-07, -1.0779857357512E-05, -7.6462712454814E-05, 1.4052392818316E-05, -3.1083814331434E-05, -1.0302738212103E-06, 2.821728163504E-07, 1.2704902271945E-06, 7.3803353468292E-08, -1.1030139238909E-08, -8.1456365207833E-14, -2.5180545682962E-11, -1.7565233969407E-18, 8.6934156344163E-15];
    Ts = 0;
    hs = h / 2000;
    for i = 1 : 38
        Ts = Ts + ni(i) * (p - 2) ^ (Ii(i)) * (hs - 2.6) ^ Ji(i);
    end
    T2_ph = Ts;
otherwise
    %Subregion C
    %Table 22, Eq 24, page 24
    Ji = [0, 4, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 4, 8, 4, 0, 1, 4, 10, 12, 16, 20, 22];
    Ii = [-7, -7, -6, -6, -5, -5, -2, -2, -1, -1, 0, 0, 1, 1, 2, 6, 6, 6, 6, 6, 6, 6, 6];
    ni = [-3236839855524.2, 7326335090218.1, 358250899454.47, -583401318515.9, -10783068217.47, 20825544563.171, 610747.83564516, 859777.2253558, -25745.72360417, 31081.088422714, 1208.2315865936, 482.19755109255, 3.7966001272486, -10.842984880077, -0.04536417267666, 1.4559115658698E-13, 1.126159740723E-12, -1.7804982240686E-11, 1.2324579690832E-07, -1.1606921130984E-06, 2.7846367088554E-05, -5.9270038474176E-04, 1.2918582991878E-03];
    Ts = 0;
    hs = h / 2000;
    for i = 1 : 23
        Ts = Ts + ni(i) * (p + 25) ^ (Ii(i)) * (hs - 1.8) ^ Ji(i);
    end
    T2_ph = Ts;
end

function T2_ps = T2_ps(p, s)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%6 Equations for Region 2,6.3.2 The Backward Equations T( p, s ) for Subregions 2a, 2b, and 2c
%Page 26
if p < 4 
    sub_reg = 1;
else
    if s < 5.85 
        sub_reg = 3;
    else
        sub_reg = 2;
    end
end
switch sub_reg
case 1
    %Subregion A
    %Table 25, Eq 25, page 26
    Ii = [-1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.25, -1.25, -1.25, -1, -1, -1, -1, -1, -1, -0.75, -0.75, -0.5, -0.5, -0.5, -0.5, -0.25, -0.25, -0.25, -0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1, 1, 1.25, 1.25, 1.5, 1.5];
    Ji = [-24, -23, -19, -13, -11, -10, -19, -15, -6, -26, -21, -17, -16, -9, -8, -15, -14, -26, -13, -9, -7, -27, -25, -11, -6, 1, 4, 8, 11, 0, 1, 5, 6, 10, 14, 16, 0, 4, 9, 17, 7, 18, 3, 15, 5, 18];
    ni = [-392359.83861984, 515265.7382727, 40482.443161048, -321.93790923902, 96.961424218694, -22.867846371773, -449429.14124357, -5011.8336020166, 0.35684463560015, 44235.33584819, -13673.388811708, 421632.60207864, 22516.925837475, 474.42144865646, -149.31130797647, -197811.26320452, -23554.39947076, -19070.616302076, 55375.669883164, 3829.3691437363, -603.91860580567, 1936.3102620331, 4266.064369861, -5978.0638872718, -704.01463926862, 338.36784107553, 20.862786635187, 0.033834172656196, -4.3124428414893E-05, 166.53791356412, -139.86292055898, -0.78849547999872, 0.072132411753872, -5.9754839398283E-03, -1.2141358953904E-05, 2.3227096733871E-07, -10.538463566194, 2.0718925496502, -0.072193155260427, 2.074988708112E-07, -0.018340657911379, 2.9036272348696E-07, 0.21037527893619, 2.5681239729999E-04, -0.012799002933781, -8.2198102652018E-06];
    Pi = p;
    Sigma = s / 2;
    teta = 0;
    for i = 1 : 46
        teta = teta + ni(i) * Pi ^ Ii(i) * (Sigma - 2) ^ Ji(i);
    end
    T2_ps = teta;
case 2
    %Subregion B
    %Table 26, Eq 26, page 27
    Ii = [-6, -6, -5, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5];
    Ji = [0, 11, 0, 11, 0, 1, 11, 0, 1, 11, 12, 0, 1, 6, 10, 0, 1, 5, 8, 9, 0, 1, 2, 4, 5, 6, 9, 0, 1, 2, 3, 7, 8, 0, 1, 5, 0, 1, 3, 0, 1, 0, 1, 2];
    ni = [316876.65083497, 20.864175881858, -398593.99803599, -21.816058518877, 223697.85194242, -2784.1703445817, 9.920743607148, -75197.512299157, 2970.8605951158, -3.4406878548526, 0.38815564249115, 17511.29508575, -1423.7112854449, 1.0943803364167, 0.89971619308495, -3375.9740098958, 471.62885818355, -1.9188241993679, 0.41078580492196, -0.33465378172097, 1387.0034777505, -406.63326195838, 41.72734715961, 2.1932549434532, -1.0320050009077, 0.35882943516703, 5.2511453726066E-03, 12.838916450705, -2.8642437219381, 0.56912683664855, -0.099962954584931, -3.2632037778459E-03, 2.3320922576723E-04, -0.1533480985745, 0.029072288239902, 3.7534702741167E-04, 1.7296691702411E-03, -3.8556050844504E-04, -3.5017712292608E-05, -1.4566393631492E-05, 5.6420857267269E-06, 4.1286150074605E-08, -2.0684671118824E-08, 1.6409393674725E-09];
    Pi = p;
    Sigma = s / 0.7853;
    teta = 0;
    for i = 1 : 44
        teta = teta + ni(i) * Pi ^ Ii(i) * (10 - Sigma) ^ Ji(i);
    end
    T2_ps = teta;
otherwise
    %Subregion C
    %Table 27, Eq 27, page 28
    Ii = [-2, -2, -1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7];
    Ji = [0, 1, 0, 0, 1, 2, 3, 0, 1, 3, 4, 0, 1, 2, 0, 1, 5, 0, 1, 4, 0, 1, 2, 0, 1, 0, 1, 3, 4, 5];
    ni = [909.68501005365, 2404.566708842, -591.6232638713, 541.45404128074, -270.98308411192, 979.76525097926, -469.66772959435, 14.399274604723, -19.104204230429, 5.3299167111971, -21.252975375934, -0.3114733441376, 0.60334840894623, -0.042764839702509, 5.8185597255259E-03, -0.014597008284753, 5.6631175631027E-03, -7.6155864584577E-05, 2.2440342919332E-04, -1.2561095013413E-05, 6.3323132660934E-07, -2.0541989675375E-06, 3.6405370390082E-08, -2.9759897789215E-09, 1.0136618529763E-08, 5.9925719692351E-12, -2.0677870105164E-11, -2.0874278181886E-11, 1.0162166825089E-10, -1.6429828281347E-10];
    Pi = p;
    Sigma = s / 2.9251;
    teta = 0;
    for i = 1 : 30
        teta = teta + ni(i) * Pi ^ Ii(i) * (2 - Sigma) ^ Ji(i);
    end
    T2_ps = teta;
end

function p2_hs = p2_hs(h, s)
%Supplementary Release on Backward Equations for Pressure as a function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%Chapter 6:Backward Equations p(h,s) for Region 2
if h < (-3498.98083432139 + 2575.60716905876 * s - 421.073558227969 * s ^ 2 + 27.6349063799944 * s ^ 3) 
    sub_reg = 1;
else
    if s < 5.85 
        sub_reg = 3;
    else
        sub_reg = 2;
    end
end
switch sub_reg
case 1
    %Subregion A
    %Table 6, Eq 3, page 8
    Ii = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 6, 7];
    Ji = [1, 3, 6, 16, 20, 22, 0, 1, 2, 3, 5, 6, 10, 16, 20, 22, 3, 16, 20, 0, 2, 3, 6, 16, 16, 3, 16, 3, 1];
    ni = [-1.82575361923032E-02, -0.125229548799536, 0.592290437320145, 6.04769706185122, 238.624965444474, -298.639090222922, 0.051225081304075, -0.437266515606486, 0.413336902999504, -5.16468254574773, -5.57014838445711, 12.8555037824478, 11.414410895329, -119.504225652714, -2847.7798596156, 4317.57846408006, 1.1289404080265, 1974.09186206319, 1516.12444706087, 1.41324451421235E-02, 0.585501282219601, -2.97258075863012, 5.94567314847319, -6236.56565798905, 9659.86235133332, 6.81500934948134, -6332.07286824489, -5.5891922446576, 4.00645798472063E-02];
    eta = h / 4200;
    Sigma = s / 12;
    Pi = 0;
    for i = 1 : 29
        Pi = Pi + ni(i) * (eta - 0.5) ^ Ii(i) * (Sigma - 1.2) ^ Ji(i);
    end
    p2_hs = Pi ^ 4 * 4;
case 2
    %Subregion B
    %Table 7, Eq 4, page 9
    Ii = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 12, 14];
    Ji = [0, 1, 2, 4, 8, 0, 1, 2, 3, 5, 12, 1, 6, 18, 0, 1, 7, 12, 1, 16, 1, 12, 1, 8, 18, 1, 16, 1, 3, 14, 18, 10, 16];
    ni = [8.01496989929495E-02, -0.543862807146111, 0.337455597421283, 8.9055545115745, 313.840736431485, 0.797367065977789, -1.2161697355624, 8.72803386937477, -16.9769781757602, -186.552827328416, 95115.9274344237, -18.9168510120494, -4334.0703719484, 543212633.012715, 0.144793408386013, 128.024559637516, -67230.9534071268, 33697238.0095287, -586.63419676272, -22140322476.9889, 1716.06668708389, -570817595.806302, -3121.09693178482, -2078413.8463301, 3056059461577.86, 3221.57004314333, 326810259797.295, -1441.04158934487, 410.694867802691, 109077066873.024, -24796465425889.3, 1888019068.65134, -123651009018773];
    eta = h / 4100;
    Sigma = s / 7.9;
    Pi = 0;
    for i = 1 : 33
        Pi = Pi + ni(i) * (eta - 0.6) ^ Ii(i) * (Sigma - 1.01) ^ Ji(i);
    end
    p2_hs = Pi ^ 4 * 100;
otherwise
    %Subregion C
    %Table 8, Eq 5, page 10
    Ii = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 10, 12, 16];
    Ji = [0, 1, 2, 3, 4, 8, 0, 2, 5, 8, 14, 2, 3, 7, 10, 18, 0, 5, 8, 16, 18, 18, 1, 4, 6, 14, 8, 18, 7, 7, 10];
    ni = [0.112225607199012, -3.39005953606712, -32.0503911730094, -197.5973051049, -407.693861553446, 13294.3775222331, 1.70846839774007, 37.3694198142245, 3581.44365815434, 423014.446424664, -751071025.760063, 52.3446127607898, -228.351290812417, -960652.417056937, -80705929.2526074, 1626980172256.69, 0.772465073604171, 46392.9973837746, -13731788.5134128, 1704703926305.12, -25110462818730.8, 31774883083552, 53.8685623675312, -55308.9094625169, -1028615.22421405, 2042494187562.34, 273918446.626977, -2.63963146312685E+15, -1078908541.08088, -29649262098.0124, -1.11754907323424E+15];
    eta = h / 3500;
    Sigma = s / 5.9;
    Pi = 0;
    for i = 1 : 31
        Pi = Pi + ni(i) * (eta - 0.7) ^ Ii(i) * (Sigma - 1.1) ^ Ji(i);
    end
    p2_hs = Pi ^ 4 * 100;
end

function T2_prho=T2_prho(p,rho) 
  %Solve by iteration. Observe that fo low temperatures this equation has 2 solutions.
  %Solve with half interval method

  if p < 16.5292 
    Low_Bound = T4_p(p);
  else
    Low_Bound = B23T_p(p);
  end
  High_Bound = 1073.15;
  rhos=-1000;
  while abs(rho - rhos) > 0.000001
    Ts = (Low_Bound + High_Bound) / 2;
    rhos = 1 / v2_pT(p, Ts);
    if rhos < rho
      High_Bound = Ts;
    else
      Low_Bound = Ts;
    end
  end
    T2_prho = Ts;

%***********************************************************************************************************
%*2.3 functions for region 3

function p3_rhoT = p3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fidelta = 0;
for i = 2 : 40
    fidelta = fidelta + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * tau ^ Ji(i);
end
fidelta = fidelta + ni(1) / delta;
p3_rhoT = rho * R * T * delta * fidelta / 1000;

function u3_rhoT = u3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fitau = 0;
for i = 2 : 40
    fitau = fitau + ni(i) * delta ^ Ii(i) * Ji(i) * tau ^ (Ji(i) - 1);
end
u3_rhoT = R * T * (tau * fitau);


function h3_rhoT = h3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fidelta = 0;
fitau = 0;
for i = 2 : 40
    fidelta = fidelta + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * tau ^ Ji(i);
    fitau = fitau + ni(i) * delta ^ Ii(i) * Ji(i) * tau ^ (Ji(i) - 1);
end
fidelta = fidelta + ni(1) / delta;
h3_rhoT = R * T * (tau * fitau + delta * fidelta);

function s3_rhoT = s3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fi = 0;
fitau = 0;
for i = 2 : 40
    fi = fi + ni(i) * delta ^ Ii(i) * tau ^ Ji(i);
    fitau = fitau + ni(i) * delta ^ Ii(i) * Ji(i) * tau ^ (Ji(i) - 1);
end
fi = fi + ni(1) * log(delta);
s3_rhoT = R * (tau * fitau - fi);

function Cp3_rhoT = Cp3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fitautau = 0;
fidelta = 0;
fideltatau = 0;
fideltadelta = 0;
for i = 2 : 40
    fitautau = fitautau + ni(i) * delta ^ Ii(i) * Ji(i) * (Ji(i) - 1) * tau ^ (Ji(i) - 2);
    fidelta = fidelta + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * tau ^ Ji(i);
    fideltatau = fideltatau + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * Ji(i) * tau ^ (Ji(i) - 1);
    fideltadelta = fideltadelta + ni(i) * Ii(i) * (Ii(i) - 1) * delta ^ (Ii(i) - 2) * tau ^ Ji(i);
end
fidelta = fidelta + ni(1) / delta;
fideltadelta = fideltadelta - ni(1) / (delta ^ 2);
Cp3_rhoT = R * (-tau ^ 2 * fitautau + (delta * fidelta - delta * tau * fideltatau) ^ 2 / (2 * delta * fidelta + delta ^ 2 * fideltadelta));

function Cv3_rhoT = Cv3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fitautau = 0;
for i = 1 : 40
    fitautau = fitautau + ni(i) * delta ^ Ii(i) * Ji(i) * (Ji(i) - 1) * tau ^ (Ji(i) - 2);
end
Cv3_rhoT = R * -(tau * tau * fitautau);

