(b) Find the rate of change of depth of water in a rectangular channel of 10 m wide and 1.5 m deep, when the water is flowing with a velocity of $1 \mathrm{~m} / \mathrm{s}$. The flow of water through the channel of bed slope 1 in 4000 is regulated in such a way that energy line is having a slope of 0.00004 .
Explanation
The rate of change of depth of water is calculated using the equation: dh/dt = (1 / A) * (Q - q) where A is the cross-sectional area of the channel, Q is the discharge, and q is the seepage discharge. The seepage discharge is given by the equation: q = k * A * (h - h0) where k is the seepage coefficient, h is the water depth, and h0 is the water depth at the downstream end.
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