Solving Second order ODE using MATLAB

A Centrifugal pump is created and analysis is done to study the various parameters. The dimensions of the pump are as follows. The diameter of the Volute casing is 90 mm. The thickness of the Volute casing is 15 mm. Rotary blade diameter is from 40mm to 80mm. A number of blades=5. The diameter of the inlet suction cylinder…

A 3D model of a flow bench is created and a baseline flow analysis is run. A plot of lift vs mass flow rate is obtained, also the pressure drop in the system. Flow bench is a device used to design the intake port. Usually, in the flowbench, we take the port which is required to be tested. Here in this project, we are simulating…

Model the flow over a NACA0017 airfoil for the angle of attacks 0,2,4,6,8,10 compare the lift and drag forces  The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics(NACA). The shape of the NACA airfoils is described using a series…

Internal Geneva Mechanism In this mechanism, the driver is connected to the driven wheel internally. The axis of the driver wheel of the internal mechanism can have a bearing only on one side. The angle by which the drive wheel has to rotate to effect one step rotation of the driven wheel is always smaller than 180°…

                     A valvetrain or valve train is a mechanical system that controls the operation of the valves in an internal combustion engine, whereby a sequence of components transmits motion throughout the assembly. A…

                     A Planetary gear  (also known as epicyclic gear train) consists of a larger Ring gear, planet gears, and a sun gear. The sun gear is mounted at the center around which the Planet gears are mounted which can revolve around them. The planet…

          Piston motion analysis is study of the reciprocating motion of the piston in the cyclinder and the motion of the assembly attached i.e. connecting rod, end cap, crank shaft & gudgeon pin.First of all for the assembly of connecting rod, crank shaft, end cap, gudgeon pin and piston…

Simulation of the flow over a cylinder with different reynolds number. A cylinder with followig dimensions are created in solidworks. Diameter = 40mm Length = 50mm Surface roughness is taken as zero. Gravity is not considered. Formula to calculate the baseline case Reynolds number.  Re = rho*U_inlet*D/mu…

A thin pipe of length 1m is simulated to carry fluid at 3 different velocities corresponding to Reynolds numbers 100, 1000 and 10000. The specifications of the pipe are as follows: Length of the pipe: 1m Diameter: 20mm Thickness: 1mm The fluid characteristics are as follows: Fluid: water Dynamic viscosity: 8.9×10−4Pa.s …

Thermodynamic data collected from simulation of a Port Fuel Injected engine is extracted and analysed from a data file using a Python program.           This data file consists of 17 columns of different thermodynamic parameters for which more than 8000 values have been recorded. The objective…

1. What does popt and pcov mean?     popt- An array of optimal values for the parameters which minimizes the sum of squares of          residuals.     pcov-2d array which contains the estimated covariance of popt. The diagonals provide the variance of the…

1. What does popt and pcov mean?     popt- An array of optimal values for the parameters which minimizes the sum of squares of          residuals.     pcov-2d array which contains the estimated covariance of popt. The diagonals provide the variance of the…

Let us consider the given function as  `f ( x , y ) = 5 − ( x − 2 )^ 2 − 2 ⋅ ( y − 1 ) ^2` and the constraint as `g ( x , y ) = x + 4 y − 3` We can use Lagrange multipliers to find the maximum or minimum value of the function. So, we can take `f(x,y)` as `f(x,y,lamda)`,…

Air cushion vehicles(ACV) are used to break ice in cold places, where ice is formed on the surface of lakes, rivers and on the roads too. Depending on the ice thickness , an ACV can readily break ice in flexure by making a depression and send cracks throgh the ice. Once a crack is made , the path of least resistance …

The program written is for simulating an Air standard cycle (Otto cycle). The Otto cycle consists of following four processes. 1-2 Isentropic compression 2-3 Constant volume heat addition 3-4 Isentropic expansion 4-1 Constant volume heat rejection This requires inputs like V1, T1, Compression ratio(cr),T3 from which P1,V2,P2,T2,P3…

Here the program is written on the forward kinematics of a 2R robotic arm. Which shows the simulation of the robot how it is going to move. If we are able to find out how a robot is going to move, we can figure out it's Workspace. The workspace refers to the possible locations that the robot can reach. We can define the…

The cyclist experiences a Drag force while riding. Here we are writing a program using python to calculate drag force against a cyclist. The factors involved are Velocity,Drag coefficient,Frontal Area,Density of air. We are incorporating a function to plot Drag force vs Velocity. Also a function to plot Drag force…

 Rankine cycle  A rankine cycle is a basic operating cycle for all the power plants which involves condensation and expansion of the working fluid. A basic rankine cycle is shown below. It involves the following 4 processes 1. 1-2 is Isentropic Expansion in the turbine:The steam at high pressure enters the turbine…

NASA  came up with polynomials that can be used to evaluate thermodynamic properties such as Cp, H and S using polynomials. They have also documented the co-efficients that are required to evaluate these polynomials for 1000+ species. The coefficients from the NASA thermodynamic file is extracted and the secific heat,…

1. In your own words, describe how Genetic Algorithm Works. A genetic algorithm (GA) is a method for solving both linear and nonlinear optimization problems based on a natural selection process that mimics biological evolution. The algorithm repeatedly modifies a population of individual solutions. At each step, the genetic…

The program written is for simulating an Air standard cycle (Otto cycle). The Otto cycle consists of following four processes. 1-2 Isentropic compression 2-3 Constant volume heat addition 3-4 Isentropic expansion 4-1 Constant volume heat rejection This requires inputs like V1, T1, Compression ratio(cr),T3 from which P1,V2,P2,T2,P3…

In Engineering, ODE is used to describe the transient behavior of a system.  A simple example is a pendulum The way the pendulum moves depends on the Newtons second law. When this law is written down, we get a second order Ordinary Differential Equation that describes the position of the "ball" w.r.t time. The…

Here we are solving a Second order ODE which is involving in a Simple Pendulum. Whenever we have a higher order ODE we need to brake it into first order ODE. It can be solved analytically as shown. Below is the solution using MATLAB clear all close all clc %constants b=.05; g=9.81; l=1; m=0.1; % initial condition theta_0…

1. Write the code to fit a linear and cubic polynomial for the Cp data. Explain if your results are good or bad.  First we are writing codes to fit a linear curve of degree 3 is as follows. clear all close all clc %Preparing the data cp_data=load('data'); temperature=cp_data(:,1); cp=cp_data(:,2); %curve fit %cp=a*T^2+b*T+c…

Here the program is written on the forward kinematics of a 2R robotic arm. Which shows the simulation of the robot how it is going to move. If we are able to find out how a robot is going to move, we can figure out it's Workspace. The workspace refers to the possible locations that the robot can reach. We can define the…

The cyclist experiences a Drag force while riding. Here we are writing a Matlab program to calculate drag force against a cyclist.The factors involved are Velocity,Drag coefficient,Frontal Area,Density of air. We are incorporating a function to plot Drag force vs Velocity. Also a function to plot Drag force vs…

A matrix  is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. In MATLAB a Row matrix and a Column matrix can be created as follows. >> A=[1 2 3] A = 1 2 3 >> B=[4;5;6] B = 4 5 6