function w3_rhoT = w3_rhoT(rho, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%7 Basic Equation for Region 3, Section. 6.1 Basic Equation
%Table 30 and 31, Page 30 and 31
Ii = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11];
Ji = [0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26];
ni = [1.0658070028513, -15.732845290239, 20.944396974307, -7.6867707878716, 2.6185947787954, -2.808078114862, 1.2053369696517, -8.4566812812502E-03, -1.2654315477714, -1.1524407806681, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 4.8972281541877, -3.0502617256965, 0.039420536879154, 0.12558408424308, -0.2799932969871, 1.389979956946, -2.018991502357, -8.2147637173963E-03, -0.47596035734923, 0.0439840744735, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.022175400873096, 0.094260751665092, 0.16436278447961, -0.013503372241348, -0.014834345352472, 5.7922953628084E-04, 3.2308904703711E-03, 8.0964802996215E-05, -1.6557679795037E-04, -4.4923899061815E-05];
R = 0.461526; %kJ/(KgK)
tc = 647.096; %K
pc = 22.064; %MPa
rhoc = 322; %kg/m3
delta = rho / rhoc;
tau = tc / T;
fitautau = 0;
fidelta = 0;
fideltatau = 0;
fideltadelta = 0;
for i = 2 : 40
    fitautau = fitautau + ni(i) * delta ^ Ii(i) * Ji(i) * (Ji(i) - 1) * tau ^ (Ji(i) - 2);
    fidelta = fidelta + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * tau ^ Ji(i);
    fideltatau = fideltatau + ni(i) * Ii(i) * delta ^ (Ii(i) - 1) * Ji(i) * tau ^ (Ji(i) - 1);
    fideltadelta = fideltadelta + ni(i) * Ii(i) * (Ii(i) - 1) * delta ^ (Ii(i) - 2) * tau ^ Ji(i);
end
fidelta = fidelta + ni(1) / delta;
fideltadelta = fideltadelta - ni(1) / (delta ^ 2);
w3_rhoT = (1000 * R * T * (2 * delta * fidelta + delta ^ 2 * fideltadelta - (delta * fidelta - delta * tau * fideltatau) ^ 2 / (tau ^ 2 * fitautau))) ^ 0.5;

function T3_ph = T3_ph(p, h)
%Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%2004
%Section 3.3 Backward Equations T(p,h) and v(p,h) for Subregions 3a and 3b
%Boundary equation, Eq 1 Page 5
h3ab = 2014.64004206875 + 3.74696550136983 * p - 2.19921901054187E-02 * p ^ 2 + 8.7513168600995E-05 * p ^ 3;
if h < h3ab 
    %Subregion 3a
    %Eq 2, Table 3, Page 7
    Ii = [-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -5, -3, -2, -2, -2, -1, -1, 0, 0, 1, 3, 3, 4, 4, 10, 12];
    Ji = [0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2, 0, 1, 3, 4, 0, 2, 0, 1, 1, 0, 1, 0, 3, 4, 5];
    ni = [-1.33645667811215E-07, 4.55912656802978E-06, -1.46294640700979E-05, 6.3934131297008E-03, 372.783927268847, -7186.54377460447, 573494.7521034, -2675693.29111439, -3.34066283302614E-05, -2.45479214069597E-02, 47.8087847764996, 7.64664131818904E-06, 1.28350627676972E-03, 1.71219081377331E-02, -8.51007304583213, -1.36513461629781E-02, -3.84460997596657E-06, 3.37423807911655E-03, -0.551624873066791, 0.72920227710747, -9.92522757376041E-03, -0.119308831407288, 0.793929190615421, 0.454270731799386, 0.20999859125991, -6.42109823904738E-03, -0.023515586860454, 2.52233108341612E-03, -7.64885133368119E-03, 1.36176427574291E-02, -1.33027883575669E-02];
    ps = p / 100;
    hs = h / 2300;
    Ts = 0;
    for i = 1 : 31
        Ts = Ts + ni(i) * (ps + 0.24) ^ Ii(i) * (hs - 0.615) ^ Ji(i);
    end
    T3_ph = Ts * 760;
else
    %Subregion 3b
    %Eq 3, Table 4, Page 7,8
    Ii = [-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, -1, -1, 0, 0, 1, 3, 5, 6, 8];
    Ji = [0, 1, 0, 1, 5, 10, 12, 0, 1, 2, 4, 10, 0, 1, 2, 0, 1, 5, 0, 4, 2, 4, 6, 10, 14, 16, 0, 2, 1, 1, 1, 1, 1];
    ni = [3.2325457364492E-05, -1.27575556587181E-04, -4.75851877356068E-04, 1.56183014181602E-03, 0.105724860113781, -85.8514221132534, 724.140095480911, 2.96475810273257E-03, -5.92721983365988E-03, -1.26305422818666E-02, -0.115716196364853, 84.9000969739595, -1.08602260086615E-02, 1.54304475328851E-02, 7.50455441524466E-02, 2.52520973612982E-02, -6.02507901232996E-02, -3.07622221350501, -5.74011959864879E-02, 5.03471360939849, -0.925081888584834, 3.91733882917546, -77.314600713019, 9493.08762098587, -1410437.19679409, 8491662.30819026, 0.861095729446704, 0.32334644281172, 0.873281936020439, -0.436653048526683, 0.286596714529479, -0.131778331276228, 6.76682064330275E-03];
    hs = h / 2800;
    ps = p / 100;
    Ts = 0;
    for i = 1 : 33
        Ts = Ts + ni(i) * (ps + 0.298) ^ Ii(i) * (hs - 0.72) ^ Ji(i);
    end
    T3_ph = Ts * 860;
end

function v3_ph = v3_ph(p, h)
%Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%2004
%Section 3.3 Backward Equations T(p,h) and v(p,h) for Subregions 3a and 3b
%Boundary equation, Eq 1 Page 5
h3ab = 2014.64004206875 + 3.74696550136983 * p - 2.19921901054187E-02 * p ^ 2 + 8.7513168600995E-05 * p ^ 3;
if h < h3ab 
    %Subregion 3a
    %Eq 4, Table 6, Page 9
    Ii = [-12, -12, -12, -12, -10, -10, -10, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 8];
    Ji = [6, 8, 12, 18, 4, 7, 10, 5, 12, 3, 4, 22, 2, 3, 7, 3, 16, 0, 1, 2, 3, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2];
    ni = [5.29944062966028E-03, -0.170099690234461, 11.1323814312927, -2178.98123145125, -5.06061827980875E-04, 0.556495239685324, -9.43672726094016, -0.297856807561527, 93.9353943717186, 1.92944939465981E-02, 0.421740664704763, -3689141.2628233, -7.37566847600639E-03, -0.354753242424366, -1.99768169338727, 1.15456297059049, 5683.6687581596, 8.08169540124668E-03, 0.172416341519307, 1.04270175292927, -0.297691372792847, 0.560394465163593, 0.275234661176914, -0.148347894866012, -6.51142513478515E-02, -2.92468715386302, 6.64876096952665E-02, 3.52335014263844, -1.46340792313332E-02, -2.24503486668184, 1.10533464706142, -4.08757344495612E-02];
    ps = p / 100;
    hs = h / 2100;
    vs = 0;
    for i = 1 : 32
        vs = vs + ni(i) * (ps + 0.128) ^ Ii(i) * (hs - 0.727) ^ Ji(i);
    end
    v3_ph = vs * 0.0028;
else
    %Subregion 3b
    %Eq 5, Table 7, Page 9
    Ii = [-12, -12, -8, -8, -8, -8, -8, -8, -6, -6, -6, -6, -6, -6, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, -1, 0, 1, 1, 2, 2];
    Ji = [0, 1, 0, 1, 3, 6, 7, 8, 0, 1, 2, 5, 6, 10, 3, 6, 10, 0, 2, 1, 2, 0, 1, 4, 5, 0, 0, 1, 2, 6];
    ni = [-2.25196934336318E-09, 1.40674363313486E-08, 2.3378408528056E-06, -3.31833715229001E-05, 1.07956778514318E-03, -0.271382067378863, 1.07202262490333, -0.853821329075382, -2.15214194340526E-05, 7.6965608822273E-04, -4.31136580433864E-03, 0.453342167309331, -0.507749535873652, -100.475154528389, -0.219201924648793, -3.21087965668917, 607.567815637771, 5.57686450685932E-04, 0.18749904002955, 9.05368030448107E-03, 0.285417173048685, 3.29924030996098E-02, 0.239897419685483, 4.82754995951394, -11.8035753702231, 0.169490044091791, -1.79967222507787E-02, 3.71810116332674E-02, -5.36288335065096E-02, 1.6069710109252];
    ps = p / 100;
    hs = h / 2800;
    vs = 0;
    for i = 1 : 30
        vs = vs + ni(i) * (ps + 0.0661) ^ Ii(i) * (hs - 0.72) ^ Ji(i);
    end
    v3_ph = vs * 0.0088;
end

function T3_ps = T3_ps(p, s)
%Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%2004
%3.4 Backward Equations T(p,s) and v(p,s) for Subregions 3a and 3b
%Boundary equation, Eq 6 Page 11
if s <= 4.41202148223476 
    %Subregion 3a
    %Eq 6, Table 10, Page 11
    Ii = [-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10];
    Ji = [28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1, 4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2];
    ni = [1500420082.63875, -159397258480.424, 5.02181140217975E-04, -67.2057767855466, 1450.58545404456, -8238.8953488889, -0.154852214233853, 11.2305046746695, -29.7000213482822, 43856513263.5495, 1.37837838635464E-03, -2.97478527157462, 9717779473494.13, -5.71527767052398E-05, 28830.794977842, -74442828926270.3, 12.8017324848921, -368.275545889071, 6.64768904779177E+15, 0.044935925195888, -4.22897836099655, -0.240614376434179, -4.74341365254924, 0.72409399912611, 0.923874349695897, 3.99043655281015, 3.84066651868009E-02, -3.59344365571848E-03, -0.735196448821653, 0.188367048396131, 1.41064266818704E-04, -2.57418501496337E-03, 1.23220024851555E-03];
    Sigma = s / 4.4;
    Pi = p / 100;
    teta = 0;
    for i = 1 : 33
        teta = teta + ni(i) * (Pi + 0.24) ^ Ii(i) * (Sigma - 0.703) ^ Ji(i);
    end
    T3_ps = teta * 760;
else
    %Subregion 3b
    %Eq 7, Table 11, Page 11
    Ii = [-12, -12, -12, -12, -8, -8, -8, -6, -6, -6, -5, -5, -5, -5, -5, -4, -3, -3, -2, 0, 2, 3, 4, 5, 6, 8, 12, 14];
    Ji = [1, 3, 4, 7, 0, 1, 3, 0, 2, 4, 0, 1, 2, 4, 6, 12, 1, 6, 2, 0, 1, 1, 0, 24, 0, 3, 1, 2];
    ni = [0.52711170160166, -40.1317830052742, 153.020073134484, -2247.99398218827, -0.193993484669048, -1.40467557893768, 42.6799878114024, 0.752810643416743, 22.6657238616417, -622.873556909932, -0.660823667935396, 0.841267087271658, -25.3717501764397, 485.708963532948, 880.531517490555, 2650155.92794626, -0.359287150025783, -656.991567673753, 2.41768149185367, 0.856873461222588, 0.655143675313458, -0.213535213206406, 5.62974957606348E-03, -316955725450471, -6.99997000152457E-04, 1.19845803210767E-02, 1.93848122022095E-05, -2.15095749182309E-05];
    Sigma = s / 5.3;
    Pi = p / 100;
    teta = 0;
    for i = 1 : 28
        teta = teta + ni(i) * (Pi + 0.76) ^ Ii(i) * (Sigma - 0.818) ^ Ji(i);
    end
    T3_ps = teta * 860;
end

function v3_ps = v3_ps(p, s)
%Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%2004
%3.4 Backward Equations T(p,s) and v(p,s) for Subregions 3a and 3b
%Boundary equation, Eq 6 Page 11
if s <= 4.41202148223476 
    %Subregion 3a
    %Eq 8, Table 13, Page 14
    Ii = [-12, -12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -5, -4, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 2, 4, 5, 6];
    Ji = [10, 12, 14, 4, 8, 10, 20, 5, 6, 14, 16, 28, 1, 5, 2, 4, 3, 8, 1, 2, 0, 1, 3, 0, 0, 2, 2, 0];
    ni = [79.5544074093975, -2382.6124298459, 17681.3100617787, -1.10524727080379E-03, -15.3213833655326, 297.544599376982, -35031520.6871242, 0.277513761062119, -0.523964271036888, -148011.182995403, 1600148.99374266, 1708023226634.27, 2.46866996006494E-04, 1.6532608479798, -0.118008384666987, 2.537986423559, 0.965127704669424, -28.2172420532826, 0.203224612353823, 1.10648186063513, 0.52612794845128, 0.277000018736321, 1.08153340501132, -7.44127885357893E-02, 1.64094443541384E-02, -6.80468275301065E-02, 0.025798857610164, -1.45749861944416E-04];
    Pi = p / 100;
    Sigma = s / 4.4;
    omega = 0;
    for i = 1 : 28
        omega = omega + ni(i) * (Pi + 0.187) ^ Ii(i) * (Sigma - 0.755) ^ Ji(i);
    end
    v3_ps = omega * 0.0028;
else
    %Subregion 3b
    %Eq 9, Table 14, Page 14
    Ii = [-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -5, -5, -5, -4, -4, -4, -4, -3, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 2];
    Ji = [0, 1, 2, 3, 5, 6, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 1, 0, 1, 2, 3, 4, 12, 0, 1, 2, 0, 2, 2];
    ni = [5.91599780322238E-05, -1.85465997137856E-03, 1.04190510480013E-02, 5.9864730203859E-03, -0.771391189901699, 1.72549765557036, -4.67076079846526E-04, 1.34533823384439E-02, -8.08094336805495E-02, 0.508139374365767, 1.28584643361683E-03, -1.63899353915435, 5.86938199318063, -2.92466667918613, -6.14076301499537E-03, 5.76199014049172, -12.1613320606788, 1.67637540957944, -7.44135838773463, 3.78168091437659E-02, 4.01432203027688, 16.0279837479185, 3.17848779347728, -3.58362310304853, -1159952.60446827, 0.199256573577909, -0.122270624794624, -19.1449143716586, -1.50448002905284E-02, 14.6407900162154, -3.2747778718823];
    Pi = p / 100;
    Sigma = s / 5.3;
    omega = 0;
    for i = 1 : 31
        omega = omega + ni(i) * (Pi + 0.298) ^ Ii(i) * (Sigma - 0.816) ^ Ji(i);
    end
    v3_ps = omega * 0.0088;
end


