Equations · equation
Bernoulli's Equation
Fluid Dynamics · 1738
- Equation
- p + ½ρv² + ρgh = constant
- Field
- Fluid Dynamics
- Named After
- Daniel Bernoulli
- Year
- 1738
Symbols
p pressure · ρ density · v flow speed · g gravitational acceleration · h height · holds along a streamline for steady, frictionless, incompressible flow
Significance
Where a fluid speeds up along a streamline its pressure drops — energy bookkeeping for steady, frictionless, incompressible flow. It is why a carburettor and a scent atomiser draw liquid up into a fast stream, why a Venturi meter reads a flow rate from nothing but a pressure difference, why a roof lifts off in a gale rather than being pushed in, and why two ships running close alongside are drawn together. What it is not is the reason a wing lifts. The popular account has air taking equal time over a longer upper surface, which is not what air does; lift is circulation, and the mass of air the wing throws downward. Bernoulli holds perfectly well over a wing — the pressure on top really is lower — but it is describing the flow, not causing it.
Referenced by
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skill
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