Problem $3(30$ points$)$

The velocity distribution for the flow of crude oil at $40C(=0\mathrm{.}06(N).\frac{s}{m^2})$ between two parallel

plates is given by $u(y)=4y(0\mathrm{.}04-y)\frac{m}{s},$ where $y=0$ at the bottom plate surface and $y=B$ at the

top plate surface $($measured in meters$).$ The distance between the plate surfaces $($adjacent to the

fluid$)$ is $B=0\mathrm{.}04m.$ Determine the shear stress at the surfaces of both plates. Draw a qualitative

plot showing the velocity distribution $u(y)$ vs $y.$