Problem $5$

The velocity distribution over$\_$a plate is given by $u(y)=ay-$by ${?}^2.$ Here, $u$ is the velocity in $\frac{m}{s}$ at a distance y meter above the plate. a & b are constants. $$ is the dynamic viscosity of the fluid.

a$)$ Obtain a relation for the wall stress in terms of $a,b$&$.$

b$)$ If $a=\frac{4}{5},b=2$& dynamic viscosity of the fluid is $9$ poises, determine the shear stress at $y=0m$ and $y=0\mathrm{.}3m.$

Answer is: $0\mathrm{.}72$ N$/$m$^2,0\mathrm{.}2$ N$/$m$^2$