Bernoulli’s principle states that as the speed of a moving fluid increases, the pressure within that fluid decreases. The reverse is also true: slower-moving fluid exerts higher pressure. This relationship between speed and pressure holds for any fluid, including both liquids and gases like air, and it explains phenomena ranging from how airplanes fly to why a curveball curves.
The principle is rooted in the conservation of energy. A fluid in motion carries two relevant forms of energy: the energy of its movement (kinetic energy) and the energy stored as pressure (potential energy). Because energy in a closed system can’t be created or destroyed, when one form increases the other must decrease. Speed up the fluid, and its pressure drops. Slow it down, and the pressure rises.
The Core Equation
NASA’s Glenn Research Center expresses Bernoulli’s equation in a compact form: the static pressure of a fluid plus its dynamic pressure equals a constant called total pressure. Static pressure is the baseline pressure the fluid exerts even when its molecules are just bouncing around randomly. Dynamic pressure is the additional pressure created by the fluid’s bulk motion, calculated as one half of the fluid’s density multiplied by the square of its velocity.
Because the total pressure stays constant along a flow path, you can compare two points in the same flow. If the velocity at one point is higher, the dynamic pressure there is larger, which forces the static pressure to be lower. That tradeoff is the entire principle in a nutshell. When height differences between two points become significant, a gravity term (density times gravitational acceleration times height) gets added to account for the fluid’s weight, but the core logic stays the same.
Conditions Where It Applies
Bernoulli’s principle describes an idealized situation. It assumes the fluid is incompressible, meaning its density doesn’t change as it flows. It also assumes steady flow, where the speed at any given point isn’t fluctuating over time, and it ignores energy lost to friction. Real fluids always have some friction and compressibility, so Bernoulli’s equation is an approximation. For water moving through pipes or air flowing at speeds well below the speed of sound, that approximation is extremely good. At very high speeds, near or above the speed of sound, air compresses significantly and the simple form of the equation breaks down.
The Venturi Tube: Bernoulli in a Pipe
One of the clearest demonstrations of the principle is a venturi tube, a pipe that narrows in the middle and then widens again. When fluid enters the narrow section, it speeds up because the same volume of fluid has to squeeze through a smaller space. That increase in velocity drops the pressure in the narrow section. If you poke a small hole in the narrow part of the tube, outside air actually gets pulled inward because the pressure inside is lower than the pressure outside. Bernoulli himself experimented with this setup, and the effect it demonstrates is sometimes called the Venturi effect.
This same mechanism powers everyday devices. A perfume atomizer, for instance, uses a squeeze bulb to blow a fast jet of air across the top of a thin tube that dips into the perfume. The fast-moving air creates low pressure at the top of the tube, and the higher pressure on the perfume’s surface pushes liquid up and into the airstream, where it breaks into a fine mist. Paint sprayers and old-style carburetors in engines work on the same idea. The process is called entrainment: high-velocity fluid pulling other fluids along with it.
How It Helps Explain Flight
Bernoulli’s principle plays a central role in generating lift on airplane wings. A wing’s cross-section, called an airfoil, is shaped so that air flowing over the top moves faster than air flowing underneath. Faster air on top means lower pressure above the wing. Slower air beneath means higher pressure below. That pressure difference pushes the wing upward.
There is, however, a widely taught explanation of this that gets the details wrong. The “equal transit time” theory claims air molecules split at the front of the wing and must rejoin at the back at the same moment, forcing the top molecules to move faster because they travel a longer path over the curved upper surface. NASA has directly debunked this. In reality, the air over the top moves much faster than equal transit time would predict, and the molecules going over the top actually arrive at the trailing edge before the ones traveling underneath. Symmetric airfoils, where the top and bottom surfaces are the same length, still generate plenty of lift, which the equal transit time theory can’t explain at all. Bernoulli’s principle is genuinely part of the lift story, but the reason air speeds up over the top of a wing involves the wing’s angle of attack and the way it deflects airflow, not a race to meet at the trailing edge.
Why a Curveball Curves
When a pitcher throws a curveball, the ball spins as it moves through the air. That spin drags air along with it on one side and pushes against the airflow on the other. On the side where the ball’s spin moves in the same direction as the oncoming air, the air speeds up. On the opposite side, where the spin fights the airflow, the air slows down. Bernoulli’s principle tells you what happens next: faster air on one side means lower pressure there, and the ball gets pushed toward that low-pressure zone. The result is a curving flight path. This broader phenomenon is called the Magnus effect, and it shows up in soccer free kicks, tennis topspin, and golf drives.
Blood Flow and Narrowed Arteries
Bernoulli’s principle also applies inside the human body. Blood is a fluid, and it follows the same speed-pressure relationship as it moves through vessels. When an artery narrows due to plaque buildup (a condition called stenosis), blood has to speed up to get through the constricted section, just like fluid in a venturi tube. That increased velocity causes a pressure drop across the narrowed segment. Doctors can estimate that pressure drop using a simplified formula derived from Bernoulli’s principle: the pressure drop in millimeters of mercury roughly equals four times the square of the maximum blood velocity in meters per second through the narrowed area. This calculation, applied to ultrasound measurements of blood flow speed, helps assess how severely a narrowed artery is restricting circulation without needing invasive testing.
The Bigger Picture
At its core, Bernoulli’s principle is a statement about energy conservation applied to moving fluids. Faster flow trades pressure for speed. Slower flow trades speed for pressure. The total energy along a streamline stays constant. That single idea connects airplane wings to perfume bottles to clogged arteries, making it one of the most practically useful principles in physics. Understanding it doesn’t require advanced math. You just need to remember that when a fluid speeds up, something has to give, and that something is pressure.