Bernoulli's Equation Flow Calculator
Solve Bernoulli's equation for pressure, velocity, or height at two points in a fluid flow.
Supports water, air, and custom fluid density.
Bernoulli’s equation expresses conservation of energy for steady, incompressible, inviscid fluid flow:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where:
- P = Static pressure (Pa)
- ρ = Fluid density (kg/m³)
- v = Flow velocity (m/s)
- g = Gravitational acceleration = 9.81 m/s²
- h = Height above reference level (m)
Dynamic pressure: q = ½ρv² (increases as speed increases) Static pressure: P (decreases as speed increases) Total pressure: P₀ = P + ½ρv² (constant along a streamline)
Real-world applications:
- Airplane wings: Curved upper surface → faster air → lower pressure → lift force
- Carburetors: Fast-moving air through venturi creates low pressure to draw in fuel
- Water towers: High elevation provides pressure in pipes below
- Pitot tubes: Measure aircraft airspeed by comparing static and stagnation pressures
- Garden hoses: Covering part of the nozzle increases velocity (continuity) and decreases pressure
Assumptions and limitations: Bernoulli’s equation assumes:
- Steady flow (no turbulence)
- Incompressible fluid (good for liquids, valid for air below Mach 0.3)
- No viscosity (friction) along the streamline
- No work done by pumps or extracted by turbines
For real pipes, add a friction head loss term or use the Darcy-Weisbach equation.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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