# Thread: Velocity potential for two-dimensional flow

1. ## Velocity potential for two-dimensional flow

A velocity potential for two-dimensional flow of an inviscid fluid around the outside of the circular cylinder $x^2+y^2=a^2$ is $\phi$(x,y)= Ux(1+ $a^2/(x^2+y^2$)), where U and a are constants.

(a) calculate the corresponding velocity field u= $\bigtriangledown$ $\phi$

(b) what is the velocity in the limit as you move far away from the cylinder?

(c) Hence, what velocity potentil describes this flow with the cylinder removed?

(d)show there are two stagnation points on the cylinder where the fluid is at rest.

(e) show that nofluid penetrates the cylinder wall by demonstrating that the normal velocity component u $\cdot$n vanishes on the cylinder surface, where n=(x/a,y/a) is a unit normal vector to the cylinder surface.