Mathematical Methods in the Physical Sciences · Problem 10.2

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · fluid-flow-irrotational

Problem

A fluid flow is called irrotational if V×V=0\mathbf{V} \times \mathbf{V} = 0 where V=\mathbf{V} = velocity of fluid (Chapter 6, Section 11); then V=∇Φ\mathbf{V} = \nabla\Phi. Use Problem 10.15 of Chapter 6 to show that if the fluid is incompressible, then Φ\Phi satisfies Laplace's equation. (Caution: In Chapter 6, we used V=vρ\mathbf{V} = v\rho, with vv = velocity; here V\mathbf{V} = velocity.)

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