À vertical cylindrical tank of height h and radius R has a narrow crack of width w running vertically from top to bottom. If the tank is initially filled with water and allowed to drain through the crack under the influence of gravity, find the instantaneous depth of the water as a function of time. How long will it take the tank to empty? Hint: First imagine the crack to be a series of adjacent orifices, anc integrate to find the total efflux from the crack in the infinites imal time interval dt. 3:43

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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A vertical cylindrical tank of height
h and radius R has a narrow crack
of width w running vertically from
top to bottom. If the tank is initially
filled with water and allowed to drain
through the crack under the influence
of gravity, find the instantaneous
depth of the water as a function of
time. How long will it take the tank to
empty? Hint: First imagine the crack
to be a series of adjacent orifices, and
integrate to find the total efflux from
the crack in the infinites imal time
interval dt.
P 3:43
Transcribed Image Text:A vertical cylindrical tank of height h and radius R has a narrow crack of width w running vertically from top to bottom. If the tank is initially filled with water and allowed to drain through the crack under the influence of gravity, find the instantaneous depth of the water as a function of time. How long will it take the tank to empty? Hint: First imagine the crack to be a series of adjacent orifices, and integrate to find the total efflux from the crack in the infinites imal time interval dt. P 3:43
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