Constraint Minimization using Lagrange Multipliers

AIM: You will be running simulations on NACA air foils. OBJECTIVE:  Model the flow over a NACA0017 airfoil For the angle of attacks 0,2,4,6,8,10 compare the lift and drag forces SOLUTION: Angle of Attacks:           In aerodynamics, angle of attack specifies the angle between the…

AIM: For this challenge, you will simulate flow over a cylinder at different reynolds number. OBJECTIVE: Calculate the baseline case Reynolds number.  Re = rho*U_inlet*D/mu D = cylinder diameter mu = dynamic viscosity rho = density Run a baseline simulation and then calculate the Reynolds number. Then increase…

AIM:  Run a pipe flow simulation with an inlet Reynolds number of 100,1000 and 10,000. For each of these cases do the following 1. Place line probes at 95%, 90% and 85% of the pipe length. 2. Compare the normalized velocity profile at each of these locations 3. Normalize the velocity profile by the inlet velocity.…

AIM: For this challenge, you will be create a data visualizer tool. Your task is to write a script that does the following. Data visualizer: Your script should take column numbers as the input and plot the respective columns as separate images Each file should be saved by the name of the column The plot labels…

AIM: For this problem, you will minimize a simple non-linear function by using Lagrange Multipliers. Minimize the following function, 5-(x-2)^2 -2(y-1)^2  subject to the following constraint x + 4y = 3.  SOLUTION: What is Lagrange Multipliers?       In mathematical optimization,…

AIM: Write a python code to fit a linear and cubic polynomial for the given Cp data. SOLUTION: Coding: """ Linear and Cubic Polynomial curve fit for the cp data """ import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit # Linear polynomial curve fit def fun1(t1, a1, b1): return a1*t1…

AIM: In determining the minimum cushion pressure needed to break a given thickness of iceusing an air cushion vehicle, Muller (“Ice Breaking with an Air Cushion Vehicle”) inMathematical Modeling: Classroom Notes in Applied Mathematics, SIAM 1987) derivedthe equation            …

AIM: write a python code that can solve an otto cycle and create a PV diagram and output the thermal efficiency of the engine. SOLUTION: Coding: """ Otto Cycle """ import math import matplotlib.pyplot as plt #engine kinematics def engine_kinematics(bore,stroke,con_rod,cr,start_a,end_a): #geometric parameters…

AIM: Write a program in python to simulate the forward kinematics of a 2R Robotic Arm and create a animation file of the plots. SOLUTION: Coding: # Simulation of 2R robotic arm import math import matplotlib.pyplot as plt # total number of theta tot_theta=10 # starting and ending of theta theta_start=0 theta_end=math.pi/2…

AIM: Write a Python program to calculate drag force against a cyclist. Write a program to plot Velocity vs Drag force(25 points) and Write a program to plot Drag Co-efficient vs Drag force(25 points). SOLUTION:  Coding:  Velocity vs Drag force """ Calculation of drag force against a cyclist """ import matplotlib.pyplot…

AIM:  Create a Rankine Cycle Simulator using MATLAB. Your code should calculate the state points of the Rankine Cycle (any type of your choice) based on user inputs.  Then, plot the corresponding T-s and h-s plots for the given set of inputs. Title and axes labels are a must, while legends could be used if necessary.…

AIM: To Write a function that extracts the 14 co-efficients and calculates the enthalpy, entropy and specific heats for all the species in the data file. To Calculate the molecular weight of each species and to display it in the command window. To Plot the Cp, Enthalpy and Entropy for the local temperature range specific…

AIM: Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function. SOLUTION: Genetic Alogorithm: Genetic algorithm is the way of developing the different random solutions at first and takes the random samples as the parents for the new genration and develops…

AIM: Write a MatLab code to fit a linear and cubic polynomial for the given Cp data and Plot the linear and cubic fit curves along with the raw data points.    SOLUTION: What is Curve Fitting ? Curve fitting is the process of constructing a curve, or mathematical functions, which possess the closest…

AIM: Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm SOLUTION: Coding: %Initial Values length1=1; length2=0.5; %Assigning theta values theta1=linspace(0,90,10); theta2=linspace(0,90,10); %Calculating count=1; for i=1:length(theta1) o1=theta1(i); for j=1:length(theta2) o2=theta2(j);…

AIM: Write a MatLab program to simulate the transient behaviour of a simple                                 pendulum and to create an animation of it\'s motion. SOLUTION: Coding: Main program %Given values b=0.05; %damping coefficient…

AIM: write a MatLab code that can solve an otto cycle and make pv diagram. SOLUTION: Coding: %Given %Engine geometric parameters bore=0.1; stroke=0.1; connecting_rod_length=0.15; cr=12; %Compression ratio %Given state variables p1=101325; t1=500; t3=2300; gamma=1.4; %Find v1,v2,v3,v4 and p1,p2,p3,p4 and draw PV diagram…