In an irrotational region of flow, we write the velocity

Chapter 10, Problem 48P

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Problem 48P

In an irrotational region of flow, we write the velocity vector as the gradient of the scalar velocity potential function, . The components of  in cylindrical coordinates. (r, θ, z) and (u r, uθ, 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.

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