Constraint Minimization using Lagrange Multipliers

OBJECTIVE To Create a Flow Over a NACA0017 Airfoil. To Vary the Angle of Attack from 0 to 10 by an increase of 2. To Compare the Lift force and the Drag force for different Angle of Attack. INTRODUCTION        An Airfoil is the cross-sectional shape of a wing. An airfoil-shaped body moved through…

Aim To run a pipe flow simulation at different Reynold\'s number. To place a line probe a different pipe length. Compare the velocity at each probe. To create cut plots to see the profile of the flow. Procedure The pipe is created using SOLIDWORKS CAD TOOLS. The pipe created is of length 1000 mm outer diameter 40 mm and…

Minimization of the function using Lagrange Multipliers Given  f(x,y) = 5 - (x - 2)² - 2(y - 1)²  g(x,y) = x + 4y - 3  Solution  Lagrangian Expression   L(x, y, λ)   =   f(x, y) - λ*g(x, y)      L(x, y, λ)   = …

Theory            This method starts with a function f which is defined over real numbers, the function\'s derivative f\', and initial guess x_guess for the root of the function.                 x_guess = x_guess + (f(x_guess)/f\'(x_guess)) Based on…

Description                     The Program consists of two links L1 and L2. For Varying the angles for loop is used and the theta start and theta end are mentioned. Then using for loop position of the links are varied. Then by savefig comment the plots are saved. The Plots…

OBJECTIVE  To Run a baseline simulation for the flow over the cylinder.  Increase the Reynold\'s Number by a factor of 20% , 40% , 100% to run a Transient        flow simulation.  To Calculate the Simulation End Time. INTRODUCTION         Reynold\'s Number is is…

OBJECTIVE To Create a 3D Model of Centrifugal Pump and to run a Flow Simulation. To Obtain a relation between Pressure ratio and Mass Flow rate. INTRODUCTION       Centrifugal Pumps are the sub class of the Turbomachinery. Centrifugal pumps are used to transport fluids by the conversion of rotational…

OBJECTIVE To run a Grid Dependancy test for getting the fine grid. To get the Effect of Valve Lift on Mass flow rate INTRODUCTION       An air flow bench is a device used for testing the internal aerodynamic qualities of an engine component. It is used primarily for testing the intake…

Objective To take column as input and plot the respective columns. To save the file in the name of column. To check the Compatability of the file. To calculate the area under the PV diagram. To calculate the Power output and Specific fuel consumption. Description           In this code I am provided…

Description                     In this code I used numpy module, matplotlib module, scipy module. I created two functions one is for the Linear polynomial and other is for the Cubic polynomial. Then I created a seperate function the read the data file and extracts the…

Theory             The Otto Cycle is an air standard cycle which describes the working of the petrol engine. The otto cycle consists of four processes. First is Isentropic Compression second the Constant Volume Heat Addition then the Isentropic Expansion and last the Constant Volume Heat…

Objective    To plot Drag force vs Velocity    To plot Drag force vs Drag Coefficient Description            In this Program I have created two codes one is to calculate the Drag Force by keeping the Drag Coefficient constant and other is to calculate the Drag Force by…

Objective  Function to extract 14 coefficient of the given species.  Function to calculate the Specific Heat, Enthalpy, Entropy of the species.  Function to calculate the Molecular Weight of the species.  To create the Folder for each species and save the plot of each species in the     …

Theory           A genetic algorithm is a method to solve constrained and unconstrained optimization problems.The genetic algorithm changes the population of individual solution repeatedly.The genetic algorithm randomly selects the individual from current population and use them as parents to produce…

Description                  Curve Fitting is a process of constructing a mathematical function that has to fit the series of data points. First I have seperated the given data into temperature and specific heat. Then I have taken two figures seperately one denoting the linear…

Theory                 The Otto Cycle is an air standard cycle which describes the working of the petrol engine. The otto cycle consists of four processes. First is Isentropic Compression second the Constant Volume Heat Addition then the Isentropic Expansion and last the Constant…

Theory               A Pendulum is a ball suspended from a piviot point so that it can swing freely. When the pendulum is displaced from its resting position the ball or bob goes to and fro motion and comes to rest. The time for one complete oscillation is called Period. The period depends…