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Bernoulli Equation Calculator

Apply Bernoulli’s equation to relate pressure, velocity and elevation along a streamline.

About Bernoulli Equation Calculator

Bernoulli’s equation is energy conservation along a streamline: pressure, kinetic and potential terms trade against each other. Where a fluid speeds up, its pressure must fall — the venturi effect. It assumes inviscid, incompressible steady flow, so real systems need a head-loss term added for friction.

Formula

Bernoulli Equation

p₁ + ½ρv₁² + ρgh₁ = p₂ + ½ρv₂² + ρgh₂

total head
Pressure, velocity and elevation head summed, constant along a streamline
velocity head
v² ÷ 2g, the kinetic contribution expressed as a height

Worked example

With the default values below, Bernoulli Equation Calculator returns Pressure at Point 2 of 154,570.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Pressure at point 1minimum 0 Pa
200,000 Pa
Velocity at point 1minimum 0 m/s
2 m/s
Elevation at point 1minimum -100 m
0 m
Velocity at point 2minimum 0 m/s
6 m/s
Elevation at point 2minimum -100 m
3 m
Fluid densityminimum 0.01 kg/m3
1,000 kg/m3

Results

Pressure at Point 2
154,570.00 Pa
Pressure Change
45,430.00 Pa
Change in Velocity Head
1.631 m
Change in Elevation Head
3.000 m
Total Head at Point 1
20.591 m

Step by step

  1. 1Values used
  2. 2Bernoulli Equation
  3. 3Pressure at Point 2= 154,570.00 Pa
  4. 4Pressure Change= 45,430.00 Pa
  5. 5Change in Velocity Head= 1.631 m
  6. 6Change in Elevation Head= 3.000 m
  7. 7Total Head at Point 1= 20.591 m

Assumptions and limits

  • The result is derived only from the 6 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Bernoulli Equation calculated?

p₁ + ½ρv₁² + ρgh₁ = p₂ + ½ρv₂² + ρgh₂ Bernoulli’s equation is energy conservation along a streamline: pressure, kinetic and potential terms trade against each other. Where a fluid speeds up, its pressure must fall — the venturi effect.

Why does Bernoulli Equation matter?

It assumes inviscid, incompressible steady flow, so real systems need a head-loss term added for friction.

What values do I need to enter?

This calculator takes 6 inputs: Pressure at point 1, Velocity at point 1, Elevation at point 1, Velocity at point 2, Elevation at point 2, Fluid density. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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