Q. Velocity distribution and flow formulae?

Variation in velocity along a vertical in channel cross section is known to follow logarithmic distribution, maximum velocity being at the top and minimum at the bottom. Mean velocity is obtained at 0.632 depth from top. Average of velocities measured at 0.2 and 0.8 depths from top also gives the mean velocity. The velocity distribution along a vertical depends on depth and relative roughness of bed material. If bottom roughness is increased, the bottom velocity is decreased and top velocity correspondingly increased.