Homework 3 Solution

# Homework 3 Solution - MAE 3241 AERODYNAMICS AND FLIGHT...

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MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Homework #4 Solution: Questions (1) – (4) Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

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2 QUESTION 1: SAMPLE MATLAB SCRIPT close all; clear all; % Question 1 a=1; lambda=1; [x,y]=meshgrid(-5:0.01:5,-5:0.01:5); psi=lambda./2./pi.*atan(2.*x.*y./(x.^2-y.^2+a.^2)); % Now I am going to set some fixed values of the streamfunction psi to % plot. I am setting up a vector V which will range from the minimum value % of psi to the maximum value. I use the double command min(min(psi)) since % psi is two-dimensional, and the first min will find the minimum row and % the second the minimum of that row, or a single value. Same idea with % max(max(psi)). Since I wanted to plot 10+1 values of constant psi, I % arranged them to be equally spaced between the minimum and maximum value. V=[min(min(psi)):(max(max(psi))-min(min(psi)))/10:max(max(psi))]; cs=contour(x,y,psi,V); % Note the use of the contour function here. To use the streamline command we could have % found the the u and v components of the velocity, which would have added some complexity % to this problem. Since we are only interested in sketching some of the streamlines, % I simply plotted a constant values of psi without any regard for the exact values. % Note that this would involve iteration to solve the resulting equation for either x or y given % a constant value of psi. xlabel('x-direction'); ylabel('y-direction'); title('Homework #4: Question 1'); grid; % clabel(cs,V); % If you uncomment the above line, MATLAB will label all the contours for % you as well. It is a little messy so use the zooming tool to see what is % really going on, especially in Quesiton #2.
3 QUESTION 1: STREAMLINE PLOT Find the stream function and plot some streamlines for the combination of a line source, Λ , at (x,y)=(0,a) and an equal line source located at (0,-a)

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