Problem 1: In actual membrane filtration systems, the transmembrane flow is very small compared to the streamwise flow (i.e. the flow in the x-direction). Suppose we argue the streamwise velocity scales

like u~ Uo, and that the velocity field varies over the characteristic length h in the y-direction. We wish now to find a characteristic velocity in the y-direction and a characteristic length over which the velocity field varies in the streamwise x-direction. Use the continuity equation to argue that h ~, where € = V/U₁ is a small number, y~h, y~h, u~ Uo, v~ €Uo, i.e. € < 1. (3)