Bernoulli Equation Calculator
Solve Bernoulli's equation between two points in a fluid flow.
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Formulas
P1 + ½ρv1² = P2 + ½ρv2²For horizontal flow (same height). Add ρgh terms for height changes.
Bernoulli's Principle
As fluid speed increases, pressure decreases. Explains airplane lift, Venturi effect, and why shower curtains blow inward. Assumes incompressible, inviscid, steady flow along a streamline.
Understanding Bernoulli's Equation
Bernoulli's equation expresses conservation of energy for a flowing fluid. Along a streamline, the sum of pressure, kinetic, and potential energy per unit volume stays constant:
P1 + ½ρv1² + ρgh1 = P2 + ½ρv2² + ρgh2P is pressure, ρ is fluid density, v is velocity, g is gravity, and h is height.
The key insight: where a fluid speeds up, its pressure drops. This explains lift on a wing, the lift of a spinning ball, and the suction of a carburettor.
Worked Example
Water (ρ = 1000) accelerates from 2 m/s to 6 m/s at constant height. The pressure change is:
ΔP = ½ρ(v1² - v2²) = 0.5 × 1000 × (4 - 36) = -16000 Pa
Pressure falls by 16 kPa as the fluid speeds up.
The Three Energy Terms
| Term | Represents |
|---|---|
| P | Pressure energy |
| ½ρv² | Kinetic energy (dynamic pressure) |
| ρgh | Potential energy (elevation) |
As one term rises, another must fall to keep the total constant along the streamline.
Frequently Asked Questions
What are the assumptions?
Bernoulli's equation assumes steady, incompressible, frictionless flow along a single streamline. Real flows with viscosity or turbulence need correction terms.
How does it explain wing lift?
Air moves faster over the curved top of a wing, lowering pressure there relative to the underside, producing a net upward force.
Why does pressure drop when speed rises?
Energy is conserved. If kinetic energy (½ρv²) increases, pressure energy must decrease to keep the total constant.