Pressure in a moving fluid
A fluid is a liquid or a gas. Even when it moves, it has pressure. In 1738 a scientist named Daniel Bernoulli noticed something strange: when a fluid moves faster, its pressure becomes lower, and when it moves slower, its pressure is higher.
This is the Bernoulli principle. It is about the pressure inside the moving fluid, the pressure that is pushing sideways on the pipe wall or on things in the stream.
The narrowing pipe
Water flows through a pipe that has a narrow part. The same amount of water must pass through the narrow part every second as through the wide part. So in the narrow part the water must move faster.
Glass tubes standing on the pipe show the pressure: the higher the liquid in the tube, the higher the pressure. Over the narrow part the liquid is lower, so the pressure is lower where the water moves faster.
Real uses: a carburettor, a paint spray gun and an atomiser mix a liquid into a fast stream of air this way.
Aircraft lift
An aeroplane wing has a curved top and a flatter, slightly tilted bottom. The air that passes over the top has to move faster than the air under the wing. By Bernoulli's principle:
- Above the wing: fast air, low pressure.
- Below the wing: slower air, higher pressure.
The higher pressure below pushes the wing up harder than the lower pressure above pushes it down. This net upward force is lift. When lift is bigger than the weight of the plane, it rises. The wing also tilts a little, so it deflects the air downwards, which pushes the plane up too (Newton's third law). Both ideas work together.
Other examples
- Blow between two hanging sheets of paper: they move towards each other.
- A ping-pong ball stays in a stream of air from a hair dryer.
- A roof may blow off in a strong wind: the air outside moves fast, pressure falls, and the higher pressure inside pushes the roof up.
- Standing too close to a fast train is dangerous because air rushing past pulls you towards it.
Try it
(1) Hold two sheets of paper a few centimetres apart, hanging down. Blow between them. What happens? (2) Hold a paper strip below your lower lip and blow across the top. The strip rises. (3) Hold a spoon loosely under a running tap, with its back touching the stream. Feel the spoon being pulled into the water. In the 3D above, guess how the middle gauge will change before you move the flow slider.
Key formulas and definitions
- Faster fluid ⇒ lower pressure; slower fluid ⇒ higher pressure
- In a pipe: narrow part ⇒ faster flow ⇒ lower pressure
- Lift on a wing = (pressure below − pressure above) × wing area
- Lift > weight ⇒ the plane rises
Worked examples
1. Water flows through a pipe that narrows. Where is the pressure lowest, and why?
In the narrow part. Water must move faster there, and fast-moving fluid has lower pressure.
2. Why do two sheets of paper move together when you blow between them?
The air between them moves fast, so the pressure between them is lower than outside. The higher pressure outside pushes the sheets together.
3. The pressure below a wing is 100 100 Pa and above it is 99 900 Pa. The wing area is 20 m². Find the lift.
Pressure difference = 100 100 − 99 900 = 200 Pa. Lift = 200 × 20 = 4000 N.
Common mistakes
- Thinking fast-moving fluid has higher pressure. It has lower pressure.
- Saying air is "sucked" up over the wing. The higher pressure below pushes the wing up.
- Thinking the principle works for any fast flow, even when something blows air at a wall (a jet hitting a wall makes a high pressure at the wall).
- Forgetting that the same amount of fluid passes every second, so the narrow part must be faster.