Find the stagnation points of the fluid of where the complex velocity potential is given by w :

Question

w = A + Bi = m*ln(z-a) - m*ln(z+a) - u*z , where z = x+ iy = r*(e^(i*theta))

Here A= velocity
potential and B=stream function of the 2-D flow

So to find stagnation points I need to seperate A, B values or could someone help me with any way to find the stagnation points?

Thank you!

Answer 1

Don't you need f'(z) = 0?
Is u a constant? If so, then
df/dz = m/(z-a) - m/(z+a) - u
df/dz=0 when m-u(z^2-a^2) = 0 and z^2-a^2 ≠ 0

Answer 2

Yes, u and a are real valued constants. Thank you very much for the explanation!