Answer Happy

A viscous oil with density p and viscosity p is forced into the gap h() between a fixed block and a wall moving at velocity U. If the gap is thin, h > L, we can assume that the pressure only varies in x and the flow is 2-dimensional (v = 0). Neglecting gravity, reduce the Navier-Stokes equations to a single differential equation for uly). State your boundary conditions, and integrate to show that 1 dp uy) (i? – yh) +U(1 - (5) 2u da h h=h(x) being the gap width that varies slowly in . Remember to state all assumptions you make, and how do those assumptions crosses out the terms in the Navier-Stokes equation. Oil inlet Fixed slipper block Oil outlet ho h(x) u(y) U Moving wall