Complex Analysis: Theory and Applications · Problem 10.7.3

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · fluid-flow-hyperbolic-channel

Problem

Consider the ideal fluid flow in the channel bounded by the hyperbolas xy=1xy = 1 and xy=4xy = 4 in the first quadrant, where the complex potential is given by F(z)=A2z2F(z) = \frac{A}{2}z^2 and AA is a positive real number. (a) Find the speed at each point, and find the point on the boundary at which the speed attains a minimum value. (b) Where is the pressure greatest?

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