(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Develop a source-panel computer program to numerically calculate the potential flow pressure distribution on a right circular cylinder with and without circulation.

1.) Tabulate and plot your numerical results for the pressure coefficient distribution on the cylinder together with the corresponding exact analytic solution as a function of the angular variable omega, measured clockwise from the negative x-axis to the center of panels, from 0-360 degrees. Tabulate the following results:

i, omega, q, numerical Cp, theoretical Cp, % error.

2.) Do your calculations for the following values of circulation: K =[itex]\Gamma/\left(2\pi\right)[/itex] = 0, -1, -2, and -3. For K=0 do your calculations for N=4 and 250. For all other values of K, use only N=250.

2. Relevant equations

w=omega

Theoretical C_{p}=1-4*sin(w)^2

w=(360/N)(i-0.5)

θ_{i}= ARCtan((y_{i+1}-y_{i})/(x_{i+1}-x_{i}))

ζ_{i}=0.5(x_{i}+x_{i+1})

η_{i}=0.5(y_{i}+y_{i+1})

y_{i}=sin(w_{i})

x_{i}=cos(w_{i})

U_{0}sin(θ_{i}- α) =(q_{i})/2 - SUM^{N}_{j=1}q_{j}c_{ij}j does NOT equal i

c_{ij}=sin(θ_{i}-[itex]\Phi[/itex]_{ij})/2[itex]\pi[/itex]r_{ij}ΔS

rij=[(ζ_{i}-ζ_{j})^{2}+(η_{i}-η_{j})^{2}]^{1/2}

[itex]\Phi_{ij}[/itex]=ARCtan(η_{j}-η_{i})/(ζ_{j}-ζ_{i})

Sorry but I am making some mistake with the complex symbol program on this forum.

3. The attempt at a solution

I have calculated i, ω_{i}, η_{i}, ζ_{i}, x_{i}, y_{i}, θ_{i}for N=250. I can't find the j components of those needed.

Also I'm having trouble finding out the length of each panel. If a square was inside the unit circle, each length would be 1.414 right? But N=250 not 4.

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# Source Panel method for flow pressure distribution over cylinder

Can you offer guidance or do you also need help?

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