In preparation for a polymerization process atank of volume $($V$)$ and cross sectional area $($A$)$is fed through a horizontal pipeline at a constant mass flow rate Min$*$ To adiust the level ofthe fluid U the tank, a valve located at the bottom of the tank allows to control the outflow;Tiout' also pawunsseto be constant.$($a$)$ Write a balance equation to derive a general expression for the variation of the fluidheight, knowing that itis initily $($ho$).$Assume the fluid to be incompressible$($b$)$ What: should be the discharge volumetric flow rate if wewant the tank to fill in exactlyone hour? The following information is given: A$=1$m$^2,$ h$\_0-=0\mathrm{.}2$m$,$ total height of the tank isH$=2$m and the inlet flow from the pipe is $11/$s$.($c$)$ What is the shortest time to fill completely the tank whichwas initially empty whileensuring that the flow in the pipe remains laminar? The following information is supplied:A$=1$m$^2$ H$=2$m$,$ Gout$=0\mathrm{.}5$ m$^3/$h$.$ The pipe Cross sectionalarea is a$=0.04$m and the kinematicviscosity of the fluid lisv$=10-6$m $/$s