A tall, open cylindrical tank filled with water drains through a small hole located…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A tall, open cylindrical tank filled with water drains through a small hole located at the center of its flat bottom. During the process, observers notice that the water initially shoots outward in a long, fast jet but the outflow gradually weakens as the level of water in the tank drops.
(a) Describe how the gauge pressure at the hole changes as the depth of water above the hole decreases. In your answer, refer to the relevant physical quantity that connects pressure to depth.
(b) Explain qualitatively why the speed of the water emerging from the hole decreases over time even though the hole’s area remains constant.
(c) Using the principle of mass conservation, explain why the instantaneous volume flow rate through the hole must equal the negative rate of change of the water volume remaining in the tank. State any assumptions you make about the fluid.