Homework 8 Solution Manual
A) 5 points
Figure 1
As can be seen in Fig.1, if less than 40 panels are used, the maximum velocity (and velocity at
maximum thickness) depends on number of panels used. The maximum velocity is highest when
seven panels are used and oscillates slightly between seven and 40 panels. After 40 panels, the
maximum velocity remains constant at approximately 1.15. Therefore all computations should be
done with at least 40 panels. Matlab code for this part is presented in Fig2 and 3.
i = 0;
for
N = 1:100
i = i+1;
mid = int16(N/4+1)
S = ellipse_examp (N)
Smax(i) = max (S)
Smid(i) = S(mid)
end
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View Full Documentplot (1:100, Smax)
title (
'Max Velocity vs Number of Panels'
)
xlabel(
'Number of Panels'
)
ylabel(
'Max Velocity'
)
Figure 2. MATLAB CODE for part A
function
[Speed] = ellipse_examp (N)
% example
% % flow over an ellipse
ep = .15;
% thickness/chord of ellipse
%N=50;
th=linspace(0,2*pi,N+1);
x=cos(th);
y=ep*sin(th);
NOTHING ELSE WAS CHANGED IN THE PROVIDED CODE
Figure 3: Ellipse code turned into a function.
No real changes were made to the ellipse code.
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 Fall '09
 matlab, Numerical Analysis, DNA, Max Analytical

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