Three identical vessels A, B and C are filled with water, mercury and kerosene respectively up to an equal height. The three vessels are provided with identical taps at the bottom of the vessels. If the three taps are opened simultaneously, then which vessel is emptied first?

The correct answer is Option 1 (Vessel B). This phenomenon is explained by Torricelli’s Law and the principles of fluid dynamics.

According to Torricelli’s Law, the velocity of efflux (v) of a liquid from an orifice at depth 'h' is given by the formula v = √(2gh). Since all three vessels are filled to an equal height (h), the initial velocity of discharge is theoretically the same for water, mercury, and kerosene, regardless of their densities.

However, the rate of flow is also influenced by the momentum and viscosity of the fluid. Mercury has the highest density among the three. Due to its significantly higher mass per unit volume, mercury possesses greater hydrostatic pressure at the bottom and higher inertia once in motion. More importantly, mercury's high density leads to a higher Reynolds number, reducing the relative impact of viscous drag compared to its weight. Consequently, Vessel B containing mercury empties the fastest.

Options 2, 3, and 4 are incorrect as they ignore the impact of fluid density and pressure dynamics on the actual discharge rate.