A hemispherical tank of radius 0.50 m is completely filled with water and is open at…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A hemispherical tank of radius 0.50 m is completely filled with water and is open at the top. A small circular orifice of area 1.0 cm² is fitted at the lowest point of the tank.
(i) Establish an expression for the area of the horizontal cross-section of water when the free surface is at a depth y below the top of the hemisphere.
(ii) Using your result in part (i), set up an integral for the time required for the water level to fall from the top (y = 0) to the mid-point of the hemisphere (y = 0.25 m).
(iii) Evaluate the integral to obtain the numerical value of the required time. Take g = 9.8 m s⁻² and present the answer in minutes.