Problem$2$

In preparation for a polymerization process, a tank of volume $($V$)$ and cross sectional area $($A$)$

is fed through a horizontal pipeline at a constant mass flow rate $m_{in}^{}.$ To adjust the level of

the fluid in the tank, a valve located at the bottom of the tank allows to control the outflow;

$m_{\text{o}\text{u}\text{t}}^{},$ also assumed to be constant.

$($a$)$ Write a balance equation to derive a general expression for the variation of the fluid

height, knowing that it is initially $(h_0).$ Assume the fluid to be incompressible.

$($b$)$ What should be the discharge volumetric flow rate if we want the tank to fill in exactly

one hour? The following information is given: $A=1m^2,h_0=0\mathrm{.}2m,$ total height of the tank is

$H=2m$ and the inlet flow from the pipe is $1\frac{l}{s}.$

$($c$)$ What is the shortest time to fill completely the tank which was initially empty while

ensuring that the flow in the pipe remains laminar? The following information is supplied:

$A=1m^2,H=2m,q_{\text{o}\text{u}\text{t}}=0\mathrm{.}5\frac{m^3}{h}.$ The pipe cross sectional area is $a=0\mathrm{.}04m$ and the kinematic

viscosity of the fluid is $v={10}^{-6}\frac{m^2}{s}.$ Give me the proper solution as their are two solution already on the chegg but i need the proper and step by step solution.