Torricelli's law

Torricelli’s law, also known as Torricelli’s theorem, is a particular case of Bernoulli’s equation which allows to calculate the speed of a fluid flowing out of an orifice as a function of the height of fluid above the opening (see figure below).

In order to calculate v1, the speed of the fluid leaving the vessel, we apply the Bernoulli’s equation to states 1 and 2 (the latter being the open surface of the fluid). If we assume that the level of the liquid does not change over time, then v2, the speed of the fluid at the surface, is zero. Moreover, the pressure both at the surface and the orifice is the atmospheric pressure p0. In this situation, Bernoulli’s equation is:

Isolating v1:

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At a hydroelectric power plant, water arrives at the generator with a certain speed caused by the difference in height between the source and the water’s outflow. The potential energy of the dammed water is converted into kinetic energy, and this kinetic energy is then used to make the turbine rotate thus producing electricity (see figure below).

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