• id: JME-09-N08
• title: Torricelli's Theorem — Speed of Efflux
• tags: torricelli, efflux, projectile

If a tank has a small hole at depth $h$ below the free surface, the speed of efflux is $v = \sqrt{2gh}$ — the same speed as a body falling freely through height $h$. Derivation: Apply Bernoulli between the surface (large area, $v \approx 0$) and the hole. After exit, the stream follows projectile motion. The horizontal range from a hole at height $y$ above the ground with water surface at height $H$: $R = 2\sqrt{y(H-y)}$. Maximum range occurs when $y = H/2$ (hole at mid-height), giving $R_{\max} = H$. Time to empty a tank: requires integration since $h$ changes with time.