A wide channel carries per unit width at a subcritical depth of

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Long waves of finite height: bores, jumps and solitary waves

Problem

A wide channel carries

q = 2.0\,\mathrm{m^2\,s^{-1}}

per unit width at a subcritical depth of

1.2\,\mathrm{m}

. A smooth bump of height

b = 0.30\,\mathrm{m}

is built across the bed. ((a)) Decide whether the bump chokes the flow at this depth, by comparing

b

with the headroom

E - E_{\min}

. ((b)) If it does, find the upstream depth once the flow has backed up far enough for the bump to be just passed. ((c)) Find the depth over the crest of the bump in that state.

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