function p3_hs = p3_hs(h, s)
%Supplementary Release on Backward Equations ( ) , p h s for Region 3,
%Equations as a function of h and s for the Region Boundaries, and an Equation
%( ) sat , T hs for Region 4 of the IAPWS Industrial formulation 1997 for the
%Thermodynamic Properties of Water and Steam
%2004
%Section 3 Backward functions p(h,s), T(h,s), and v(h,s) for Region 3
if s < 4.41202148223476 
    %Subregion 3a
    %Eq 1, Table 3, Page 8
    Ii = [0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 10, 10, 14, 18, 20, 22, 22, 24, 28, 28, 32, 32];
    Ji = [0, 1, 5, 0, 3, 4, 8, 14, 6, 16, 0, 2, 3, 0, 1, 4, 5, 28, 28, 24, 1, 32, 36, 22, 28, 36, 16, 28, 36, 16, 36, 10, 28];
    ni = [7.70889828326934, -26.0835009128688, 267.416218930389, 17.2221089496844, -293.54233214597, 614.135601882478, -61056.2757725674, -65127225.1118219, 73591.9313521937, -11664650591.4191, 35.5267086434461, -596.144543825955, -475.842430145708, 69.6781965359503, 335.674250377312, 25052.6809130882, 146997.380630766, 5.38069315091534E+19, 1.43619827291346E+21, 3.64985866165994E+19, -2547.41561156775, 2.40120197096563E+27, -3.93847464679496E+29, 1.47073407024852E+24, -4.26391250432059E+31, 1.94509340621077E+38, 6.66212132114896E+23, 7.06777016552858E+33, 1.75563621975576E+41, 1.08408607429124E+28, 7.30872705175151E+43, 1.5914584739887E+24, 3.77121605943324E+40];
    Sigma = s / 4.4;
    eta = h / 2300;
    Pi = 0;
    for i = 1 : 33
        Pi = Pi + ni(i) * (eta - 1.01) ^ Ii(i) * (Sigma - 0.75) ^ Ji(i);
    end
    p3_hs = Pi * 99;
else
    %Subregion 3b
    %Eq 2, Table 4, Page 8
    Ii = [-12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -8, -6, -6, -6, -6, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -1, 0, 2, 2, 5, 6, 8, 10, 14, 14];
    Ji = [2, 10, 12, 14, 20, 2, 10, 14, 18, 2, 8, 2, 6, 7, 8, 10, 4, 5, 8, 1, 3, 5, 6, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 3, 7];
    ni = [1.25244360717979E-13, -1.26599322553713E-02, 5.06878030140626, 31.7847171154202, -391041.161399932, -9.75733406392044E-11, -18.6312419488279, 510.973543414101, 373847.005822362, 2.99804024666572E-08, 20.0544393820342, -4.98030487662829E-06, -10.230180636003, 55.2819126990325, -206.211367510878, -7940.12232324823, 7.82248472028153, -58.6544326902468, 3550.73647696481, -1.15303107290162E-04, -1.75092403171802, 257.98168774816, -727.048374179467, 1.21644822609198E-04, 3.93137871762692E-02, 7.04181005909296E-03, -82.910820069811, -0.26517881813125, 13.7531682453991, -52.2394090753046, 2405.56298941048, -22736.1631268929, 89074.6343932567, -23923456.5822486, 5687958081.29714];
    Sigma = s / 5.3;
    eta = h / 2800;
    Pi = 0;
    for i = 1 : 35
        Pi = Pi + ni(i) * (eta - 0.681) ^ Ii(i) * (Sigma - 0.792) ^ Ji(i);
    end
    p3_hs = 16.6 / Pi;
end

function h3_pT = h3_pT(p, T)
%Not avalible with if 97
%Solve function T3_ph-T=0 with half interval method.
%ver2.6 Start corrected bug
if p < 22.06395    %Bellow tripple point
  Ts = T4_p(p);    %Saturation temperature
  if T <= Ts      %Liquid side
    High_Bound = h4L_p(p); %Max h är liauid h.
    Low_Bound = h1_pT(p, 623.15);
  else
    Low_Bound = h4V_p(p);  %Min h är Vapour h.
    High_Bound = h2_pT(p, B23T_p(p));
  end 
else                  %Above tripple point. R3 from R2 till R3.
  Low_Bound = h1_pT(p, 623.15);
  High_Bound = h2_pT(p, B23T_p(p));
end
%ver2.6 End corrected bug
Ts = T+1;
while abs(T - Ts) > 0.00001
    hs = (Low_Bound + High_Bound) / 2;
    Ts = T3_ph(p, hs);
    if Ts > T 
        High_Bound = hs;
    else
        Low_Bound = hs;
    end
end
h3_pT = hs;

function T3_prho = T3_prho(p, rho)
  %Solve by iteration. Observe that fo low temperatures this equation has 2 solutions.
  %Solve with half interval method
  Low_Bound = 623.15;
  High_Bound = 1073.15;
  ps=-1000;
  while abs(p - ps) > 0.00000001
    Ts = (Low_Bound + High_Bound) / 2;
    ps = p3_rhoT(rho, Ts);
    if ps > p
      High_Bound = Ts;
    else
      Low_Bound = Ts;
    end
  end
  T3_prho = Ts;
  


%***********************************************************************************************************
%*2.4 functions for region 4
function p4_T = p4_T(T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Section 8.1 The Saturation-Pressure Equation
%Eq 30, Page 33
teta = T - 0.23855557567849 / (T - 650.17534844798);
a = teta ^ 2 + 1167.0521452767 * teta - 724213.16703206;
B = -17.073846940092 * teta ^ 2 + 12020.82470247 * teta - 3232555.0322333;
C = 14.91510861353 * teta ^ 2 - 4823.2657361591 * teta + 405113.40542057;
p4_T = (2 * C / (-B + (B ^ 2 - 4 * a * C) ^ 0.5)) ^ 4;


function T4_p = T4_p(p)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Section 8.2 The Saturation-Temperature Equation
%Eq 31, Page 34
beta = p ^ 0.25;
E = beta ^ 2 - 17.073846940092 * beta + 14.91510861353;
f = 1167.0521452767 * beta ^ 2 + 12020.82470247 * beta - 4823.2657361591;
G = -724213.16703206 * beta ^ 2 - 3232555.0322333 * beta + 405113.40542057;
D = 2 * G / (-f - (f ^ 2 - 4 * E * G) ^ 0.5);
T4_p = (650.17534844798 + D - ((650.17534844798 + D) ^ 2 - 4 * (-0.23855557567849 + 650.17534844798 * D)) ^ 0.5) / 2;

function h4_s = h4_s(s)
%Supplementary Release on Backward Equations ( ) , p h s for Region 3,Equations as a function of h and s for the Region Boundaries, and an Equation( ) sat , T hs for Region 4 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%4 Equations for Region Boundaries Given Enthalpy and Entropy
% Se picture page 14
if (s > -0.0001545495919 & s <= 3.77828134)==1
    %hL1_s
    %Eq 3,Table 9,Page 16
    Ii = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 12, 12, 14, 14, 16, 20, 20, 22, 24, 28, 32, 32];
    Ji = [14, 36, 3, 16, 0, 5, 4, 36, 4, 16, 24, 18, 24, 1, 4, 2, 4, 1, 22, 10, 12, 28, 8, 3, 0, 6, 8];
    ni = [0.332171191705237, 6.11217706323496E-04, -8.82092478906822, -0.45562819254325, -2.63483840850452E-05, -22.3949661148062, -4.28398660164013, -0.616679338856916, -14.682303110404, 284.523138727299, -113.398503195444, 1156.71380760859, 395.551267359325, -1.54891257229285, 19.4486637751291, -3.57915139457043, -3.35369414148819, -0.66442679633246, 32332.1885383934, 3317.66744667084, -22350.1257931087, 5739538.75852936, 173.226193407919, -3.63968822121321E-02, 8.34596332878346E-07, 5.03611916682674, 65.5444787064505];
    Sigma = s / 3.8;
    eta = 0;
    for i = 1 : 27
        eta = eta + ni(i) * (Sigma - 1.09) ^ Ii(i) * (Sigma + 0.0000366) ^ Ji(i);
    end
    h4_s = eta * 1700;
elseif (s > 3.77828134 & s <= 4.41202148223476 )==1
    %hL3_s
    %Eq 4,Table 10,Page 16
    Ii = [0, 0, 0, 0, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 10, 10, 10, 32, 32];
    Ji = [1, 4, 10, 16, 1, 36, 3, 16, 20, 36, 4, 2, 28, 32, 14, 32, 36, 0, 6];
    ni = [0.822673364673336, 0.181977213534479, -0.011200026031362, -7.46778287048033E-04, -0.179046263257381, 4.24220110836657E-02, -0.341355823438768, -2.09881740853565, -8.22477343323596, -4.99684082076008, 0.191413958471069, 5.81062241093136E-02, -1655.05498701029, 1588.70443421201, -85.0623535172818, -31771.4386511207, -94589.0406632871, -1.3927384708869E-06, 0.63105253224098];
    Sigma = s / 3.8;
    eta = 0;
    for i = 1 : 19
        eta = eta + ni(i) * (Sigma - 1.09) ^ Ii(i) * (Sigma + 0.0000366) ^ Ji(i);
    end
    h4_s = eta * 1700;
elseif (s > 4.41202148223476 & s <= 5.85 )==1
    %Section 4.4 Equations ( ) 2ab " h s and ( ) 2c3b "h s for the Saturated Vapor Line
    %Page 19, Eq 5
    %hV2c3b_s(s)
    Ii = [0, 0, 0, 1, 1, 5, 6, 7, 8, 8, 12, 16, 22, 22, 24, 36];
    Ji = [0, 3, 4, 0, 12, 36, 12, 16, 2, 20, 32, 36, 2, 32, 7, 20];
    ni = [1.04351280732769, -2.27807912708513, 1.80535256723202, 0.420440834792042, -105721.24483466, 4.36911607493884E+24, -328032702839.753, -6.7868676080427E+15, 7439.57464645363, -3.56896445355761E+19, 1.67590585186801E+31, -3.55028625419105E+37, 396611982166.538, -4.14716268484468E+40, 3.59080103867382E+18, -1.16994334851995E+40];
    Sigma = s / 5.9;
    eta = 0;
    for i = 1 : 16
        eta = eta + ni(i) * (Sigma - 1.02) ^ Ii(i) * (Sigma - 0.726) ^ Ji(i);
    end
    h4_s = eta ^ 4 * 2800;
elseif (s > 5.85 & s < 9.155759395)==1
    %Section 4.4 Equations ( ) 2ab " h s and ( ) 2c3b "h s for the Saturated Vapor Line
    %Page 20, Eq 6
    Ii = [1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36];
    Ji = [8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24, 2, 7, 12, 14, 24, 10, 12, 20, 22, 28];
    ni = [-524.581170928788, -9269472.18142218, -237.385107491666, 21077015581.2776, -23.9494562010986, 221.802480294197, -5104725.33393438, 1249813.96109147, 2000084369.96201, -815.158509791035, -157.612685637523, -11420042233.2791, 6.62364680776872E+15, -2.27622818296144E+18, -1.71048081348406E+31, 6.60788766938091E+15, 1.66320055886021E+22, -2.18003784381501E+29, -7.87276140295618E+29, 1.51062329700346E+31, 7957321.70300541, 1.31957647355347E+15, -3.2509706829914E+23, -4.18600611419248E+25, 2.97478906557467E+34, -9.53588761745473E+19, 1.66957699620939E+24, -1.75407764869978E+32, 3.47581490626396E+34, -7.10971318427851E+38];
    Sigma1 = s / 5.21;
    Sigma2 = s / 9.2;
    eta = 0;
    for i = 1 : 30
        eta = eta + ni(i) * (1 / Sigma1 - 0.513) ^ Ii(i) * (Sigma2 - 0.524) ^ Ji(i);
    end
    h4_s = exp(eta) * 2800;
else
    h4_s = -99999;
end

function p4_s = p4_s(s)
%Uses h4_s and p_hs for the diffrent regions to determine p4_s
h_sat = h4_s(s);
if (s > -0.0001545495919 & s <= 3.77828134)==1
    p4_s = p1_hs(h_sat, s);
elseif (s > 3.77828134 & s <= 5.210887663)==1
    p4_s = p3_hs(h_sat, s);
elseif (s > 5.210887663 & s < 9.155759395)==1
    p4_s = p2_hs(h_sat, s);
else
    p4_s = -99999;
end

function h4L_p = h4L_p(p)
if (p > 0.000611657 & p < 22.06395)==1
    Ts = T4_p(p);
    if p < 16.529 
        h4L_p = h1_pT(p, Ts);
    else
        %Iterate to find the the backward solution of p3sat_h
        Low_Bound = 1670.858218;
        High_Bound = 2087.23500164864;
        ps=-1000;
        while abs(p - ps) > 0.00001
            hs = (Low_Bound + High_Bound) / 2;
            ps = p3sat_h(hs);
            if ps > p 
                High_Bound = hs;
            else
                Low_Bound = hs;
            end
        end
        
        h4L_p = hs;
    end
else
    h4L_p = -99999;
end

function h4V_p = h4V_p(p)
if (p > 0.000611657 & p < 22.06395)==1
    Ts = T4_p(p);
    if p < 16.529 
        h4V_p = h2_pT(p, Ts);
    else
        %Iterate to find the the backward solution of p3sat_h
        Low_Bound = 2087.23500164864;
        High_Bound = 2563.592004+5;
        ps=-1000;
        while abs(p - ps) > 0.000001
            hs = (Low_Bound + High_Bound) / 2;
            ps = p3sat_h(hs);
            if ps < p 
                High_Bound = hs;
            else
                Low_Bound = hs;
            end
        end
        h4V_p = hs;
    end
else
    h4V_p = -99999;
end

function x4_ph = x4_ph(p, h)
%Calculate vapour fraction from hL and hV for given p
h4v = h4V_p(p);
h4L = h4L_p(p);
if h > h4v 
    x4_ph = 1;
elseif h < h4L 
    x4_ph = 0;
else
    x4_ph = (h - h4L) / (h4v - h4L);
end

function x4_ps = x4_ps(p, s)
if p < 16.529 
    ssv = s2_pT(p, T4_p(p));
    ssL = s1_pT(p, T4_p(p));
else
    ssv = s3_rhoT(1 / (v3_ph(p, h4V_p(p))), T4_p(p));
    ssL = s3_rhoT(1 / (v3_ph(p, h4L_p(p))), T4_p(p));
end
if s < ssL 
    x4_ps = 0;
elseif s > ssv 
    x4_ps = 1;
else
    x4_ps = (s - ssL) / (ssv - ssL);
end

