Halliday, Resnick & Walker — Fluids: Problem Problem_56

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2. (a) What is the ratio \(\rho_1/\rho_2\) of the densities of the liquids if the mass flow rate is the same for the two holes? (b) What is the ratio \(R_{V1}/R_{V2}\) of the volume flow rates from the two tanks? (c) At one instant, the liquid in tank 1 is 12.0 cm above the hole. If the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?