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The bottom of a cylindrical vessel has a...

The bottom of a cylindrical vessel has a circlular hole of radius r and at depth h below the water] level. If the diameter of the vessel is D, the find then speed with which the water level in the] vessel drops.

Text Solution

Verified by Experts

The velocity of efflux = `sqrt2gh`
The rate of-flow of liquid out of hole = Av = `pir^(2) sqrt(2gh)`
By using equation of continuity
`(AV)_(container) = (AV)_(hole)`
`pi D^(2)/4 v = pir^(2) sqrt(2gh)`
v = `(4r^(2))/D^(2) sqrt(2gh)`
`:.` Speed with which water level falls = `(4r^(2))/D sqrt(2gh)`
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