Hydraulics and Fluid Mechanics in ME
The discharge through a channel of trapezoidal section is maximum when

The sloping side is equal to the width at the bottom
Width of channel at the top is equal to twice the width at the bottom
The sloping side is equal to half the width at the top
Depth of channel is equal to the width at the bottom

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Hydraulics and Fluid Mechanics in ME
The discharge over a rectangular weir, considering the velocity of approach, is (whereH1 = H + Ha = Total height of water above the weir, H = Height of water over the crest of the weir, and Ha = Height of water due to velocity of approach)

(2/3) Cd × L.√2g [H12 - Ha2]
(2/3) Cd × L. √2g [H13/2 - Ha3/2]
(2/3) Cd × L. √2g [H15/2 - Ha5/2]
(2/3) Cd × L.√2g [H1 - Ha]

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Hydraulics and Fluid Mechanics in ME
For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal

ratio of inertial force to force due to gravitation
ratio of inertial force to force due to surface tension
all the four ratios of inertial force to force due to viscosity, gravitation, surface tension, and elasticity
ratio of inertial force to force due to viscosity

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