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.
Pressure at Point 2
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.