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Bernoulli's principle
Intermediate
Faster flow means lower pressure along a streamline.
P + ½ρv² + ρgh = constAlong a streamline P + ½ρv² + ρgh = constant (energy conservation per unit volume). Where speed is high, pressure is low.
Water speeding up through a constriction has lower pressure.
Valid for steady, incompressible, non-viscous flow.
In more detail
Bernoulli's principle states that in steady flow of an ideal fluid, pressure decreases where speed increases. It is an energy conservation statement for fluids.
Real-world uses
- Airplane wings generate lift partly through Bernoulli effects.
- Atomisers and carburettors draw liquid using low pressure in fast-flowing air.
- An aircraft wing is shaped so air moves faster over the top, producing lower pressure there and an upward lift.
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Frequently asked questions
Why does fast air have lower pressure?
Because kinetic energy increases at high speed, so pressure must fall for total energy to stay constant.
Is Bernoulli the whole story for lift?
No. Lift also depends on the angle of attack and the flow turning, which Bernoulli alone does not capture.
Is Bernoulli's principle the whole explanation for lift?
It is part of it. Lift also depends on the angle of attack and the deflection of air downward, which Bernoulli alone does not capture.
Related topics in Fluids & Elasticity
Fluid dynamics · Streamline and turbulent flow · Equation of continuity · Applications of Bernoulli · Torricelli's theorem · Venturi meter