To deliver medications to the stenosis area with a specific pressure to disrupt the lesion, a

tubular catheter connected to a two parallel plate is inserted into a blood vessel. The

medication is dispensed from the narrow tube catheter $($radios $R)$ with a known flow rate of

$Q$ to the space between two parallel plates. The gap between the plates $($h$)$ is sufficiently

large to neglect shear stress, resulting in liquid velocity being independent of the gap size

and denoted as $V=V(x,y).$ If we assume that $V_x=\frac{1}{x}$ for the liquid's velocity component in

the $x$ direction at the distance between the plates $($where $x>R),$ this holds true.

Please use the general mass and momentum balance equations to:

a$)$ Extract the mass and momentum balance equations governing liquid flow between the

plates

b$)$ Obtain $V_y$ and $V(x,y)$

c$)$ Obtain the equation for pressure $P(x,y)$ at the distance between plates