A uniform stream of speed in the -plane

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Potential flow, conformal mapping and the finite wing

Problem

A uniform stream of speed U=4.0 m s−1U = 4.0\,\mathrm{m\,s^{-1}} in the ZZ-plane, with complex potential W=UZW = UZ, is mapped by ζ=(ℓZ)1/2\zeta = (\ell Z)^{1/2}, with ℓ=1.0 m\ell = 1.0\,\mathrm{m}, into flow inside a right-angled corner in the ζ\zeta-plane. ((a)) Find the speed of the fluid at the point ζ=2+2i\zeta = 2 + 2i (metres) in the corner flow. ((b)) State how the speed there varies with distance r=∣ζ∣r = |\zeta| from the corner, and check your answer to part (a) against this.

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