When the force $P$ is applied to the plate, the velocity profile for a Newtonian fluid that is confined under the plate is approximated by $u=(12y^{\frac{1}{4}})m\frac{m}{s},$ where $y$ is in mm $.$ Determine the shear stress within the fluid at $y=8mm.$ Take $=0\mathrm{.}5({10}^{-3})N*\frac{s}{m^2}.$

$1-34.$ The velocity profile for a thin film of a Newtonian fluid that is confined between the plate and a fixed surface is defined by $u=(10y-0\mathrm{.}25y^2)m\frac{m}{s}$ where $y$ is in mm$.$ Determine the force $P$ that must be applied to the plate to cause this motion. The plate has a surface area of $5000m{m}^2$ in contact with the fluid. Take $=0\mathrm{.}532N*\frac{s}{m^2}.$