A viscous fluid $($specific weight $=80l\frac{b}{f}{t}^3$; viscosity $=0\mathrm{.}03lb*\frac{s}{f}{t}^2)$ is contained between two infinite, horizontal parallel plates as shown in the figure below. The fluid moves between the plates under the action of a pressure gradient, and the upper plate moves with a velocity $U$ while the bottom plate is fixed. A $U-$tube manometer connected between two points along the bottom indicates a differential reading of $0\mathrm{.}1$ in $.$ If the upper plate moves with a velocity of $0\mathrm{.}02f\frac{t}{s},$ at what distance from the bottom plate does the maximum velocity in the gap between the two plates occur? Assume laminar flow.

$y_m=$

$$ in$.$