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Classical Mechanics

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Continuity Equation: Filling a Leaky Bucket

CLMECH-AYIEU9

A large bucket is filled to a depth $h$ with water. A small hole with area $a$ is pierced in the bottom of the bucket and is allowing the water to leak out. At the same time, a hose with cross-sectional area $A$ is being used to fill the bucket.

How fast ($v$) must the water leave the hose if the water level in the bucket is to remain constant?

A

$v = \cfrac{a}{A}$

B

$v = \sqrt{2gh}$

C

$v = \sqrt{2gh}\cfrac{a}{A}$

D

$v = \sqrt{2gh + a/A}\cfrac{a}{A}$