function T4_hs = T4_hs(h, s)
%Supplementary Release on Backward Equations ( ) , p h s for Region 3,
%Chapter 5.3 page 30.
%The if 97 function is only valid for part of region4. Use iteration outsida.
Ii = [0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 8, 10, 10, 12, 14, 14, 16, 16, 18, 18, 18, 20, 28];
Ji = [0, 3, 12, 0, 1, 2, 5, 0, 5, 8, 0, 2, 3, 4, 0, 1, 1, 2, 4, 16, 6, 8, 22, 1, 20, 36, 24, 1, 28, 12, 32, 14, 22, 36, 24, 36];
ni = [0.179882673606601, -0.267507455199603, 1.162767226126, 0.147545428713616, -0.512871635973248, 0.421333567697984, 0.56374952218987, 0.429274443819153, -3.3570455214214, 10.8890916499278, -0.248483390456012, 0.30415322190639, -0.494819763939905, 1.07551674933261, 7.33888415457688E-02, 1.40170545411085E-02, -0.106110975998808, 1.68324361811875E-02, 1.25028363714877, 1013.16840309509, -1.51791558000712, 52.4277865990866, 23049.5545563912, 2.49459806365456E-02, 2107964.67412137, 366836848.613065, -144814105.365163, -1.7927637300359E-03, 4899556021.00459, 471.262212070518, -82929439019.8652, -1715.45662263191, 3557776.82973575, 586062760258.436, -12988763.5078195, 31724744937.1057];
if (s > 5.210887825 & s < 9.15546555571324)==1
    Sigma = s / 9.2;
    eta = h / 2800;
    teta = 0;
    for i = 1 : 36
        teta = teta + ni(i) * (eta - 0.119) ^ Ii(i) * (Sigma - 1.07) ^ Ji(i);
    end
    T4_hs = teta * 550;
else
    %function psat_h
    if (s > -0.0001545495919 && s <= 3.77828134)==1
        Low_Bound = 0.000611;
        High_Bound = 165.291642526045;
        hL=-1000;
        while abs(hL - h) > 0.00001 && abs(High_Bound - Low_Bound) > 0.0001
            PL = (Low_Bound + High_Bound) / 2;
            Ts = T4_p(PL);
            hL = h1_pT(PL, Ts);
            if hL > h 
                High_Bound = PL;
            else
                Low_Bound = PL;
            end
        end
    elseif s > 3.77828134 && s <= 4.41202148223476 
        PL = p3sat_h(h);
    elseif s > 4.41202148223476 && s <= 5.210887663 
        PL = p3sat_h(h);
    end
    Low_Bound = 0.000611;
    High_Bound = PL;
    sss=-1000;
    while (abs(s - sss) > 0.000001 & abs(High_Bound - Low_Bound) > 0.0000001)==1
        p = (Low_Bound + High_Bound) / 2;
        %Calculate s4_ph
        Ts = T4_p(p);
        xs = x4_ph(p, h);
        if p < 16.529 
            s4v = s2_pT(p, Ts);
            s4L = s1_pT(p, Ts);
        else
            v4v = v3_ph(p, h4V_p(p));
            s4v = s3_rhoT(1 / v4v, Ts);
            v4L = v3_ph(p, h4L_p(p));
            s4L = s3_rhoT(1 / v4L, Ts);
        end
        sss = (xs * s4v + (1 - xs) * s4L);
        
        if sss < s 
            High_Bound = p;
        else
            Low_Bound = p;
        end
    end
    T4_hs = T4_p(p);
end
%***********************************************************************************************************
%*2.5 functions for region 5
function h5_pT = h5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_tau = 0;
for i = 1 : 6
    gamma0_tau = gamma0_tau + ni0(i) * Ji0(i) * tau ^ (Ji0(i) - 1);
end
gammar_tau = 0;
for i = 1 : 5
    gammar_tau = gammar_tau + nir(i) * Pi ^ Iir(i) * Jir(i) * tau ^ (Jir(i) - 1);
end
h5_pT = R * T * tau * (gamma0_tau + gammar_tau);



function v5_pT = v5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_pi = 1 / Pi;
gammar_pi = 0;
for i = 1 : 5
    gammar_pi = gammar_pi + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * tau ^ Jir(i);
end
v5_pT = R * T / p * Pi * (gamma0_pi + gammar_pi) / 1000;


function u5_pT = u5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_pi = 1 / Pi;
gamma0_tau = 0;
for i = 1 : 6
    gamma0_tau = gamma0_tau + ni0(i) * Ji0(i) * tau ^ (Ji0(i) - 1);
end
gammar_pi = 0;
gammar_tau = 0;
for i = 1 : 5
    gammar_pi = gammar_pi + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * tau ^ Jir(i);
    gammar_tau = gammar_tau + nir(i) * Pi ^ Iir(i) * Jir(i) * tau ^ (Jir(i) - 1);
end
u5_pT = R * T * (tau * (gamma0_tau + gammar_tau) - Pi * (gamma0_pi + gammar_pi));

function Cp5_pT = Cp5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_tautau = 0;
for i = 1 : 6
    gamma0_tautau = gamma0_tautau + ni0(i) * Ji0(i) * (Ji0(i) - 1) * tau ^ (Ji0(i) - 2);
end
gammar_tautau = 0;
for i = 1 : 5
    gammar_tautau = gammar_tautau + nir(i) * Pi ^ Iir(i) * Jir(i) * (Jir(i) - 1) * tau ^ (Jir(i) - 2);
end
Cp5_pT = -R * tau ^ 2 * (gamma0_tautau + gammar_tautau);


function s5_pT = s5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0 = log(Pi);
gamma0_tau = 0;
for i = 1 : 6
    gamma0_tau = gamma0_tau + ni0(i) * Ji0(i) * tau ^ (Ji0(i) - 1);
    gamma0 = gamma0 + ni0(i) * tau ^ Ji0(i);
end
gammar = 0;
gammar_tau = 0;
for i = 1 : 5
    gammar = gammar + nir(i) * Pi ^ Iir(i) * tau ^ Jir(i);
    gammar_tau = gammar_tau + nir(i) * Pi ^ Iir(i) * Jir(i) * tau ^ (Jir(i) - 1);
end
s5_pT = R * (tau * (gamma0_tau + gammar_tau) - (gamma0 + gammar));

function Cv5_pT = Cv5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_tautau = 0;
for i = 1 : 6
    gamma0_tautau = gamma0_tautau + ni0(i) * (Ji0(i) - 1) * Ji0(i) * tau ^ (Ji0(i) - 2);
end
gammar_pi = 0;
gammar_pitau = 0;
gammar_pipi = 0;
gammar_tautau = 0;
for i = 1 : 5
    gammar_pi = gammar_pi + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * tau ^ Jir(i);
    gammar_pitau = gammar_pitau + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * Jir(i) * tau ^ (Jir(i) - 1);
    gammar_pipi = gammar_pipi + nir(i) * Iir(i) * (Iir(i) - 1) * Pi ^ (Iir(i) - 2) * tau ^ Jir(i);
    gammar_tautau = gammar_tautau + nir(i) * Pi ^ Iir(i) * Jir(i) * (Jir(i) - 1) * tau ^ (Jir(i) - 2);
end
Cv5_pT = R * (-(tau ^ 2 *(gamma0_tautau + gammar_tautau)) - (1 + Pi * gammar_pi - tau * Pi * gammar_pitau)^2 / (1 - Pi ^ 2 * gammar_pipi));

function w5_pT = w5_pT(p, T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam, September 1997
%Basic Equation for Region 5
%Eq 32,33, Page 36, Tables 37-41
Ji0 = [0, 1, -3, -2, -1, 2];
ni0 = [-13.179983674201, 6.8540841634434, -0.024805148933466, 0.36901534980333, -3.1161318213925, -0.32961626538917];
Iir = [1, 1, 1, 2, 3];
Jir = [0, 1, 3, 9, 3];
nir = [-1.2563183589592E-04, 2.1774678714571E-03, -0.004594282089991, -3.9724828359569E-06, 1.2919228289784E-07];
R = 0.461526; %kJ/(kg K)
tau = 1000 / T;
Pi = p;
gamma0_tautau = 0;
for i = 1 : 6
    gamma0_tautau = gamma0_tautau + ni0(i) * (Ji0(i) - 1) * Ji0(i) * tau ^ (Ji0(i) - 2);
end
gammar_pi = 0;
gammar_pitau = 0;
gammar_pipi = 0;
gammar_tautau = 0;
for i = 1 : 5
    gammar_pi = gammar_pi + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * tau ^ Jir(i);
    gammar_pitau = gammar_pitau + nir(i) * Iir(i) * Pi ^ (Iir(i) - 1) * Jir(i) * tau ^ (Jir(i) - 1);
    gammar_pipi = gammar_pipi + nir(i) * Iir(i) * (Iir(i) - 1) * Pi ^ (Iir(i) - 2) * tau ^ Jir(i);
    gammar_tautau = gammar_tautau + nir(i) * Pi ^ Iir(i) * Jir(i) * (Jir(i) - 1) * tau ^ (Jir(i) - 2);
end
w5_pT = (1000 * R * T * (1 + 2 * Pi * gammar_pi + Pi ^ 2 * gammar_pi ^ 2) / ((1 - Pi ^ 2 * gammar_pipi) + (1 + Pi * gammar_pi - tau * Pi * gammar_pitau) ^ 2 / (tau ^ 2 * (gamma0_tautau + gammar_tautau)))) ^ 0.5;


function T5_ph = T5_ph(p, h)
%Solve with half interval method
Low_Bound = 1073.15;
High_Bound = 2273.15;
hs=h-1;
while abs(h - hs) > 0.00001
    Ts = (Low_Bound + High_Bound) / 2;
    hs = h5_pT(p, Ts);
    if hs > h 
        High_Bound = Ts;
    else
        Low_Bound = Ts;
    end
end
T5_ph = Ts;


function T5_ps = T5_ps(p, s)
%Solve with half interval method
Low_Bound = 1073.15;
High_Bound = 2273.15;
ss=s-1;
while abs(s - ss) > 0.00001
    Ts = (Low_Bound + High_Bound) / 2;
    ss = s5_pT(p, Ts);
    if ss > s 
        High_Bound = Ts;
    else
        Low_Bound = Ts;
    end
end
T5_ps = Ts;

function T5_prho=T5_prho(p,rho)
  %Solve by iteration. Observe that fo low temperatures this equation has 2 solutions.
  %Solve with half interval method
  
    Low_Bound = 1073.15;
    High_Bound = 2073.15;
    rhos=-1000;
  while abs(rho - rhos) > 0.000001
    Ts = (Low_Bound + High_Bound) / 2;
    rhos = 1 / v2_pT(p, Ts);
    if rhos < rho
      High_Bound = Ts;
    else
      Low_Bound = Ts;
    end
  end
    T5_prho = Ts;

%***********************************************************************************************************
%*3 Region Selection
%***********************************************************************************************************
%*3.1 Regions as a function of pT
function region_pT = region_pT(p, T)
if T > 1073.15 && p < 10 && T < 2273.15 && p > 0.000611 
    region_pT = 5;
elseif T <= 1073.15 && T > 273.15 && p <= 100 && p > 0.000611 
    if T > 623.15 
        if p > B23p_T(T) 
            region_pT = 3;
            if T < 647.096 
                ps = p4_T(T);
                if abs(p - ps) < 0.00001
                    region_pT = 4;
                end
            end
        else
            region_pT = 2;
        end
    else
        ps = p4_T(T);
        if abs(p - ps) < 0.00001 
            region_pT = 4;
        elseif p > ps
            region_pT = 1;
        else
            region_pT = 2;
        end
    end
else
    region_pT = 0; %**Error, Outside valid area
end
%***********************************************************************************************************
%*3.2 Regions as a function of ph
function region_ph = region_ph(  p,   h)
%Check if outside pressure limits
if p < 0.000611657 || p > 100 
    region_ph = 0;
    return
end

%Check if outside low h.
if h < 0.963 * p + 2.2  %Linear adaption to h1_pt()+2 to speed up calcualations.
    if h < h1_pT(p, 273.15) 
        region_ph = 0;
        return
    end
end

if p < 16.5292  %Bellow region 3,Check  region 1,4,2,5
    %Check Region 1
    Ts = T4_p(p);
    hL = 109.6635 * log(p) + 40.3481 * p + 734.58; %Approximate function for hL_p
    if abs(h - hL) < 100  %if approximate is not god enough use real function
        hL = h1_pT(p, Ts);
    end
    if h <= hL 
        region_ph = 1;
        return
    end
    %Check Region 4
    hV = 45.1768 * log(p) - 20.158 * p + 2804.4; %Approximate function for hV_p
    if abs(h - hV) < 50  %if approximate is not god enough use real function
        hV = h2_pT(p, Ts);
    end
    if h < hV 
        region_ph = 4;
        return
    end
    %Check upper limit of region 2 Quick Test
    if h < 4000 
        region_ph = 2;
        return
    end
    %Check region 2 (Real value)
    h_45 = h2_pT(p, 1073.15);
    if h <= h_45 
        region_ph = 2;
        return
    end
    %Check region 5
    if p > 10 
        region_ph = 0;
        return
    end
    h_5u = h5_pT(p, 2273.15);
    if h < h_5u 
        region_ph = 5;
        return
    end
    region_ph = 0;
    return
else %for p>16.5292
    %Check if in region1
    if h < h1_pT(p, 623.15) 
        region_ph = 1;
        return
    end
    %Check if in region 3 or 4 (Bellow Reg 2)
    if h < h2_pT(p, B23T_p(p)) 
        %Region 3 or 4
        if p > p3sat_h(h) 
            region_ph = 3;
            return
        else
            region_ph = 4;
            return
        end
    end
    %Check if region 2
    if h < h2_pT(p, 1073.15) 
        region_ph = 2;
        return
    end
end
region_ph = 0;


%***********************************************************************************************************
%*3.3 Regions as a function of ps
function region_ps = region_ps(  p,   s)
if p < 0.000611657 || p > 100 || s < 0 || s > s5_pT(p, 2273.15) 
    region_ps = 0;
    return
end

%Check region 5
if s > s2_pT(p, 1073.15) 
    if p <= 10 
        region_ps = 5;
        return
    else
        region_ps = 0;
        return
    end
end

%Check region 2
if p > 16.529 
    ss = s2_pT(p, B23T_p(p)); %Between 5.047  & 5.261. Use to speed up!
else
    ss = s2_pT(p, T4_p(p));
end
if s > ss 
    region_ps = 2;
    return
end

%Check region 3
ss = s1_pT(p, 623.15);
if p > 16.529  && s > ss 
    if p > p3sat_s(s) 
        region_ps = 3;
        return
    else
        region_ps = 4;
        return
    end
end

%Check region 4 (Not inside region 3)
if p < 16.529  && s > s1_pT(p, T4_p(p)) 
    region_ps = 4;
    return
end

%Check region 1
if p > 0.000611657  && s > s1_pT(p, 273.15) 
    region_ps = 1;
    return
end
region_ps = 1;

%***********************************************************************************************************
%*3.4 Regions as a function of hs
function region_hs = region_hs(  h,   s)
if s < -0.0001545495919 
    region_hs = 0;
    return
end
%Check linear adaption to p=0.000611. if bellow region 4.
hMin = (((-0.0415878 - 2500.89262) / (-0.00015455 - 9.155759)) * s);
if s < 9.155759395  && h < hMin 
    region_hs = 0;
    return
end

%******Kolla 1 eller 4. (+liten bit över B13)
if s >= -0.0001545495919  && s <= 3.77828134 
    if h < h4_s(s) 
        region_hs = 4;
        return
    elseif s < 3.397782955  %100MPa line is limiting
        TMax = T1_ps(100, s);
        hMax = h1_pT(100, TMax);
        if h < hMax 
            region_hs = 1;
            return
        else
            region_hs = 0;
            return
        end
    else %The point is either in region 4,1,3. Check B23
        hB = hB13_s(s);
        if h < hB 
            region_hs = 1;
            return
        end
        TMax = T3_ps(100, s);
        vmax = v3_ps(100, s);
        hMax = h3_rhoT(1 / vmax, TMax);
        if h < hMax 
            region_hs = 3;
            return
        else
            region_hs = 0;
            return
        end
    end
end

