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Bernoulli equation fluid dynamics explained
It sounds like you're asking about Bernoulli's equation (sometimes called Bernoulli's principle) - formulated by Swiss mathematician Daniel Bernoulli in 1738. Here's a full breakdown:
Bernoulli's Equation
P + ½ρv² + ρgh = constant
| Term | Name | Meaning |
|---|---|---|
| P | Static pressure | Force per unit area exerted by the fluid |
| ½ρv² | Dynamic pressure | Kinetic energy per unit volume |
| ρgh | Hydrostatic pressure | Gravitational potential energy per unit volume |
The Core Idea
As stated in Bernoulli's principle (Byju's): as the speed of a moving fluid increases, the pressure within the fluid decreases, and vice versa. It's essentially a statement of conservation of energy applied to fluid flow.
Assumptions (when it applies)
- Steady flow (not changing with time)
- Incompressible fluid (constant density - valid for most liquids, low-speed gases)
- No friction (inviscid flow)
- Flow along a streamline
Real-World Applications
- Airplane lift - air moves faster over the curved top of a wing, creating lower pressure above and lift
- Pitot tube - measures aircraft airspeed using pressure difference
- Venturi meter - measures fluid flow rate in pipes
- Shower curtain effect - fast-moving water/air creates low pressure, pulling the curtain inward
- Carburetors - use pressure drop to draw fuel into airflow
Modified Form (with losses)
For real-world pipe systems, the equation is extended to include head losses and pump work:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ + losses
This is described in the DOE Engineering Handbook on Bernoulli's Equation.
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