Source Panel method for flow pressure distribution over cylinder

[frozenguy]

Homework Statement

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 =$\Gamma/\left(2\pi\right)$ = 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.

Homework 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)

U₀sin(θ_i - α) =(q_i)/2 - SUM^{N}_{j=1}q_jc_ij j does NOT equal i
c_ij=sin(θ_i-$\Phi$_ij)/2$\pi$r_ijΔS
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.

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.

 

[LightHero]

So this would be wrong. I'm also having trouble understanding the U0sin(θi-α) part. I've been stuck on this problem for a while. Any help would be much appreciated.