%******Kolla region 2 eller 4. (Övre delen av område b23-> max)
if s >= 5.260578707  && s <= 11.9212156897728 
    if s > 9.155759395  %Above region 4
        Tmin = T2_ps(0.000611, s);
        hMin = h2_pT(0.000611, Tmin);
        %function adapted to h(1073.15,s)
        hMax = -0.07554022 * s ^ 4 + 3.341571 * s ^ 3 - 55.42151 * s ^ 2 + 408.515 * s + 3031.338;
        if h > hMin  && h < hMax 
            region_hs = 2;
            return
        else
            region_hs = 0;
            return
        end
    end
    
    hV = h4_s(s);
    
    if h < hV   %Region 4. Under region 3.
        region_hs = 4;
        return
    end
    if s < 6.04048367171238 
        TMax = T2_ps(100, s);
        hMax = h2_pT(100, TMax);
    else
        %function adapted to h(1073.15,s)
        hMax = -2.988734 * s ^ 4 + 121.4015 * s ^ 3 - 1805.15 * s ^ 2 + 11720.16 * s - 23998.33;
    end
    if h < hMax   %Region 2. Över region 4.
        region_hs = 2;
        return
    else
        region_hs = 0;
        return
    end
end

%Kolla region 3 eller 4. Under kritiska punkten.
if s >= 3.77828134  && s <= 4.41202148223476 
    hL = h4_s(s);
    if h < hL 
        region_hs = 4;
        return
    end
    TMax = T3_ps(100, s);
    vmax = v3_ps(100, s);
    hMax = h3_rhoT(1 / vmax, TMax);
    if h < hMax 
        region_hs = 3;
        return
    else
        region_hs = 0;
        return
    end
end

%Kolla region 3 eller 4 från kritiska punkten till övre delen av b23
if s >= 4.41202148223476  && s <= 5.260578707 
    hV = h4_s(s);
    if h < hV 
        region_hs = 4;
        return
    end
    %Kolla om vi är under b23 giltighetsområde.
    if s <= 5.048096828 
        TMax = T3_ps(100, s);
        vmax = v3_ps(100, s);
        hMax = h3_rhoT(1 / vmax, TMax);
        if h < hMax 
            region_hs = 3;
            return
        else
            region_hs = 0;
            return
        end
    else %Inom området för B23 i s led.
        if (h > 2812.942061)  %Ovanför B23 i h_led
            if s > 5.09796573397125 
                TMax = T2_ps(100, s);
                hMax = h2_pT(100, TMax);
                if h < hMax 
                    region_hs = 2;
                    return
                else
                    region_hs = 0;
                    return
                end
            else
                region_hs = 0;
                return
            end
        end
        if (h < 2563.592004)    %Nedanför B23 i h_led men vi har redan kollat ovanför hV2c3b
            region_hs = 3;
            return
        end
        %Vi är inom b23 området i både s och h led.
        Tact = TB23_hs(h, s);
        pact = p2_hs(h, s);
        pBound = B23p_T(Tact);
        if pact > pBound 
            region_hs = 3;
            return
        else
            region_hs = 2;
            return
        end
    end
end
region_hs = 0;

%***********************************************************************************************************
%*3.5 Regions as a function of p and rho
function Region_prho = Region_prho(p,rho)
v = 1 / rho;
if p < 0.000611657 || p > 100
    Region_prho = 0;
    return
end
if p < 16.5292  %Bellow region 3, Check region 1,4,2
    if v < v1_pT(p, 273.15) %Observe that this is not actually min of v. Not valid Water of 4°C is ligther.
        Region_prho = 0;
        return
    end
    if v <= v1_pT(p, T4_p(p))
        Region_prho = 1;
        return
    end
    if v < v2_pT(p, T4_p(p)) 
        Region_prho = 4;
        return
    end
    if v <= v2_pT(p, 1073.15)
        Region_prho = 2;
        return
    end 
    if p > 10 %Above region 5
        Region_prho = 0;
        return
    end 
    if v <= v5_pT(p, 2073.15) 
        Region_prho = 5;
        return
    end
else %Check region 1,3,4,3,2 (Above the lowest point of region 3.)
    if v < v1_pT(p, 273.15) %Observe that this is not actually min of v. Not valid Water of 4°C is ligther.
        Region_prho = 0;
        return
    end
    if v < v1_pT(p, 623.15)
        Region_prho = 1;
        return
    end
    %Check if in region 3 or 4 (Bellow Reg 2)
    if v < v2_pT(p, B23T_p(p))
        %Region 3 or 4
        if p > 22.064 %Above region 4
            Region_prho = 3;
            return
        end
        if v < v3_ph(p, h4L_p(p)) || v > v3_ph(p, h4V_p(p)) %Uses iteration!!
            Region_prho = 3;
            return
        else
            Region_prho = 4;
            return
        end 
    end 
    %Check if region 2
    if v < v2_pT(p, 1073.15)
        Region_prho = 2;
        return
    end
end 
Region_prho = 0;



%***********************************************************************************************************
%*4 Region Borders
%***********************************************************************************************************
%***********************************************************************************************************
%*4.1 Boundary between region 2 and 3.
function B23p_T = B23p_T(T)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%1997
%Section 4 Auxiliary Equation for the Boundary between Regions 2 and 3
%Eq 5, Page 5
B23p_T = 348.05185628969 - 1.1671859879975 * T + 1.0192970039326E-03 * T ^ 2;

function B23T_p = B23T_p(p)
%Release on the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water and Steam
%1997
%Section 4 Auxiliary Equation for the Boundary between Regions 2 and 3
%Eq 6, Page 6
B23T_p = 572.54459862746 + ((p - 13.91883977887) / 1.0192970039326E-03) ^ 0.5;


%***********************************************************************************************************
%*4.2 Region 3. pSat_h  & pSat_s
function p3sat_h = p3sat_h(h)
%Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h)  & T(p,s), v(p,s) for Region 3 of the IAPWS Industrial formulation 1997 for the Thermodynamic Properties of Water  & Steam
%2004
%Section 4 Boundary Equations psat(h)  & psat(s) for the Saturation Lines of Region 3
%Se pictures Page 17, Eq 10, Table 17, Page 18
Ii = [0, 1, 1, 1, 1, 5, 7, 8, 14, 20, 22, 24, 28, 36];
Ji = [0, 1, 3, 4, 36, 3, 0, 24, 16, 16, 3, 18, 8, 24];
ni = [0.600073641753024, -9.36203654849857, 24.6590798594147, -107.014222858224, -91582131580576.8, -8623.32011700662, -23.5837344740032, 2.52304969384128E+17, -3.89718771997719E+18, -3.33775713645296E+22, 35649946963.6328, -1.48547544720641E+26, 3.30611514838798E+18, 8.13641294467829E+37];
hs = h / 2600;
ps = 0;
for i = 1:14
    ps = ps + ni(i) * (hs - 1.02) ^ Ii(i) * (hs - 0.608) ^ Ji(i);
end
p3sat_h = ps * 22;


function p3sat_s = p3sat_s(s)
Ii = [0, 1, 1, 4, 12, 12, 16, 24, 28, 32];
Ji = [0, 1, 32, 7, 4, 14, 36, 10, 0, 18];
ni = [0.639767553612785, -12.9727445396014, -2.24595125848403E+15, 1774667.41801846, 7170793495.71538, -3.78829107169011E+17, -9.55586736431328E+34, 1.87269814676188E+23, 119254746466.473, 1.10649277244882E+36];
Sigma = s / 5.2;
Pi = 0;
for i = 1:10
    Pi = Pi + ni(i) * (Sigma - 1.03) ^ Ii(i) * (Sigma - 0.699) ^ Ji(i);
end
p3sat_s = Pi * 22;


%***********************************************************************************************************
%4.3 Region boundary 1to3  & 3to2 as a functions of s
function hB13_s = hB13_s(s)
%Supplementary Release on Backward Equations ( ) , p h s for Region 3,
%Chapter 4.5 page 23.
Ii = [0, 1, 1, 3, 5, 6];
Ji = [0, -2, 2, -12, -4, -3];
ni = [0.913965547600543, -4.30944856041991E-05, 60.3235694765419, 1.17518273082168E-18, 0.220000904781292, -69.0815545851641];
Sigma = s / 3.8;
eta = 0;
for i = 1 : 6
    eta = eta + ni(i) * (Sigma - 0.884) ^ Ii(i) * (Sigma - 0.864) ^ Ji(i);
end
hB13_s = eta * 1700;


function TB23_hs = TB23_hs(h, s)
%Supplementary Release on Backward Equations ( ) , p h s for Region 3,
%Chapter 4.6 page 25.
Ii = [-12, -10, -8, -4, -3, -2, -2, -2, -2, 0, 1, 1, 1, 3, 3, 5, 6, 6, 8, 8, 8, 12, 12, 14, 14];
Ji = [10, 8, 3, 4, 3, -6, 2, 3, 4, 0, -3, -2, 10, -2, -1, -5, -6, -3, -8, -2, -1, -12, -1, -12, 1];
ni = [6.2909626082981E-04, -8.23453502583165E-04, 5.15446951519474E-08, -1.17565945784945, 3.48519684726192, -5.07837382408313E-12, -2.84637670005479, -2.36092263939673, 6.01492324973779, 1.48039650824546, 3.60075182221907E-04, -1.26700045009952E-02, -1221843.32521413, 0.149276502463272, 0.698733471798484, -2.52207040114321E-02, 1.47151930985213E-02, -1.08618917681849, -9.36875039816322E-04, 81.9877897570217, -182.041861521835, 2.61907376402688E-06, -29162.6417025961, 1.40660774926165E-05, 7832370.62349385];
Sigma = s / 5.3;
eta = h / 3000;
teta = 0;
for i = 1 : 25
    teta = teta + ni(i) * (eta - 0.727) ^ Ii(i) * (Sigma - 0.864) ^ Ji(i);
end
TB23_hs = teta * 900;


%***********************************************************************************************************
%*5 Transport properties
%***********************************************************************************************************
%*5.1 Viscosity (IAPWS formulation 1985, Revised 2003)
%***********************************************************************************************************
function my_AllRegions_pT = my_AllRegions_pT(  p,   T)
h0 = [0.5132047, 0.3205656, 0, 0, -0.7782567, 0.1885447];
h1 = [0.2151778, 0.7317883, 1.241044, 1.476783, 0, 0];
h2 = [-0.2818107, -1.070786, -1.263184, 0, 0, 0];
h3 = [0.1778064, 0.460504, 0.2340379, -0.4924179, 0, 0];
h4 = [-0.0417661, 0, 0, 0.1600435, 0, 0];
h5 = [0, -0.01578386, 0, 0, 0, 0];
h6 = [0, 0, 0, -0.003629481, 0, 0];

%Calcualte density.
switch region_pT(p, T)
case 1
    rho = 1 / v1_pT(p, T);
case 2
    rho = 1 / v2_pT(p, T);
case 3
    hs = h3_pT(p, T);
    rho = 1 / v3_ph(p, hs);
case 4
    rho = NaN;
case 5
    rho = 1 / v5_pT(p, T);
otherwise
    my_AllRegions_pT = NaN;
    return
end

rhos = rho / 317.763;
Ts = T / 647.226;
ps = p / 22.115;

%Check valid area
if T > 900 + 273.15 || (T > 600 + 273.15  && p > 300) || (T > 150 + 273.15  && p > 350) || p > 500 
    my_AllRegions_pT = NaN;
    return
end
my0 = Ts ^ 0.5 / (1 + 0.978197 / Ts + 0.579829 / (Ts ^ 2) - 0.202354 / (Ts ^ 3));
Sum = 0;
for i = 0 : 5
    Sum = Sum + h0(i+1) * (1 / Ts - 1) ^ i + h1(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 1 + h2(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 2 + h3(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 3 + h4(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 4 + h5(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 5 + h6(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 6;
end
my1 = exp(rhos * Sum);
mys = my0 * my1;
my_AllRegions_pT = mys * 0.000055071;


function my_AllRegions_ph = my_AllRegions_ph(  p,   h)
h0 = [0.5132047, 0.3205656, 0, 0, -0.7782567, 0.1885447];
h1 = [0.2151778, 0.7317883, 1.241044, 1.476783, 0, 0];
h2 = [-0.2818107, -1.070786, -1.263184, 0, 0, 0];
h3 = [0.1778064, 0.460504, 0.2340379, -0.4924179, 0, 0];
h4 = [-0.0417661, 0, 0, 0.1600435, 0, 0];
h5 = [0, -0.01578386, 0, 0, 0, 0];
h6 = [0, 0, 0, -0.003629481, 0, 0];

%Calcualte density.
switch region_ph(p, h)
case 1
    Ts = T1_ph(p, h);
    T = Ts;
    rho = 1 / v1_pT(p, Ts);
case 2
    Ts = T2_ph(p, h);
    T = Ts;
    rho = 1 / v2_pT(p, Ts);
case 3
    rho = 1 / v3_ph(p, h);
    T = T3_ph(p, h);
case 4
    xs = x4_ph(p, h);
    if p < 16.529 
        v4v = v2_pT(p, T4_p(p));
        v4L = v1_pT(p, T4_p(p));
    else
        v4v = v3_ph(p, h4V_p(p));
        v4L = v3_ph(p, h4L_p(p));
    end
    rho = 1 / (xs * v4v + (1 - xs) * v4L);
    T = T4_p(p);
case 5
    Ts = T5_ph(p, h);
    T = Ts;
    rho = 1 / v5_pT(p, Ts);
otherwise
    my_AllRegions_ph = NaN;
    return
end
rhos = rho / 317.763;
Ts = T / 647.226;
ps = p / 22.115;
%Check valid area
if T > 900 + 273.15 || (T > 600 + 273.15  && p > 300) || (T > 150 + 273.15  && p > 350) || p > 500 
    my_AllRegions_ph = NaN;
    return
end
my0 = Ts ^ 0.5 / (1 + 0.978197 / Ts + 0.579829 / (Ts ^ 2) - 0.202354 / (Ts ^ 3));

Sum = 0;
for i = 0 : 5
    Sum = Sum + h0(i+1) * (1 / Ts - 1) ^ i + h1(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 1 + h2(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 2 + h3(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 3 + h4(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 4 + h5(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 5 + h6(i+1) * (1 / Ts - 1) ^ i * (rhos - 1) ^ 6;
end
my1 = exp(rhos * Sum);
mys = my0 * my1;
my_AllRegions_ph = mys * 0.000055071;

%***********************************************************************************************************
%*5.2 Thermal Conductivity (IAPWS formulation 1985)
function tc_ptrho = tc_ptrho(  p,   T,   rho)
%Revised release on the IAPWS formulation 1985 for the Thermal Conductivity of ordinary water
%IAPWS September 1998
%Page 8
%ver2.6 Start corrected bug
 if T < 273.15
   tc_ptrho = NaN; %Out of range of validity (para. B4)
   return
 elseif T < 500 + 273.15
   if p > 100
     tc_ptrho = NaN; %Out of range of validity (para. B4)
     return
   end
 elseif T <= 650 + 273.15
   if p > 70
     tc_ptrho = NaN; %Out of range of validity (para. B4)
     return
   end
 else T <= 800 + 273.15
   if p > 40
      tc_ptrho = NaN; %Out of range of validity (para. B4)
      return
   end
 end
%ver2.6 End corrected bug
T = T / 647.26;
rho = rho / 317.7;
tc0 = T ^ 0.5 * (0.0102811 + 0.0299621 * T + 0.0156146 * T ^ 2 - 0.00422464 * T ^ 3);
tc1 = -0.39707 + 0.400302 * rho + 1.06 * exp(-0.171587 * (rho + 2.39219) ^ 2);
dT = abs(T - 1) + 0.00308976;
Q = 2 + 0.0822994 / dT ^ (3 / 5);
if T >= 1 
    s = 1 / dT;
else
    s = 10.0932 / dT ^ (3 / 5);
end
tc2 = (0.0701309 / T ^ 10 + 0.011852) * rho ^ (9 / 5) * exp(0.642857 * (1 - rho ^ (14 / 5))) + 0.00169937 * s * rho ^ Q * exp((Q / (1 + Q)) * (1 - rho ^ (1 + Q))) - 1.02 * exp(-4.11717 * T ^ (3 / 2) - 6.17937 / rho ^ 5);
tc_ptrho = tc0 + tc1 + tc2;

