Torricelli's Theorem

Torricelli's Theorem is Bernoulli's equation with certain assumption made. This deals with the set up where you have a large tank with a narrow opening allowing for the the liquid to flow out. Both the Tank and the the narrow opening (nozzle) are open to the atmosphere. The fluid velocity of the tank (water level) is very much slower than the fluid velocity of the nozzle.

The pressure will be the same because they are open to the atmosphere. The fluid velocity at region 2 is much slower then the fluid velocity at region 1. Therefore the fluid velocity at region 2 is negligible. The value of y1=0. The equation simplifies to



Example

A pump and its horizontal intake pipe are located 12m beneath the surface of a reservoir. The speed of the water in the intake pipe causes the pressure there decrease in accord with Bernoulli's Principle. Assuming non-viscous flow, what is the maximum speed with which the water can flow through the intake pipe?