A flow of water in the horizontal xy-plane (no gravity effects) is described by the stream function
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Question:
A flow of water in the horizontal xy-plane (no gravity effects) is described by the stream function ψ = Axy, with A > 0 a constant
(a) Find both velocity components u and v.
(b) Does a velocity potential φ exist (for certain A or for arbitrary A)? If so, determine it.
(c) Assume that φ exists for A = 2 s−1. We now want to describe how the flow changes when we introduce an impenetrable wall at x = −1 m (). Show that by superimposing a uniform flow of speed U to the given flow you can indeed make x = −1 m a streamline. How large must U be?
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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