Torricelli's Law, named after Evangelista Torricelli, relates initial velocity, gravity, and height to the flow of a liquid out of an opening: where is the speed out of the opening, the initial speed, gravity, and the distance from the top of the hole to the top of the liquid.
Torricelli's Law may be derived by considering the mass of water at the top of the liquid. This water has potential energy relative to the hole and kinetic energy , for total energy of . At the level of the hole, this water will have converted all potential energy into kinetic energy, so the total energy will now be . By the First Law of Thermodynamics, , so ; solving for ,