Consider the turbulent flow in a rectangular duct. Assume that turbulence is fully developed,  only. The flow is driven by a mean pressure gradient in the stream wise direction, which is a function of...

Consider the turbulent flow in a rectangular duct. Assume that turbulence is fully developed,
 only. The flow is driven by a mean pressure gradient in the stream wise direction, which is a function of the turbulent fluctuations in both the stream wise and transverse directions. Develop an expression for the total mean stress distribution across the channel.