I have to set up a differential equation for a leaking cylindrical container that is being refilled at a constant rate. Its leaking from the bottom, refilled from the top, and starts empty.(adsbygoogle = window.adsbygoogle || []).push({});

Wondered if someone could check if what i have done so far is right..?

h=height of water

A=cylinder cross section

a=hole cross section

v=speed of water out = Sqrt(2gh) using Torricelli’s Law

b=rate of water going in

Rate of change of volume dV/dt= -av+b = A*dh/dt

Sub in v = Sqrt(2gh):

A*dh/dt=-a*sqrt(2gh)+b -----> dh/dt = (-a*Sqrt(2gh)+b)/A

Any errors?!

Thanks!

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# Refilled Leaking container ODE

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