Sailboats use Bernoulli’s principle to generate forward thrust.

The Bernoulli effect, or Bernoulli’s principle or Bernoulli’s law, is a statement of the relationship between flow velocity and pressure in a fluid system; in essence, when the velocity of horizontal flow through a fluid increases, the pressure decreases. This effect, and the principle that formally states it, was discovered by the renowned mathematician Daniel Bernoulli, who first published his formulation in 1738. Since the word “fluid” in physics refers to the behavior of liquids and gases, such as air , the Bernoulli effect can be observed both in hydrodynamic or fluid systems and in aerodynamic or gaseous systems.

A racing car’s spoilers and rear fins generate downforce that helps it stay on track during sharp turns.

A common example used to explain the Bernoulli effect is the flow of fluid through a pipe. If the fluid is moving uniformly through the tube, the only forces acting on the fluid are its own weight and the pressure of the fluid itself. Now, if the tube narrows, the fluid must accelerate because the same amount of fluid is traveling through a smaller space. However, if the fluid is moving uniformly and the weight has not changed, then the only way the fluid will move faster is if the pressure behind the fluid is greater than the pressure in front of it. Therefore, the pressure must decrease as the velocity increases.

Aircraft and glider wings use the Bernoulli effect to generate lift.

Since air can be considered a fluid (in physics, anything that flows is considered a fluid), the Bernoulli effect is often used in modeling aerodynamic systems. Race cars use the Bernoulli effect to help keep them on the road at high speeds; using a tail fin angled so that the air pressure above the fin is greater than below, the car is essentially held down by atmospheric pressure. This keeps the car on the road, eliminating “drift” and allowing the driver greater control and safety. Airplanes use the Bernoulli effect in the opposite way to help generate lift. Other common real-world applications of the Bernoulli effect include carburetors, which apply the effect to pull and mix air and fuel, and sailing ships, which can generate propelling force from both wind and the pressure differential described by Bernoulli’s principle.

A common real-world application of the Bernoulli effect is the carburetor, which applies the effect to draw in and mix air and fuel.

Although there are different formulations of the Bernoulli equation, which is a formal mathematical statement of the principle, the Bernoulli effect can be observed in each type of system that the formulations describe. Each formulation describes a different set of fluid characteristics – incompressible flow, unstable potential flow, and so on – but the Bernoulli effect is generally observable in each system. However, there are certain cases where the principle is invalid, and in those cases, so is the effect.