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Question:
the bottom of a cylindrical vessel has a circular hole of radius 'r' at depth'h'below the water level. if the diameter of the vessel is 'D', find the speed with which the water level in the vessel drops
Answer:

Torricelli Theorem

This is based on Torricellis theorem. According to Torricelli, the velocity with which the liquid flows out through the narrow hole, is equal to the velocity which the freely falling body would acquire in falling through a vertical distance equal to the depth of the narrow hole below the free surface of liquid.

By Torricelli theorem, v = √ (2gh)

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