A large cylindrical tank contains a hole of area A at its bottom. Water is poured into the tank via a tube of the same cross-sectional area A , which ejects water at a speed v .

Step-by-step solution

Let h be the height of water in the tank at any time t . The rate of volume of water entering the tank is given by Q_ in = A v . The velocity of efflux from the hole at the bottom of the tank is v_ eff = 2gh . The rate of volume of water leaving the tank is Q_ out = A 2gh . The water level will rise as long as the rate of inflow is greater than the rate of outflow, i.e., Q_ in > Q_ out . The water level will stop rising when the rate of inflow becomes equal to the rate of outflow. A v = A 2gh v = 2gh h = v^2 2g Thu