Problem on turbulent flow, The approximate equation for the velocity distribution in a

Problem on turbulent flow

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

655_turbulent flow.jpg

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

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The approximate equation for the velocity distribution in a rectangular channel with the turbulent flow is 655_turbulent flow.jpg

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