Derive or lookup the relationship between the maximum flow velocity and mean flow velocity for a 1/p power-law velocity profile for a flow of depth d with a free surface in a wide rectangular channel (i.e. ignore side walls), u/U=(y/d)^(1/p), where U is the maximum velocity at the surface. To do this, integrate u to find the discharge and then divide by the depth to find the mean as usual. For p=7, sketch or plot, approximately to scale, the normalized velocity profile, u(y)/U, as a function of y/, where U=u() is the maximum velocity, u is the local velocity, y is distance from the boundary, and is the boundary layer thickness or water depth. What does this suggest if you want to measure the details of the velocity profile