A large cylindrical tank of constant cross-sectional area drains through a small orifice at its bottom. Neglect viscosity. Which statement correctly describes the motion of the free surface while the tank empties?
Options

Question

A large cylindrical tank of constant cross-sectional area drains through a small orifice at its bottom. Neglect viscosity. Which statement correctly describes the motion of the free surface while the tank empties?

Options

G1 Physics · Accepted Answer

At water depth h above the hole, Torricelli's theorem gives v = √(2gh). The volume-flow rate through the hole is Q = av = a√(2gh). For a tank of constant cross-sectional area A, −A dh/dt = a√(2gh). Therefore, |dh/dt| ∝ √h. As h decreases, √h decreases. Hence the free surface falls more slowly as the tank becomes empty. Correct option: C.