# Bernoulli's principle

Bernoulli's Principle relates the pressure, velocity, and relative height of a point in the flow of a fluid. It is one of the most used relationships in aerodynamics.

The integrated form of Bernoulli's equation for a point is:

$P + {1 \over 2} \rho V^2 + \rho g h = constant$

where

P is pressure
ρ is fluid density
V is the speed of the flow
g is the acceleration due to gravity and
h is the height of the flow above the reference, or datum, point.

This equation applies to all points along a streamline of a flow, unless the flow is irrotational, in which case it applies everywhere in the flow.

In aerodynamics, flows are often fast enough where ρgh term (the gravitation potential term) is very small in relation to the other terms and can be neglected. In this case, Bernoulli's equation says that points of higher speed in the flow have lower pressure. This conclusion is fundamental to the principles of flight. When air flows over an airfoil it travels faster over the top of the wing because of its shape. From Bernoulli's equation, the pressure on the top of the wing is lower than the pressure on the bottom because of this difference in speed. This pressure difference is where lift comes from, which is essential for flight.