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For a most economical trapezoidal section with side slope of (n) horizontally to (1) vertically, the conditions of maximum discharge are:
~ Sloping side must be equal to to half the top width.
ie d(n^2 + 1)^1/2 = (b + 2nd)/2
~ The hydraulic mean depth (R) = Half the channel depth. ie R= d/2.
The basis for this is that discharge (Q) will be maximum when the wetted Perimeter (P) is minimum. And for minimum perimeter, dp/dd =0.
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