$($a$)$ Consider two parallel plates separated by a distance $h,$ with a fluid of viscosity

$$ between the plates. Derive an expression for the damping constant when one plate

moves with a velocity $v$ relative to the other as shown in Fig. $(1\mathrm{.}10$a$).(5$ Marks$)$

$($b$)$ A bearing, which can be approximated as two flat plates separated by a thin film

of lubricant $($Fig$.1\mathrm{.}10$b$),$ is found to offer a resistance of $400$ N when SAE $30$ oil is used

as the lubricant and the relative velocity between the plates is $10\frac{m}{s}.$ If the area of

the plates $(A)$ is $0\mathrm{.}1m^2,$ determine the clearance between the plates. Assume the

absolute viscosity of SAE $30$ oil as $50$ ureyn or $0\mathrm{.}3445$ Pa$-$s$.(5$ Marks$)$