4. Incompressible newtonian fluid with constant density and viscosity flows between two parallel plates with infinite width. Body forces are neglected. Given are the plate height h and the components...

4. Incompressible newtonian fluid with constant density and viscosity

flows between two parallel plates with infinite width. Body forces are

neglected. Given are the plate height h and the components of the pressure

gradient:

and the velocity field between the plates is given by:

1. Show that the given velocity field satisfies the continuity and the

Navier-Stokes equations.

2. Determine the components of the stress tensor.

3. Calculate the dissipation function Φ.

4. Find the energy per unit depth, length, and time dissipated in heat

within the gap.

5. Calculate the principal stresses and their directions.