An incompressible viscous fluid is placed between two large parallel plates as shown in Fig. P6.8. 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

\[ u=U \frac{y}{b} \]

Determine:

(a) the volumetric dilatation rate,

(b) the rotation vector,

(c) the vorticity, 

(d) the rate of angular deformation.

Figure P6.8

b U Moving plate Fixed plate