%***********************************************************************************************************
%5.3 Surface Tension
function Surface_Tension_T = Surface_Tension_T(  T)
%IAPWS Release on Surface Tension of Ordinary Water Substance,
%September 1994
tc = 647.096; %K
B = 0.2358;    %N/m
bb = -0.625;
my = 1.256;
if T < 0.01 || T > tc 
    Surface_Tension_T = NaN; %"Out of valid region"
    return
end
tau = 1 - T / tc;
Surface_Tension_T = B * tau ^ my * (1 + bb * tau);


%***********************************************************************************************************
%*6 Units                                                                                      *
%***********************************************************************************************************
function toSIunit_p = toSIunit_p( Ins )
%Translate bar to MPa
toSIunit_p = Ins / 10;
function fromSIunit_p = fromSIunit_p( Ins )
%Translate bar to MPa
fromSIunit_p = Ins * 10;
function toSIunit_T = toSIunit_T( Ins )
%Translate degC to Kelvon
toSIunit_T = Ins + 273.15;
function fromSIunit_T = fromSIunit_T( Ins )
%Translate Kelvin to degC
fromSIunit_T = Ins - 273.15;
function toSIunit_h = toSIunit_h( Ins )
toSIunit_h = Ins;
function  fromSIunit_h = fromSIunit_h( Ins )
fromSIunit_h = Ins;
function toSIunit_v = toSIunit_v( Ins )
toSIunit_v = Ins;
function fromSIunit_v = fromSIunit_v( Ins )
fromSIunit_v = Ins;
function toSIunit_s = toSIunit_s( Ins )
toSIunit_s = Ins;
function fromSIunit_s = fromSIunit_s( Ins )
fromSIunit_s = Ins;
function toSIunit_u = toSIunit_u( Ins )
toSIunit_u = Ins;
function fromSIunit_u = fromSIunit_u( Ins )
fromSIunit_u = Ins;
function toSIunit_Cp = toSIunit_Cp( Ins )
toSIunit_Cp = Ins;
function fromSIunit_Cp = fromSIunit_Cp( Ins )
fromSIunit_Cp = Ins;
function toSIunit_Cv = toSIunit_Cv( Ins )
toSIunit_Cv = Ins;
function fromSIunit_Cv = fromSIunit_Cv( Ins )
fromSIunit_Cv = Ins;
function toSIunit_w = toSIunit_w( Ins )
toSIunit_w = Ins;
function fromSIunit_w = fromSIunit_w( Ins )
fromSIunit_w = Ins;
function toSIunit_tc = toSIunit_tc( Ins )
toSIunit_tc = Ins;
function fromSIunit_tc = fromSIunit_tc( Ins )
fromSIunit_tc = Ins;
function toSIunit_st = toSIunit_st( Ins )
toSIunit_st = Ins;
function fromSIunit_st = fromSIunit_st( Ins )
fromSIunit_st = Ins;
function toSIunit_x = toSIunit_x( Ins )
toSIunit_x = Ins;
function fromSIunit_x = fromSIunit_x( Ins )
fromSIunit_x = Ins;
function toSIunit_vx = toSIunit_vx( Ins )
toSIunit_vx = Ins;
function fromSIunit_vx = fromSIunit_vx( Ins )
fromSIunit_vx = Ins;
function toSIunit_my = toSIunit_my( Ins )
toSIunit_my = Ins;
function fromSIunit_my = fromSIunit_my( Ins )
fromSIunit_my = Ins;

%***********************************************************************************************************
%*7 Verification                                                                                      *
%***********************************************************************************************************

function err = check()
err=0;
%*********************************************************************************************************
%* 7.1 Verifiy region 1
%IF-97 Table 5, Page 9
p=[30/10,800/10,30/10];
T=[300,300,500];
Fun={'v1_pT','h1_pT','u1_pT','s1_pT','Cp1_pT','w1_pT'};
IF97=[0.00100215168,0.000971180894,0.001202418;...
        115.331273,184.142828,975.542239;...
        112.324818,106.448356,971.934985;...
        0.392294792,0.368563852,2.58041912;...
        4.17301218,4.01008987,4.65580682;...
        1507.73921,1634.69054,1240.71337];
R1=zeros(6,3);
for i=1:3
    for j=1:6
        R1(j,i)=eval([char(Fun(j)),'(',num2str(p(i)),',',num2str(T(i)),');']);
    end
end
Region1_error=abs((R1-IF97)./IF97)
err=err+sum(sum(Region1_error>1E-8))

%IF-97 Table 7, Page 11
p=[30/10,800/10,800/10];
h=[500,500,1500];
IF97=[391.798509,378.108626,611.041229];
R1=zeros(1,3);
for i=1:3
    R1(i)=T1_ph(p(i),h(i));
end
T1_ph_error=abs((R1-IF97)./IF97)
err=err+sum(sum(T1_ph_error>1E-8))

%IF-97 Table 9, Page 12
p=[30/10,800/10,800/10];
s=[0.5,0.5,3];
IF97=[307.842258,309.979785,565.899909];
R1=zeros(1,3);
for i=1:3
    R1(i)=T1_ps(p(i),s(i));
end
T1_ps_error=abs((R1-IF97)./IF97)
err=err+sum(sum(T1_ps_error>1E-8))

%Supplementary Release on Backward Equations 
%for Pressure as a Function of Enthalpy and Entropy p(h,s) 
%Table 3, Page 6
h=[0.001,90,1500];
s=[0,0,3.4];
IF97=[0.0009800980612,91.929547272,58.68294423];
R1=zeros(1,3);
for i=1:3
    R1(i)=p1_hs(h(i),s(i));
end
p1_hs_error=abs((R1-IF97)./IF97)
err=err+sum(sum(p1_hs_error>1E-8))

%*********************************************************************************************************
%* 7.2 Verifiy region 2
% IF-97 Table 15, Page 17
p=[0.035/10,0.035/10,300/10];
T=[300,700,700];
Fun={'v2_pT','h2_pT','u2_pT','s2_pT','Cp2_pT','w2_pT'};
IF97=[39.4913866,92.3015898,0.00542946619;...
        2549.91145,3335.68375,2631.49474;...
        2411.6916,3012.62819,2468.61076;...
        8.52238967,10.1749996,5.17540298;...
        1.91300162,2.08141274,10.3505092;...
        427.920172,644.289068,480.386523];
R2=zeros(6,3);
for i=1:3
    for j=1:6
        R2(j,i)=eval([char(Fun(j)),'(',num2str(p(i)),',',num2str(T(i)),');']);
    end
end
Region2_error=abs((R2-IF97)./IF97)
err=err+sum(sum(Region2_error>1E-8))

%IF-97 Table 24, Page 25
p=[0.01/10,30/10,30/10,50/10,50/10,250/10,400/10,600/10,600/10];
h=[3000,3000,4000,3500,4000,3500,2700,2700,3200];
IF97=[534.433241,575.37337,1010.77577,801.299102,1015.31583,875.279054,743.056411,791.137067,882.75686];
R2=zeros(1,9);
for i=1:9
    R2(i)=T2_ph(p(i),h(i));
end
T2_ph_error=abs((R2-IF97)./IF97)
err=err+sum(sum(T2_ph_error>1E-8))

%IF-97 Table 29, Page 29
p=[1/10,1/10,25/10,80/10,80/10,900/10,200/10,800/10,800/10];
s=[7.5,8,8,6,7.5,6,5.75,5.25,5.75];
IF97=[399.517097,514.127081,1039.84917,600.48404,1064.95556,1038.01126,697.992849,854.011484,949.017998];
R2=zeros(1,9);
for i=1:9
    R2(i)=T2_ps(p(i),s(i));
end
T2_ps_error=abs((R2-IF97)./IF97)
err=err+sum(sum(T2_ps_error>1E-8))

%Supplementary Release on Backward Equations for Pressure as a Function of Enthalpy and Entropy p(h,s) 
%Table 3, Page 6
h=[2800,2800,4100,2800,3600,3600,2800,2800,3400];
s=[6.5,9.5,9.5,6,6,7,5.1,5.8,5.8];
IF97=[1.371012767,0.001879743844,0.1024788997,4.793911442,83.95519209,7.527161441,94.3920206,8.414574124,83.76903879];
R2=zeros(1,9);
for i=1:9
    R2(i)=p2_hs(h(i),s(i));
end
p2_hs_error=abs((R2-IF97)./IF97)
err=err+sum(sum(p2_hs_error>1E-8))

%*********************************************************************************************************
%* 7.3 Verifiy region 3
% IF-97 Table 33, Page 32
T=[650,650,750];
rho=[500,200,500];
Fun={'p3_rhoT','h3_rhoT','u3_rhoT','s3_rhoT','Cp3_rhoT','w3_rhoT'};
IF97=[25.5837018,22.2930643,78.3095639;...
        1863.43019,2375.12401,2258.68845;...
        1812.26279,2263.65868,2102.06932;...
        4.05427273,4.85438792,4.46971906;...
        13.8935717,44.6579342,6.34165359;...
        502.005554,383.444594,760.696041];
R3=zeros(6,3);
for i=1:3
    for j=1:6
        R3(j,i)=eval([char(Fun(j)),'(',num2str(rho(i)),',',num2str(T(i)),');']);
    end
end
Region3_error=abs((R3-IF97)./IF97)
err=err+sum(sum(Region3_error>1E-8))

%T3_ph
p=[200/10,500/10,1000/10,200/10,500/10,1000/10];
h=[1700,2000,2100,2500,2400,2700];
IF97=[629.3083892,690.5718338,733.6163014,641.8418053,735.1848618,842.0460876];
R3=zeros(1,6);
for i=1:6
    R3(i)=T3_ph(p(i),h(i));
end
T3_ph_error=abs((R3-IF97)./IF97)
err=err+sum(sum(T3_ph_error>1E-8))

%v3_ph
p=[200/10,500/10,1000/10,200/10,500/10,1000/10];
h=[1700,2000,2100,2500,2400,2700];
IF97=[0.001749903962,0.001908139035,0.001676229776,0.006670547043,0.0028012445,0.002404234998];
R3=zeros(1,6);
for i=1:6
    R3(i)=v3_ph(p(i),h(i));
end
v3_ph_error=abs((R3-IF97)./IF97)
err=err+sum(sum(v3_ph_error>1E-7))

%T3_ps
p=[200/10,500/10,1000/10,200/10,500/10,1000/10];
s=[3.7,3.5,4,5,4.5,5];
IF97=[620.8841563,618.1549029,705.6880237,640.1176443,716.3687517,847.4332825];
R3=zeros(1,6);
for i=1:6
    R3(i)=T3_ps(p(i),s(i));
end
T3_ps_error=abs((R3-IF97)./IF97)
err=err+sum(sum(T3_ps_error>1E-8))

%v3_ps
p=[200/10,500/10,1000/10,200/10,500/10,1000/10];
s=[3.7,3.5,4,5,4.5,5];
IF97=[0.001639890984,0.001423030205,0.001555893131,0.006262101987,0.002332634294,0.002449610757];
R3=zeros(1,6);
for i=1:6
    R3(i)=v3_ps(p(i),s(i));
end
v3_ps_error=abs((R3-IF97)./IF97)
err=err+sum(sum(v3_ps_error>1E-8))

%p3_hs
h=[1700,2000,2100,2500,2400,2700];
s=[3.8,4.2,4.3,5.1,4.7,5];
IF97=[25.55703246,45.40873468,60.7812334,17.20612413,63.63924887,88.39043281];
R3=zeros(1,6);
for i=1:6
    R3(i)=p3_hs(h(i),s(i));
end
p3_hs_error=abs((R3-IF97)./IF97)
err=err+sum(sum(p3_hs_error>1E-8))

%h3_pT (Iteration)
p=[255.83702,222.93064,783.09564]./10;
T=[650,650,750];
IF97=[1863.271389,2375.696155,2258.626582];
R3=zeros(1,3);
for i=1:3
    R3(i)=h3_pT(p(i),T(i));
end
h3_pT_error=abs((R3-IF97)./IF97)
err=err+sum(sum(h3_pT_error>1E-6)) %Decimals in IF97

%*********************************************************************************************************
%* 7.4 Verifiy region 4
%Saturation pressure, If97, Table 35, Page 34
T=[300,500,600];
IF97=[0.0353658941, 26.3889776, 123.443146]/10;
R3=zeros(1,3);
for i=1:3
    R4(i)=p4_T(T(i));
end
p4_t_error=abs((R4-IF97)./IF97)
err=err+sum(sum( p4_t_error>1E-7))

T=[1,10,100]/10;
IF97=[372.755919,453.035632,584.149488];
R3=zeros(1,3);
for i=1:3
    R4(i)=T4_p(T(i));
end
T4_p_error=abs((R4-IF97)./IF97)
err=err+sum(sum( T4_p_error>1E-7))

s=[1,2,3,3.8,4,4.2,7,8,9,5.5,5,4.5];
IF97=[308.5509647,700.6304472,1198.359754,1685.025565,1816.891476,1949.352563,2723.729985,2599.04721,2511.861477,2687.69385,2451.623609,2144.360448];
R3=zeros(1,12);
for i=1:12
    R4(i)=h4_s(s(i));
end
h4_s_error=abs((R4-IF97)./IF97)
err=err+sum(sum( h4_s_error>1E-7)) 

%*********************************************************************************************************
%* 7.5 Verifiy region 5
% IF-97 Table 42, Page 39
T=[1500,1500,2000];
p=[5,80,80]/10;
Fun={'v5_pT','h5_pT','u5_pT','s5_pT','Cp5_pT','w5_pT'};
IF97=[1.38455354,0.0865156616,0.115743146;...
        5219.76332,5206.09634,6583.80291;...
        4527.48654,4513.97105,5657.85774;...
        9.65408431,8.36546724,9.15671044;...
        2.61610228,2.64453866,2.8530675;...
        917.071933,919.708859,1054.35806];
R5=zeros(6,3);
for i=1:3
    for j=1:6
        R5(j,i)=eval([char(Fun(j)),'(',num2str(p(i)),',',num2str(T(i)),');']);
    end
end
Region5_error=abs((R5-IF97)./IF97)
err=err+sum(sum(Region5_error>1E-8))

