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Overview
Bernoulli's principle describes a relationship between pressure, speed, and height in a moving fluid under idealized conditions. It is often used to analyze flow in pipes, nozzles, airfoils, sprays, and many fluid systems. The principle is an expression of energy conservation for flowing fluids.
Ideal Fluid Assumptions
Introductory Bernoulli analysis often assumes steady, incompressible, nonviscous flow along a streamline. Real fluids may deviate from these assumptions because of viscosity, turbulence, and compressibility.
Speed and Pressure
In many horizontal ideal flows, higher fluid speed corresponds to lower pressure, while lower speed corresponds to higher pressure.
Height Effect
Height also matters because gravitational potential energy is part of the energy balance. Fluid at greater height can have different pressure or speed than fluid at lower height.
Energy Conservation View
Bernoulli's principle can be understood as conservation of mechanical energy per unit volume in a flowing fluid.
Pipes and Nozzles
When a pipe narrows, fluid speed can increase. Under ideal conditions, pressure can decrease in the faster-moving region.
Airfoils
Bernoulli's principle can help explain aspects of lift, but real aircraft lift also requires circulation, angle of attack, airflow deflection, viscosity, and Newton's laws.
Limitations
Bernoulli's principle is powerful but limited. It should not be applied blindly to strongly turbulent, highly viscous, compressible, or energy-adding flows without modification.
Common Mistakes
A common mistake is using Bernoulli's principle as a complete explanation for all flight. It is one part of fluid analysis, not the whole story.
Why This Matters in Physics
Bernoulli's principle connects energy conservation to fluid flow and supports analysis of pipes, sprays, wings, blood flow, turbines, and engineering systems.