Consider a fully developed turbulent couette flow in a channel between two infinitely long and wide parallel plane walls. The distance between the wall is 2, the lower wall is at rest and the upper wall moves with a velocity in its own plane. Assume the flow consists of two layers which match at the centreline of the channel. Find an expression for the friction coefficient at the lower wall ( = 2 2 2 , where is the mean velocity at the centreline) in terms of the appropriate reynolds number. Estimate the additive constant in the velocity profile by assuming that near the wall, there exist "viscous sublayers" in which the reynolds number is so small that the reynolds stress is negligible. The thickness of these sublayers is equal to 10 . Sketch the profile in the channel
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