Substitute the components of the velocity vector given in Prob. 10–66 into the Laplace equation in cylindrical coordinates. Showing all your algebra, verify that the Laplace equation is valid in an irrotational region of flow.

Data from Problem 66

In an irrotational region of flow, we write the velocity vector as the gradient of the scalar velocity potential function,

V(vector) in cylindrical coordinates, (r, u, z) and (u_r, u_θ, u_z), are

From Chap. 9, we also write the components of the vorticity vector in cylindrical coordinates as

Substitute the velocity components into the vorticity components to show that all three components of the vorticity vector are indeed zero in an irrotational region of flow.

Transcribed Image Text:

V = Vo.