Response to the following problem:
A cylindrical storage tank of diameter D contains a liquid at depth (or head) h(x, t). Liquid is supplied to the tank at a rate of qi (m3/day) and drained at a rate of q0 (m3/day). Use the principle of conservation of mass to arrive at the governing equation of the flow problem.
sol:
The conservation of mass requires
Time rate of change in mass = mass inflow - mass outflow
The above equation for the problem at hand becomes
d/dt(pAh) = pqi - pq0 or d(Ah)/dt = qi - q0
where A is the area of cross section of the tank (A = πD2/4) and ρ is the mass density of the liquid.