Problem #$2$

A two$-$dimensional channel $($width $H)$ has a slot $($width $h)$ as shown in Fig. $2.$ Incompressible fluid $($density $)$ is injected through the slot at an angle $$ relative to the horizontal. Body forces can be neglected. Velocity and pressure can be assumed as uniform across the channel.

$($a$)$ Derive an equation for mass conservation.

$($b$)$ Derive an equation for conservation of $x-$momentum.