Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes

In this lecture, we’ll derive the velocity distribution for two examples of laminar flow. First we’ll consider a wide river, by which we mean wide compared with its depth (which we take to be uniform) and we ignore the more complicated flow pattern near the banks. Our second example is smooth flow down a circular pipe. For the wide river, the water flow can be thought of as being in horizontal “sheets”, so all the water at the same depth is moving at the same velocity.
galileo.phys.virginia.edu