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 Quote by coelho Could you outline how did you arrive at the expression you found after integrating?
I found one (stupid) mistake I made in my original equation (divided out the Qleak term rather than adding it to the other side). So ignore that equation... Below is how I arrived at the new equation, and this one still has a problem.

Qleak = a*C*sqrt(2*g*h)
Qi = constant
Qe = constant

integrate dH from Hi to Hf
integrate dt from 0 to T
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1. -A * (dH/dt) = Qleak - Qi + Qe

2. ... simplify by combining constants... Qi + Qe = Qtot

3. dH = (-Qleak/A + Qtot/A)dt

4. dH = 1/A*(-Qleak + Qtot)dt

5. (A*dH) / (-Qleak + Qtot) = dt

6. int((A*dH) / (-Qleak + Qtot)) = int(dt)

7. ... integrate dt from 0 to T

8. int((A*dH) / (-Qleak + Qtot)) = T

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This is where I stopped since I could not find an easy way to integrate the left side. The basic form of the integral would be: dH/(h^1/2 + constant)

Any tips on where I may have gone wrong, or how to solve that integral would be appreciated! Thanks