Consider an open cylindrical barrel of diameter 0.5 m. Installed in the bottom of the barrel is a pipe (10 cm in diameter) which permits liquid to flow out under gravity. At the same time, liquid is added to the tank from above through a pipe with a diameter of 5 cm.
a. If the velocity of the liquid leaving through the bottom pipe is 2.21 m/s, what is the velocity of the liquid entering the tank (from pipe above) if the level of the liquid in the tank is constant?
b. If the velocity of the liquid leaving through the bottom pipe is 2.21 m/s and at that instant it is observed that the level in the tank is increasing at the rate of 1 cm/s, what is the velocity of the liquid entering the tank from the inlet pipe?