The velocity profile for flow between two flat plates is

$u=-\frac{dp}{dx}\frac{h^2}{2}(1-\frac{y^2}{h^2})$

where the distance between plates is $"2$ h$,"$ and the origin of the coordinate system is placed right in the middle $($see the following figure$).$

Fixed

$($a$)$ Find shear stress as a function of $y.$ Suppose the pressure gradient in the x $-$direction is $5\frac{Pa}{m},$ the distance between two flat plates is $10$ cm $,$ and the working fluid is water at $20C.$ Draw the shear stress profile between flat plates.

$($b$)$ Where does the maximum shear stress occur $($middle or at the walls$)?$ Why?

$($c$)$ How does the shear stress profile change with the distance between two flat plates? Hint: Does shear stress increase if we increase $"h"?$

$($d$)$ Discuss the effect of viscosity on the shear stress profile found in part $($a$).$