A rectangular tank with dimensions of width and depth equal to $L($see figure$)$ is initially filled with an incompressible fluid of density $$ and viscosity $$ up to a height of $H_0.$ The top of the tank is open to the atmosphere. At the bottom, the tank is connected to a circular pipe of length $l$ and radius $R.$ The fluid flows through the pipe and exits to the atmosphere. The acceleration of gravity is $g.$

a$.$ Find the expression for the height $h(t)$ of the fluid in the tank as a function of time. Assume steady, laminar, fully developed flow in the pipe. $[15$ pts$]$

b$.$ After how long will the tank empty? Can you explain your result? $[5$ pts$]$