Velocity distribution in a rectangular channel, Physics

An approximate equation for the velocity distribution in a rectangular channel with turbulent flow is

1758_velocity distribution in a rectangular channel.png

where umax is the velocity at the surface, y is the distance from the floor of the channel, d is the depth of flow, and n is an exponent. Derive a formula for α as a function of n. What is the value of α for n = 1/7 (typical for turbulent flows)?

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