Water flows into a vertical cylindrical tank of cross-sectional area A ft at the rate of Q ft/min. At the same time, the water drains out under the influence of gravity through a hole of area a ft' in the base of the tank. If the water is initially h ft deep, find the instantaneous depth as a function of time. What is the limiting depth of the water as time increases indefinitely?
Water flows into a vertical cylindrical tank of cross-sectional area A ft at the rate of Q ft/min. At the same time, the water drains out under the influence of gravity through a hole of area a ft' in the base of the tank. If the water is initially h ft deep, find the instantaneous depth as a function of time. What is the limiting depth of the water as time increases indefinitely?
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Transcribed Image Text:to the instantaneous depth of the water in the tank.
20 Water flows into a vertical cylindrical tank of cross-sectional area A ft at the rate of Q ft/min.
At the same time, the water drains out under the influence of gravity through a hole of area a
ft' in the base of the tank. If the water is initially h ft deep, find the instantaneous depth as a
function of time. What is the limiting depth of the water as time increases indefinitely?
21 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.
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