Show the differentiation of the maximum flow rate


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Q: Given is the flow of a channel of large width b under a sluice gate, as in Fig. Assuming frictionless steady flow with negligible upstream kinetic energy, derive a formula for the dimensionless flow ratio 2 3 2 Q /(y1b g) as a function of the ratio y2/y1.
Show by differentiation that the maximum flow rate occurs at y2 = 2y1/3.

2249_Flow of channel.jpg

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Mechanical Engineering: Show the differentiation of the maximum flow rate
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