Serway & Jewett — Fluid Mechanics: Problem 42

A woman is draining her fish tank by siphoning the water into an outdoor drain as shown in Figure P14.42. The rectangular tank has footprint area \(A\) and depth \(h\). The drain is located a distance \(d\) below the surface of the water in the tank, where \(d \gg h\). The cross-sectional area of the siphon tube is \(A'\). Model the water as flowing without friction. Show that the time interval required to empty the tank is given by \[\Delta t = \frac{Ah}{A'\sqrt{2gd}}\]