Answer/Explanation:
In a cylindrical coordinates,
The components of the velocity field are given by:
Vr = (1/r)partial derivative of ψ with respect to θ = -U cos θ + q/(2πr)
Vθ = - partial derivative of ψ with respect to r = U sin θ
At stagnation points, the magnitude of velocity is equal to zero /V/ = 0, which means the each velocity components is equal to zero.
- U cos θ + q/2πr = 0
U sin θ = 0
Since θ E [0, 2π]
-U + q/2πr = 0, since cos 0 = 1
Therefore, q/2πr = U, and the r coordinate of the stagnation is given by r = q/2πU
Putting θ = 0 and r = q/2πU into the stream function, we obtain
ψ(r, θ) = -Ur sin θ + qθ/2π = -0 + 0 = 0