Bernoulli's principle states that in fluid flow, an increase in velocity happens simultaneously with decrease in pressure. It was discovered by the Swiss mathematician/scientist Daniel Bernoulli. For a mathematical formulation, see Bernoulli's equation. In a fluid flow with no viscosity, therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion.

One way of understanding how an airfoil develops lift relies upon the pressure differential above and below a wing. This can be calculated by finding the velocities around the wing and using Bernoulli's principle. However, this explanation often uses false information, such as the incorrect assumption that the air that separates at the leading edge of a wing must meet at the trailing edge. There are other, more intuitive ways, of understanding aerodynamic lift (see Coanda Effect).

Bernoulli's principle is also important in carburetors. In a carburetor, air is passed through a Venturi tube to increase its speed and therefore decrease its pressure. The low pressure air is routed over a tube leading to a fuel tank. The low pressure sucks the fuel into the airflow so that the combined fuel and air can be sent to the engine. This same effect can be observed by blowing over a straw; the liquid level will rise as the flow over the top of the straw increases in speed.

Another important application is cavitation, or the prevention of such cavitation. As an example, a propeller rotating at high speed may cause the local water (or other liquid) pressure to decrease enough for the liquid to become a gas, producing bubbles. When these collapse, pitting occurs on the face of the propeller, and noise results. This latter may be detected by means of sonar.