PRoblem $[3$ Points$]$ Given the following velocity profile for air discharging from a rectangular orifice

of width $1\mathrm{.}5m$ and height $3m.$ If $U_{\text{m}\text{a}\text{x}}=8\frac{m}{s}$ and $U_{\text{m}\text{i}\text{n}}=3\mathrm{.}5\frac{m}{s}.$ The profile only varies in

the $y-$direction $({}_{\text{a}\text{i}\text{r}}=1\mathrm{.}2\frac{kg}{m^3}).$ Assuming this velocity is the only flow in the $x-$direction and no

other relevant forces are at play, calculate the rate of linear momentum crossing the orifice in

$kg\frac{m}{s^2}.$

Momentum rate through a $CS={\displaystyle \underset{cs}{\overset{\phantom{}}{}}}V(V*hat(n))dA={\displaystyle \underset{y_1}{\overset{y_2}{}}}u[ucos()]Wdy$