Tank drain-time formula

[swedish_lunacy]

Hi guys,
Need to find time required to drain a tank by gravity. I am having problems solving this one, it's got me up at nights ( semi obsessive compulsive about this one ). I know it's just a matter of differentiating or integrating or something but I can't remember which or how.

A simplified model of a draining tank is as follows:

Water tank has:
1) A hole in the bottom with an area represented by "A_drain"
2) A horizontal surface area represented by "A_surface" ( ie if tank was cylindrical this would be pi.r^2, but tank model could be round or square so please leave as just an area )
3) A water level height represented by "h"
4) Obviously a volume at any point in time represented by "A_surface * h"
5) Gravity represented by "g"

Total drain time = volume / rate of flow from hole
Volume = A_surface * h
Rate of flow from hole = A_drain * sqrt(2gh)

BUT the water-height "h" is continuously dropping so that you cannot apply sqrt(2gh) as a constant across the whole drain period. Everything is changing simultaneously and they are all dependant on each other !

Please help me with this one and also try to explain the process by which I can solve eq's like this in the future.

Thanks in advance
Nick