%T5_ph (Iteration)
p=[0.5,8,8];
h=[5219.76331549428,5206.09634477373,6583.80290533381];
IF97=[1500,1500,2000];
R5=zeros(1,3);
for i=1:3
    R5(i)=T5_ph(p(i),h(i));
end
T5_ph_error=abs((R5-IF97)./IF97)
err=err+sum(sum(T5_ph_error>1E-7)) %Decimals in IF97

%T5_ps (Iteration)
p=[0.5,8,8];
s=[9.65408430982588,8.36546724495503,9.15671044273249];
IF97=[1500,1500,2000];
R5=zeros(1,3);
for i=1:3
    R5(i)=T5_ps(p(i),s(i));
end
T5_ps_error=abs((R5-IF97)./IF97)
err=err+sum(sum(T5_ps_error>1E-4)) %Decimals in IF97

%*********************************************************************************************************
%* 7.6 Verifiy calling funtions

fun={'Tsat_p','T_ph','T_ps','T_hs','psat_T','p_hs','hV_p','hL_p','hV_T','hL_T','h_pT','h_ps','h_px','h_prho','h_Tx','vV_p','vL_p','vV_T','vL_T','v_pT','v_ph','v_ps','rhoV_p','rhoL_p','rhoV_T','rhoL_T','rho_pT','rho_ph','rho_ps','sV_p','sL_p','sV_T','sL_T','s_pT','s_ph','uV_p','uL_p','uV_T','uL_T','u_pT','u_ph','u_ps','CpV_p','CpL_p','CpV_T','CpL_T','Cp_pT','Cp_ph','Cp_ps','CvV_p','CvL_p','CvV_T','CvL_T','Cv_pT','Cv_ph','Cv_ps','wV_p','wL_p','wV_T','wL_T','w_pT','w_ph','w_ps','my_pT','my_ph','my_ps','tcL_p','tcV_p','tcL_T','tcV_T','tc_pT','tc_ph','tc_hs','st_T','st_p','x_ph','x_ps','vx_ph','vx_ps'};
In1={'1','1','1','100','100','84','1','1','100','100','1','1','1','1','100','1','1','100','100','1','1','1','1','1','100','100','1','1','1','0.006117','0.0061171','0.0001','100','1','1','1','1','100','100','1','1','1','1','1','100','100','1','1','1','1','1','100','100','1','1','1','1','1','100','100','1','1','1','1','1','1','1','1','25','25','1','1','100','100','1','1','1','1','1'};
In2={'0','100','1','0.2','0','0.296','0','0','0','0','20','1','0.5','2','0.5','0','0','0','0','100','1000','5','0','0','0','0','100','1000','1','0','0','0','0','20','84.01181117','0','0','0','0','100','1000','1','0','0','0','0','100','200','1','0','0','0','0','100','200','1','0','0','0','0','100','200','1','100','100','1','0','0','0','0','25','100','0.34','0','0','1000','4','418','4'};
Control={'99.60591861','23.84481908','73.70859421','13.84933511','1.014179779','2.295498269','2674.949641','417.4364858','2675.572029','419.099155','84.01181117','308.6107171','1546.193063','1082.773391','1547.33559210927','1.694022523','0.001043148','1.671860601','0.001043455','1.695959407','0.437925658','1.03463539','0.590310924','958.6368897','0.598135993','958.3542773','0.589636754','2.283492601','975.6236788','9.155465556','1.8359E-05','9.155756716','1.307014328','0.296482921','0.296813845','2505.547389','417.332171','2506.015308','418.9933299','2506.171426','956.2074342','308.5082185','2.075938025','4.216149431','2.077491868','4.216645119','2.074108555','4.17913573168802','4.190607038','1.552696979','3.769699683','1.553698696','3.76770022','1.551397249','4.035176364','3.902919468','472.0541571','1545.451948','472.2559492','1545.092249','472.3375235','1542.682475','1557.8585','1.22704E-05','0.000914003770302108','0.000384222','0.677593822','0.024753668','0.607458162','0.018326723','0.607509806','0.605710062','0.606283124','0.0589118685876641','0.058987784','0.258055424','0.445397961','0.288493093','0.999233827'};

for i=1:length(fun)
    
    T=['XSteam(''',char(fun(i)),''',',char(In1(i)),',',char(In2(i)),')'];
    Res=eval(T);
    Error=(Res-(str2num(char(Control(i)))))/str2num(char(Control(i)));
    Check=[T,'=',num2str(Res),' - (Control)',char(Control(i)),'=',num2str(Error)]
    if Error>1E-5
        err=err+1;
        error('To large error')
    end   
end



% cprintf.m function

function count = cprintf(style,format,varargin)
% CPRINTF displays styled formatted text in the Command Window
%
% Syntax:
%    count = cprintf(style,format,...)
%
% Description:
%    CPRINTF processes the specified text using the exact same FORMAT
%    arguments accepted by the built-in SPRINTF and FPRINTF functions.
%
%    CPRINTF then displays the text in the Command Window using the
%    specified STYLE argument. The accepted styles are those used for
%    Matlab's syntax highlighting (see: File / Preferences / Colors / 
%    M-file Syntax Highlighting Colors), and also user-defined colors.
%
%    The possible pre-defined STYLE names are:
%
%       'Text'                 - default: black
%       'Keywords'             - default: blue
%       'Comments'             - default: green
%       'Strings'              - default: purple
%       'UnterminatedStrings'  - default: dark red
%       'SystemCommands'       - default: orange
%       'Errors'               - default: light red
%       'Hyperlinks'           - default: underlined blue
%
%       'Black','Cyan','Magenta','Blue','Green','Red','Yellow','White'
%
%    STYLE beginning with '-' or '_' will be underlined. For example:
%          '-Blue' is underlined blue, like 'Hyperlinks';
%          '_Comments' is underlined green etc.
%
%    STYLE beginning with '*' will be bold (R2011b+ only). For example:
%          '*Blue' is bold blue;
%          '*Comments' is bold green etc.
%    Note: Matlab does not currently support both bold and underline,
%          only one of them can be used in a single cprintf command. But of
%          course bold and underline can be mixed by using separate commands.
%
%    STYLE also accepts a regular Matlab RGB vector, that can be underlined
%    and bolded: -[0,1,1] means underlined cyan, '*[1,0,0]' is bold red.
%
%    STYLE is case-insensitive and accepts unique partial strings just
%    like handle property names.
%
%    CPRINTF by itself, without any input parameters, displays a demo
%
% Example:
%    cprintf;   % displays the demo
%    cprintf('text',   'regular black text');
%    cprintf('hyper',  'followed %s','by');
%    cprintf('key',    '%d colored', 4);
%    cprintf('-comment','& underlined');
%    cprintf('err',    'elements\n');
%    cprintf('cyan',   'cyan');
%    cprintf('_green', 'underlined green');
%    cprintf(-[1,0,1], 'underlined magenta');
%    cprintf([1,0.5,0],'and multi-\nline orange\n');
%    cprintf('*blue',  'and *bold* (R2011b+ only)\n');
%    cprintf('string');  % same as fprintf('string') and cprintf('text','string')
%
% Bugs and suggestions:
%    Please send to Yair Altman (altmany at gmail dot com)
%
% Warning:
%    This code heavily relies on undocumented and unsupported Matlab
%    functionality. It works on Matlab 7+, but use at your own risk!
%
%    A technical description of the implementation can be found at:
%    <a href="http://undocumentedmatlab.com/blog/cprintf/">http://UndocumentedMatlab.com/blog/cprintf/</a>
%
% Limitations:
%    1. In R2011a and earlier, a single space char is inserted at the
%       beginning of each CPRINTF text segment (this is ok in R2011b+).
%
%    2. In R2011a and earlier, consecutive differently-colored multi-line
%       CPRINTFs sometimes display incorrectly on the bottom line.
%       As far as I could tell this is due to a Matlab bug. Examples:
%         >> cprintf('-str','under\nline'); cprintf('err','red\n'); % hidden 'red', unhidden '_'
%         >> cprintf('str','regu\nlar'); cprintf('err','red\n'); % underline red (not purple) 'lar'
%
%    3. Sometimes, non newline ('\n')-terminated segments display unstyled
%       (black) when the command prompt chevron ('>>') regains focus on the
%       continuation of that line (I can't pinpoint when this happens). 
%       To fix this, simply newline-terminate all command-prompt messages.
%
%    4. In R2011b and later, the above errors appear to be fixed. However,
%       the last character of an underlined segment is not underlined for
%       some unknown reason (add an extra space character to make it look better)
%
%    5. In old Matlab versions (e.g., Matlab 7.1 R14), multi-line styles
%       only affect the first line. Single-line styles work as expected.
%       R14 also appends a single space after underlined segments.
%
%    6. Bold style is only supported on R2011b+, and cannot also be underlined.
%
% Change log:
%    2020-01-20: Fix by T. Hosman for embedded hyperlinks
%    2015-06-24: Fixed a few discoloration issues (some other issues still remain)
%    2015-03-20: Fix: if command window isn't defined yet (startup) use standard fprintf as suggested by John Marozas
%    2012-08-09: Graceful degradation support for deployed (compiled) and non-desktop applications; minor bug fixes
%    2012-08-06: Fixes for R2012b; added bold style; accept RGB string (non-numeric) style
%    2011-11-27: Fixes for R2011b
%    2011-08-29: Fix by Danilo (FEX comment) for non-default text colors
%    2011-03-04: Performance improvement
%    2010-06-27: Fix for R2010a/b; fixed edge case reported by Sharron; CPRINTF with no args runs the demo
%    2009-09-28: Fixed edge-case problem reported by Swagat K
%    2009-05-28: corrected nargout behavior suggested by Andreas Gäb
%    2009-05-13: First version posted on <a href="http://www.mathworks.com/matlabcentral/fileexchange/authors/27420">MathWorks File Exchange</a>
%
% See also:
%    sprintf, fprintf

% License to use and modify this code is granted freely to all interested, as long as the original author is
% referenced and attributed as such. The original author maintains the right to be solely associated with this work.

% Programmed and Copyright by Yair M. Altman: altmany(at)gmail.com
% $Revision: 1.11 $  $Date: 2020/01/05 20:17:23 $

  persistent majorVersion minorVersion
  if isempty(majorVersion)
      %v = version; if str2double(v(1:3)) <= 7.1
      %majorVersion = str2double(regexprep(version,'^(\d+).*','$1'));
      %minorVersion = str2double(regexprep(version,'^\d+\.(\d+).*','$1'));
      %[a,b,c,d,versionIdStrs]=regexp(version,'^(\d+)\.(\d+).*');  %#ok unused
      v = sscanf(version, '%d.', 2);
      majorVersion = v(1); %str2double(versionIdStrs{1}{1});
      minorVersion = v(2); %str2double(versionIdStrs{1}{2});
  end

  % The following is for debug use only:
  %global docElement txt el
  if ~exist('el','var') || isempty(el),  el=handle([]);  end  %#ok mlint short-circuit error ("used before defined")
  if nargin<1, showDemo(majorVersion,minorVersion); return;  end
  if isempty(style),  return;  end
  if all(ishandle(style)) && length(style)~=3
      dumpElement(style);
      return;
  end

  % Process the text string
  if nargin<2, format = style; style='text';  end
  %error(nargchk(2, inf, nargin, 'struct'));
  %str = sprintf(format,varargin{:});

  % In compiled mode
  try useDesktop = usejava('desktop'); catch, useDesktop = false; end
  if isdeployed | ~useDesktop %#ok<OR2> - for Matlab 6 compatibility
      % do not display any formatting - use simple fprintf()
      % See: http://undocumentedmatlab.com/blog/bold-color-text-in-the-command-window/#comment-103035
      % Also see: https://mail.google.com/mail/u/0/?ui=2&shva=1#all/1390a26e7ef4aa4d
      % Also see: https://mail.google.com/mail/u/0/?ui=2&shva=1#all/13a6ed3223333b21
      count1 = fprintf(format,varargin{:});
  else
      % Else (Matlab desktop mode)
      % Get the normalized style name and underlining flag
      [underlineFlag, boldFlag, style, debugFlag] = processStyleInfo(style);

      % Set hyperlinking, if so requested
      if underlineFlag
          prefix = '<a href="">';
          %format = [prefix format '</a>'];  % this displayed incorrectly for embedded hyperlinks

          % Handle case of embedded hyperlinks with underline format 5/1/2020
          str = sprintf(format, varargin{:});
          str = regexprep(str,{'<a ','/a>','_@@@_'},{'_@@@_<a ',['/a>' prefix],'</a>'},'ignorecase');
          str = [prefix str '</a>'];
          format = '%s'; varargin = {str};

          % Matlab 7.1 R14 (possibly a few newer versions as well?)
          % have a bug in rendering consecutive hyperlinks
          % This is fixed by appending a single non-linked space
          if majorVersion < 7 || (majorVersion==7 && minorVersion <= 1)
              format(end+1) = ' ';
          end
      end

      % Set bold, if requested and supported (R2011b+)
      if boldFlag
          if (majorVersion > 7 || minorVersion >= 13)
              format = ['<strong>' format '</strong>'];
          else
              boldFlag = 0;
          end
      end

      % Get the current CW position
      cmdWinDoc = com.mathworks.mde.cmdwin.CmdWinDocument.getInstance;
      lastPos = cmdWinDoc.getLength;

      % If not beginning of line
      bolFlag = 0;  %#ok
      %if docElement.getEndOffset - docElement.getStartOffset > 1
          % Display a hyperlink element in order to force element separation
          % (otherwise adjacent elements on the same line will be merged)
          if majorVersion<7 || (majorVersion==7 && minorVersion<13)
              if ~underlineFlag
                  fprintf('<a href=""> </a>');  %fprintf('<a href=""> </a>\b');
              elseif format(end)~=10  % if no newline at end
                  fprintf(' ');  %fprintf(' \b');
              end
          end
          %drawnow;
          bolFlag = 1;
      %end

      % Get a handle to the Command Window component
      mde = com.mathworks.mde.desk.MLDesktop.getInstance;
      cw = mde.getClient('Command Window');

      % Fix: if command window isn't defined yet (startup), use standard fprintf()
      if (isempty(cw))
         count1 = fprintf(format,varargin{:});
         if nargout
             count = count1;
         end
         return;
      end
      
      xCmdWndView = cw.getComponent(0).getViewport.getComponent(0);

      % Store the CW background color as a special color pref
      % This way, if the CW bg color changes (via File/Preferences), 
      % it will also affect existing rendered strs
      com.mathworks.services.Prefs.setColorPref('CW_BG_Color',xCmdWndView.getBackground);

      % Display the text in the Command Window
      % Note: fprintf(2,...) is required in order to add formatting tokens, which
      % ^^^^  can then be updated below (no such tokens when outputting to stdout)
      %format(end+1) = ' ';  % Jacob D's FEX comment 14/6/2016 (sometimes makes things worse!) https://mail.google.com/mail/u/0/#inbox/15551268609f9fef
      count1 = fprintf(2,format,varargin{:});

