D$.15\mathrm{.}6$ deg C SAE $30$ flows in a $20$ cm wide channel. To analyze the flow, let's make the channel midline $y=0$ :

The vertical axis is the $y-$axis. One wall is at $y=+10cm,$ the other at $y=-10cm.$ The fluid flow profile at any $x$ is given by

$u(y)=10-0\mathrm{.}1(y^2)$ where $u$ is in meters$/$sec and $y$ is in centimeters.

i$.$ Determine the fluid velocity $($magnitude and direction$)5$ cm from the upper wall and $5$ cm from the lower wall.

ii$.$ Graph the velocity profiles at $x=1m$ and $x=4m.$

iii. Determine the fluid velocity gradient $($ie$.$ du$/$dy$)$ at the lower wall, the channel midline and at the upper wall.

Answer in $\frac{m}{sec}$ per cm and in $se{c}^{-1}.$

iv$.$ Determine the magnitude and the direction of the shear of $*$the fluid on the lower wall $*$the lower wall on the

adjacent fluid $,**$ the fluid on the upper wall $,**$ the upper wall on the adjacent fluid.