A cubical tank with a circular hole of area An 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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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A cubical tank with a circular hole of area An 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.
m
Aw,
4 m
h
circular
hole
Transcribed Image Text:A cubical tank with a circular hole of area An 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. m Aw, 4 m h circular hole
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