EXAMPLE 4.3. A newtonian fluid is confined between two broad parallel vertical plates, separated by a distance B, as shown in Fig. 4.5. The plate on the left is stationary; that on the right is moving vertically upward at a constant velocity vo. Assuming that the flow is laminar, find the equation for the steady-state velocity pro- file in the fluid. Solution. Use the Navier-Stokes equation for the y coordinate, Eq. (4.30). At steady state av/at = 0 and flow is in the y direction only. Hence the velocities u and z are both zero. From the continuity equation [Eq. (4.6)], au/ay = 0. Also, av/z = 0 and 80 SECTION II: Fluid Mechanics TAND Vo FIGURE 4.5 Flow between vertical plates in Example 4.3.