Fluid Mechanics

Bernoulli Equation Calculator

The Bernoulli equation relates pressure, velocity, and elevation along a streamline for steady, incompressible flow. This calculator solves for P₂ given conditions at two points. An optional user-supplied head loss term can be included — this value must be entered by the user and is not calculated from pipe friction or roughness.

TypeInteractive calculator — separate from unit conversions

Calculator

Pressure at point 1 (P₁)

Fluid density (ρ)

User-supplied — no lookup

Velocity at 1 (v₁)

Velocity at 2 (v₂)

Elevation at 1 (z₁)

Elevation at 2 (z₂)

Head loss (hL) — user-entered, not computed

Optional — enter 0 for ideal flow

Gravitational acceleration (g)

m/s²

Result

P₂198500 Pa

ΔP (P₂ − P₁)-1500 Pa

Head terms (m)

Point 1Point 2Pressure20.394320.2414Velocity0.05098580.203943Elevation00Total20.445320.4453

Formulas

Bernoulli equation

P₁/(ρg) + v₁²/(2g) + z₁ = P₂/(ρg) + v₂²/(2g) + z₂ + hL

Solve for P₂

P₂ = P₁ + ρg(z₁ − z₂) + ½ρ(v₁² − v₂²) − ρg·hL

Diagram

Worked example

P₁ = 200,000 Pa, ρ = 1000 kg/m³, g = 9.80665 m/s², v₁ = 1 m/s, v₂ = 2 m/s, z₁ = 0 m, z₂ = 0 m, hL = 0 m. What is P₂?

01P₂ = P₁ + ρg(z₁ − z₂) + ½ρ(v₁² − v₂²) − ρg·hL
02P₂ = 200,000 + 1000 × 9.80665 × (0 − 0) + 0.5 × 1000 × (1² − 2²) − 0
03P₂ = 200,000 + 0 + 0.5 × 1000 × (1 − 4)
04P₂ = 200,000 − 1,500
05P₂ = 198,500 Pa

Result

P₂ is 198,500 Pa. The pressure decreases by 1,500 Pa due to the velocity increase.

FAQ

Is this a pipe pressure-drop calculator?

No. This applies the Bernoulli equation for ideal flow. It does not calculate pipe friction loss, and does not use pipe roughness, viscosity, or any friction model.

Does this calculate friction loss?

No. The optional head loss (hL) term must be entered by the user. This calculator does not compute friction loss from pipe properties.

Does this use pipe roughness or viscosity?

No. Pipe roughness and fluid viscosity are not used. Those parameters are required for friction-based pressure drop calculations, which are outside the scope of this calculator.

Does this include pump or turbine work?

No. The Bernoulli equation implemented here does not include pump or turbine work terms. Only the pressure, velocity, elevation, and optional user-supplied head loss are considered.