A certain tank contains water whose mass density is 1.94

Chapter , Problem 7.36

(choose chapter or problem)

A certain tank contains water whose mass density is \(1.94 \ \mathrm{slug} / \mathrm{ft}^{3}\). The tank’s circular bottom area is \(A=100 \ \mathrm{ft}^{2}\). It is drained by an orifice in the bottom. The effective cross-sectional area of the orifice is \(C_{d} A_{o}=0.5 \ \mathrm{ft}^{2}\). A pipe dumps water into the tank at the volume flow rate \(q_{v}\).

a. Derive the model for the tank’s height h with the input \(q_{v}\).

b. Compute the steady-state height if the input flow rate is \(q_{v}=5 \ \mathrm{ft}^{3} / \mathrm{sec}\).

c. Estimate the tank’s time constant when the height is near the steady-state height.