An incompressible viscous fluid is placed between two large parallel plates as shown in...

An incompressible viscous fluid is placed between two large parallel plates as shown in Fig. P6.7. The bottom plate is fixed and the upper plate moves with a constant velocity, U. For these conditions the velocity distribution between the plates is linear and can be expressed as

Determine (a) the volumetric dilatation rate, (b) the rotation vector, (c) the vorticity, and (d) the rate of angular deformation.