      % Repaint the command window
      %awtinvoke(cmdWinDoc,'remove',lastPos,1);   % TODO: find out how to remove the extra '_'
      drawnow;  % this is necessary for the following to work properly (refer to Evgeny Pr in FEX comment 16/1/2011)
      xCmdWndView.repaint;
      %pause(0.01);
      %hListeners = cmdWinDoc.getDocumentListeners; for idx=1:numel(hListeners), try hListeners(idx).repaint; catch, end, end
      cmdWinLen = cmdWinDoc.getLength;

      docElement = cmdWinDoc.getParagraphElement(lastPos+1);
      if majorVersion<7 || (majorVersion==7 && minorVersion<13)
          if bolFlag && ~underlineFlag
              % Set the leading hyperlink space character ('_') to the bg color, effectively hiding it
              % Note: old Matlab versions have a bug in hyperlinks that need to be accounted for...
              %disp(' '); dumpElement(docElement)
              setElementStyle(docElement,'CW_BG_Color',1+underlineFlag,majorVersion,minorVersion); %+getUrlsFix(docElement));
              %disp(' '); dumpElement(docElement)
              el(end+1) = handle(docElement);  % #ok used in debug only
          end

          % Fix a problem with some hidden hyperlinks becoming unhidden...
          fixHyperlink(docElement);
          %dumpElement(docElement);
      end

      % Get the Document Element(s) corresponding to the latest fprintf operation
      while docElement.getStartOffset < cmdWinLen
          % Set the element style according to the current style
          if debugFlag, dumpElement(docElement); end
          specialFlag = underlineFlag | boldFlag;
          setElementStyle(docElement,style,specialFlag,majorVersion,minorVersion);
          if debugFlag, dumpElement(docElement); end
          docElement2 = cmdWinDoc.getParagraphElement(docElement.getEndOffset+1);
          if isequal(docElement,docElement2),  break;  end
          docElement = docElement2;
      end
      if debugFlag, dumpElement(docElement); end

      % Force a Command-Window repaint
      % Note: this is important in case the rendered str was not '\n'-terminated
      xCmdWndView.repaint;
      %fprintf('\b');  % Jacob D's FEX comment 14/6/2016 (sometimes makes things worse!) https://mail.google.com/mail/u/0/#inbox/15551268609f9fef

      % The following is for debug use only:
      el(end+1) = handle(docElement);  %#ok used in debug only
      %elementStart  = docElement.getStartOffset;
      %elementLength = docElement.getEndOffset - elementStart;
      %txt = cmdWinDoc.getText(elementStart,elementLength);
  end

  if nargout
      count = count1;
  end
  return;  % debug breakpoint

% Process the requested style information
function [underlineFlag,boldFlag,style,debugFlag] = processStyleInfo(style)
  underlineFlag = 0;
  boldFlag = 0;
  debugFlag = 0;

  % First, strip out the underline/bold markers
  if ischar(style)
      % Styles containing '-' or '_' should be underlined (using a no-target hyperlink hack)
      %if style(1)=='-'
      underlineIdx = (style=='-') | (style=='_');
      if any(underlineIdx)
          underlineFlag = 1;
          %style = style(2:end);
          style = style(~underlineIdx);
      end

      % Check for bold style (only if not underlined)
      boldIdx = (style=='*');
      if any(boldIdx)
          boldFlag = 1;
          style = style(~boldIdx);
      end
      if underlineFlag && boldFlag
          warning('YMA:cprintf:BoldUnderline','Matlab does not support both bold & underline')
      end

      % Check for debug mode (style contains '!')
      debugIdx = (style=='!');
      if any(debugIdx)
          debugFlag = 1;
          style = style(~debugIdx);
      end

      % Check if the remaining style sting is a numeric vector
      %styleNum = str2num(style); %#ok<ST2NM>  % not good because style='text' is evaled!
      %if ~isempty(styleNum)
      if any(style==' ' | style==',' | style==';')
          style = str2num(style); %#ok<ST2NM>
      end
  end

  % Style = valid matlab RGB vector
  if isnumeric(style) && length(style)==3 && all(style<=1) && all(abs(style)>=0)
      if any(style<0)
          underlineFlag = 1;
          style = abs(style);
      end
      style = getColorStyle(style);

  elseif ~ischar(style)
      error('YMA:cprintf:InvalidStyle','Invalid style - see help section for a list of valid style values')

  % Style name
  else
      % Try case-insensitive partial/full match with the accepted style names
      matlabStyles = {'Text','Keywords','Comments','Strings','UnterminatedStrings','SystemCommands','Errors'};
      validStyles  = [matlabStyles, ...
                      'Black','Cyan','Magenta','Blue','Green','Red','Yellow','White', ...
                      'Hyperlinks'];
      matches = find(strncmpi(style,validStyles,length(style)));

      % No match - error
      if isempty(matches)
          error('YMA:cprintf:InvalidStyle','Invalid style - see help section for a list of valid style values')

      % Too many matches (ambiguous) - error
      elseif length(matches) > 1
          error('YMA:cprintf:AmbigStyle','Ambiguous style name - supply extra characters for uniqueness')

      % Regular text
      elseif matches == 1
          style = 'ColorsText';  % fixed by Danilo, 29/8/2011

      % Highlight preference style name
      elseif matches <= length(matlabStyles)
          style = ['Colors_M_' validStyles{matches}];

      % Color name
      elseif matches < length(validStyles)
          colors = [0,0,0; 0,1,1; 1,0,1; 0,0,1; 0,1,0; 1,0,0; 1,1,0; 1,1,1];
          requestedColor = colors(matches-length(matlabStyles),:);
          style = getColorStyle(requestedColor);

      % Hyperlink
      else
          style = 'Colors_HTML_HTMLLinks';  % CWLink
          underlineFlag = 1;
      end
  end

% Convert a Matlab RGB vector into a known style name (e.g., '[255,37,0]')
function styleName = getColorStyle(rgb)
  intColor = int32(rgb*255);
  javaColor = java.awt.Color(intColor(1), intColor(2), intColor(3));
  styleName = sprintf('[%d,%d,%d]',intColor);
  com.mathworks.services.Prefs.setColorPref(styleName,javaColor);

% Fix a bug in some Matlab versions, where the number of URL segments
% is larger than the number of style segments in a doc element
function delta = getUrlsFix(docElement)  %#ok currently unused
  tokens = docElement.getAttribute('SyntaxTokens');
  links  = docElement.getAttribute('LinkStartTokens');
  if length(links) > length(tokens(1))
      delta = length(links) > length(tokens(1));
  else
      delta = 0;
  end

% fprintf(2,str) causes all previous '_'s in the line to become red - fix this
function fixHyperlink(docElement)
  try
      tokens = docElement.getAttribute('SyntaxTokens');
      urls   = docElement.getAttribute('HtmlLink');
      urls   = urls(2);
      links  = docElement.getAttribute('LinkStartTokens');
      offsets = tokens(1);
      styles  = tokens(2);
      doc = docElement.getDocument;

      % Loop over all segments in this docElement
      for idx = 1 : length(offsets)-1
          % If this is a hyperlink with no URL target and starts with ' ' and is collored as an error (red)...
          if strcmp(styles(idx).char,'Colors_M_Errors')
              character = char(doc.getText(offsets(idx)+docElement.getStartOffset,1));
              if strcmp(character,' ')
                  if isempty(urls(idx)) && links(idx)==0
                      % Revert the style color to the CW background color (i.e., hide it!)
                      styles(idx) = java.lang.String('CW_BG_Color');
                  end
              end
          end
      end
  catch
      % never mind...
  end

% Set an element to a particular style (color)
function setElementStyle(docElement,style,specialFlag, majorVersion,minorVersion)
  %global tokens links urls urlTargets  % for debug only
  global oldStyles
  if nargin<3,  specialFlag=0;  end
  % Set the last Element token to the requested style:
  % Colors:
  tokens = docElement.getAttribute('SyntaxTokens');
  try
      styles = tokens(2);
      oldStyles{end+1} = cell(styles);

      % Correct edge case problem
      extraInd = double(majorVersion>7 || (majorVersion==7 && minorVersion>=13));  % =0 for R2011a-, =1 for R2011b+
      %{
      if ~strcmp('CWLink',char(styles(end-hyperlinkFlag))) && ...
          strcmp('CWLink',char(styles(end-hyperlinkFlag-1)))
         extraInd = 0;%1;
      end
      hyperlinkFlag = ~isempty(strmatch('CWLink',tokens(2)));
      hyperlinkFlag = 0 + any(cellfun(@(c)(~isempty(c)&&strcmp(c,'CWLink')),cell(tokens(2))));
      %}

      jStyle = java.lang.String(style);
      if numel(styles)==4 && isempty(char(styles(2)))
          % Attempt to fix discoloration issues - NOT SURE THAT THIS IS OK! - 24/6/2015
          styles(1) = jStyle;
      end
      styles(end-extraInd) = java.lang.String('');
      styles(end-extraInd-specialFlag) = jStyle;  % #ok apparently unused but in reality used by Java
      if extraInd
          styles(end-specialFlag) = jStyle;
      end

      oldStyles{end} = [oldStyles{end} cell(styles)];
  catch
      % never mind for now
  end
  
  % Underlines (hyperlinks):
  %{
  links = docElement.getAttribute('LinkStartTokens');
  if isempty(links)
      %docElement.addAttribute('LinkStartTokens',repmat(int32(-1),length(tokens(2)),1));
  else
      %TODO: remove hyperlink by setting the value to -1
  end
  %}

  % Correct empty URLs to be un-hyperlinkable (only underlined)
  urls = docElement.getAttribute('HtmlLink');
  if ~isempty(urls)
      urlTargets = urls(2);
      for urlIdx = 1 : length(urlTargets)
          try
              if urlTargets(urlIdx).length < 1
                  urlTargets(urlIdx) = [];  % '' => []
              else  % fix for hyperlinks by T. Hosman 25/11/2019 (via email)
                  if urlIdx > 1
                      styles(urlIdx-1) = jStyle;
                  end
                  styles(urlIdx) = jStyle; %=java.lang.String('CWLink');
              end
          catch
              % never mind...
              a=1;  %#ok used for debug breakpoint...
          end
      end
  end
  
  % Bold: (currently unused because we cannot modify this immutable int32 numeric array)
  %{
  try
      %hasBold = docElement.isDefined('BoldStartTokens');
      bolds = docElement.getAttribute('BoldStartTokens');
      if ~isempty(bolds)
          %docElement.addAttribute('BoldStartTokens',repmat(int32(1),length(bolds),1));
      end
  catch
      % never mind - ignore...
      a=1;  %#ok used for debug breakpoint...
  end
  %}
  
  return;  % debug breakpoint

% Display information about element(s)
function dumpElement(docElements)
  %return;
  disp(' ');
  numElements = length(docElements);
  cmdWinDoc = docElements(1).getDocument;
  for elementIdx = 1 : numElements
      if numElements > 1,  fprintf('Element #%d:\n',elementIdx);  end
      docElement = docElements(elementIdx);
      if ~isjava(docElement),  docElement = docElement.java;  end
      %docElement.dump(java.lang.System.out,1)
      disp(strtrim(char(docElement)))
      txt = {};
      try
          tokens = docElement.getAttribute('SyntaxTokens');
          %if isempty(tokens),  continue;  end
          links = docElement.getAttribute('LinkStartTokens');
          urls  = docElement.getAttribute('HtmlLink');
          try bolds = docElement.getAttribute('BoldStartTokens'); catch, bolds = []; end
          tokenLengths = tokens(1);
          for tokenIdx = 1 : length(tokenLengths)-1
              tokenLength = diff(tokenLengths(tokenIdx+[0,1]));
              if (tokenLength < 0)
                  tokenLength = docElement.getEndOffset - docElement.getStartOffset - tokenLengths(tokenIdx);
              end
              txt{tokenIdx} = cmdWinDoc.getText(docElement.getStartOffset+tokenLengths(tokenIdx),tokenLength).char;  %#ok
          end
      catch
          tokenLengths = 0;
      end
      lastTokenStartOffset = docElement.getStartOffset + tokenLengths(end);
      try
          txt{end+1} = cmdWinDoc.getText(lastTokenStartOffset, docElement.getEndOffset-lastTokenStartOffset).char; %#ok
      catch
          txt{end+1} = ''; %#ok<AGROW>
      end
      %cmdWinDoc.uiinspect
      %docElement.uiinspect
      txt = strrep(txt',sprintf('\n'),'\n'); %#ok<SPRINTFN>
      try
          data = [cell(tokens(2)) m2c(tokens(1)) m2c(links) m2c(urls(1)) cell(urls(2)) m2c(bolds) txt];
          if elementIdx==1
              disp('    SyntaxTokens(2,1) - LinkStartTokens - HtmlLink(1,2) - BoldStartTokens - txt');
              disp('    ==============================================================================');
          end
      catch
          try
              data = [cell(tokens(2)) m2c(tokens(1)) m2c(links) txt];
          catch
              try
                  disp([cell(tokens(2)) m2c(tokens(1)) txt]);
                  data = [m2c(links) m2c(urls(1)) cell(urls(2))];
              catch
                  % Matlab 7.1 only has urls(1)...
                  try
                      data = [m2c(links) cell(urls)];
                  catch  % no tokens
                      data = txt;
                  end
              end
          end
      end
      disp(data)
  end

% Utility function to convert matrix => cell
function cells = m2c(data)
  %datasize = size(data);  cells = mat2cell(data,ones(1,datasize(1)),ones(1,datasize(2)));
  cells = num2cell(data);

% Display the help and demo
function showDemo(majorVersion,minorVersion)
  fprintf('cprintf displays formatted text in the Command Window.\n\n');
  fprintf('Syntax: count = cprintf(style,format,...);  click <a href="matlab:help cprintf">here</a> for details.\n\n');
  url = 'http://UndocumentedMatlab.com/blog/cprintf/';
  fprintf(['Technical description: <a href="' url '">' url '</a>\n\n']);
  fprintf('Demo:\n\n');
  boldFlag = majorVersion>7 || (majorVersion==7 && minorVersion>=13);
  s = ['cprintf(''text'',    ''regular black text'');' 10 ...
       'cprintf(''hyper'',   ''followed %s'',''by'');' 10 ...
       'cprintf(''key'',     ''%d colored'',' num2str(4+boldFlag) ');' 10 ...
       'cprintf(''-comment'',''& underlined'');' 10 ...
       'cprintf(''err'',     ''elements:\n'');' 10 ...
       'cprintf(''cyan'',    ''cyan'');' 10 ...
       'cprintf(''_green'',  ''underlined green'');' 10 ...
       'cprintf(-[1,0,1],  ''underlined magenta'');' 10 ...
       'cprintf([1,0.5,0], ''and multi-\nline orange\n'');' 10];
   if boldFlag
       % In R2011b+ the internal bug that causes the need for an extra space
       % is apparently fixed, so we must insert the sparator spaces manually...
       % On the other hand, 2011b enables *bold* format
       s = [s 'cprintf(''*blue'',   ''and *bold* (R2011b+ only)\n'');' 10];
       s = strrep(s, ''')',' '')');
       s = strrep(s, ''',5)',' '',5)');
       s = strrep(s, '\n ','\n');
   end
   disp(s);
   eval(s);


%%%%%%%%%%%%%%%%%%%%%%%%%% TODO %%%%%%%%%%%%%%%%%%%%%%%%%
% - Fix: Remove leading space char (hidden underline '_')
% - Fix: Find workaround for multi-line quirks/limitations
% - Fix: Non-\n-terminated segments are displayed as black
% - Fix: Check whether the hyperlink fix for 7.1 is also needed on 7.2 etc.
% - Enh: Add font support