A cubical tank with a circular hole of area A, at the bottom has water leaking through it. Due to friction and contraction near the hole, the volume of water leaving the tank per second is reduced to cAn/2gh where c is an empirical constant with a range of values 0 < c< 1. Derive the differential equation for the height h of the remaining water at any time t. The radius of the hole is 50mm and g = 9.8.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A cubical tank with a circular hole of area A, at the bottom has water
leaking through it. Due to friction and contraction near the hole, the
volume of water leaving the tank per second is reduced to cAp/2gh
where c is an empirical constant with a range of values 0 < c< 1. Derive
the differential equation for the height h of the remaining water at any
time t. The radius of the hole is 50mm and g = 9.85.
T
4 m
h
circular
hole
Transcribed Image Text:A cubical tank with a circular hole of area A, at the bottom has water leaking through it. Due to friction and contraction near the hole, the volume of water leaving the tank per second is reduced to cAp/2gh where c is an empirical constant with a range of values 0 < c< 1. Derive the differential equation for the height h of the remaining water at any time t. The radius of the hole is 50mm and g = 9.85. T 4 m h circular hole
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