VII. Suppose water is leaking from a tank through a circular hole of area An at it's bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of the water leaving the tank per second to cAp /2gh where c(0

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VII. Suppose water is leaking from a tank through a circular hole of area A, at it's bottom. When water leaks
through a hole, friction and contraction of the stream near the hole reduce the volume of the water leaving the
tank per second to cAp 2gh where c(0 <c < 1 is an empirical constant. Determine a differential equation
for the height h of water at a time i for the cubical tank in the figure below. The radius of the hole is 7 in.,
g=32 ft/s?.
10 ft
circular
hole
Transcribed Image Text:VII. Suppose water is leaking from a tank through a circular hole of area A, at it's bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of the water leaving the tank per second to cAp 2gh where c(0 <c < 1 is an empirical constant. Determine a differential equation for the height h of water at a time i for the cubical tank in the figure below. The radius of the hole is 7 in., g=32 ft/s?. 10 ft circular hole
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