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

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

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