A certain tank contains water whose mass density is 1.94 slug/ft3. The tank's circular bottom area is A = 100 ft2. It is drained by an orifice in the bottom. The effective cross-sectional area of the orifice is CdAo = 0.5 ft2. A pipe dumps water into the tank at the volume flow rate qv.
a. Derive the model for the tank's height h with the input qv.
b. Compute the steady-state height if the input flow rate is qv = 5 ft3/sec.
c. Estimate the tank's time constant when the height is near the steady-state