Problem #$8$

Couette flow corresponds to viscous flow between $2$ parallel plates $($Fig$.1),$ where the top plate is

moving at a velocity $U$ and the bottom plate is at rest. Given the velocity profile of Couette flow

is linearly dependent on the gap between plates $h$ :

$u(y)=\frac{Uy}{h}$

determine the average velocity Bar $(u)$ in terms of $U,$ where:

Bar $(u)=\frac{1}{h}{\displaystyle \underset{0}{\overset{h}{}}}u(y)dy$

Figure $1.$ Couette flow between $2$ parallel plates.

Problem #$9$

For problem #$8,$ determine the dynamic viscosity of fluid between the plates $($in units of

slug$/$ft$.$sec$),$ given shear stress $=0\mathrm{.}1l\frac{b}{f}{t}^2,h=1in,$ and velocity $U=10f\frac{t}{sec}.$