A cylindrical water tower stores water with its free surface 12 m above a small
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A cylindrical water tower stores water with its free surface 12 m above a small, sharp-edged orifice in the side wall of the tank. The orifice has a cross-sectional area of 1.0 cm^2 and discharges straight to the atmosphere. The water surface is large enough that its level does not drop appreciably during the short interval considered. Neglect all viscous losses and take the water density as 1.0 × 10^3 kg/m^3.
(a) Derive an expression for the speed at which the water exits the orifice in terms of the given height difference and physical constants.
(b) Compute the numerical value of the exit speed.
(c) Determine the volume flow rate of the water jet.
(d) Estimate the time required for 1.0 m^3 of water to leave the tank through the orifice, assuming the height difference remains effectively constant during this interval.