# Bernoulli's principle

*150*pages on

this wiki

**Bernoulli's principle** (or **Bernoulli's equation**) is a formula that relates the height, density, pressure, and velocity of a non-viscous and non-conducting fluid. It states that

*p* is the pressure, *ρ* is the density, *h* is the elevation, *v* is the velocity of the fluid, and *g* is acceleration due to gravity.

## DerivationEdit

Since total energy in a system is conserved,

Work is equal to force times distance. Since pressure is force divided by area and distance is velocity times time, we get

Since area times velocity times time is equal to volume, we can rewrite this as mass over density, giving

The potential energy will be equal to

and the kinetic energy will equal

By substituting these values in, we get

This can be simplified by dividing both sides by *m* and multiplying by *ρ*, giving