Question

Two horizontal plates with infinite length and width are separated by a distance H in the zdirection. The bottom plate is moving at a velocity vx=U. The incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. Align gravity with positive z. Assume that the flow is fully-developed and laminar. If the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following:

1. Sketch your system.
2. Identify the coordinate system to be used.
3. Show your coordinates and origin point on the sketch.
4. List all your assumptions.
5. Apply the continuity equation to your system.
6. Apply the 3-components of Navier Stokes equations of choice to your system.
7. Solve the resulting differential equation to obtain the velocity profile within the system Make sure to list your Boundary conditions. Check units of velocity.
8. Describe the velocity profile you obtain using engineering terminology. Sketch that on the same sketch you provided in (1).
9. Obtain the equation that describes the volumetric flow rate in the system. Check the units.

Answer 1