Laminar Viscous Flow Between $2$ horizontal Plates $($section $6\mathrm{.}9\mathrm{.}1).$ SAE $30$ Engine oil flows steadily through a thin channel of width $8$ cm ; the oil's velocity is given by

vec$(V)(x,y)=(16-10,000y^2)hat()+0j$ meter$\frac{s}{sec\text{f}\text{o}\text{r}x}0,-0\mathrm{.}04my0\mathrm{.}04m$

where $x$ is the displacement along the channel length from some initial position and $y$ is the displacement from the channel midline $($which is at $y=0).$

a$)$ Graph the velocity profiles at $x=1m$ and at $x=4m($better if both profiles on same diagram$).$

b$)$ Complete the following chart for oil moving in the channel:

$\backslash$table$[[y(cm),$del$\frac{u}{d}$elx,del$\frac{u}{d}$ely,del$\frac{v}{d}$elx,del$\frac{v}{d}$ely