Answer to Question #281391 in Chemical Engineering for alireza naji

Question

The water problem flows at a constant mass flow rate of 7 kg / s into a vertical cylindrical tank. Water is discharged near the base of the tank at a mass flow rate proportional to the height of the liquid in the tank, ime = 14 kg / s, where L is the instantaneous height of the liquid, in m. The base area of ​​the circle is 0.2 m2. Water density is constant at 1000 kg / m3. If the tank is empty at first, determine the change in liquid height over time.

Answer 1

d($\rho$ AL)/dt = 7 - 14L

the solution yields;

L = -7 + C.exp (-14L/$\rho$ A)