What assumptions does Bernoulli's equation make?

Bernoulli's equation assumes steady, incompressible, inviscid (frictionless) flow along a streamline. It is most accurate for liquids at moderate velocities and does not account for viscous losses in real pipes.

What units does this calculator use?

Pressure is in Pascals (Pa), velocity in meters per second (m/s), elevation in meters (m), and density in kg/m³. Results are displayed in SI units.

Why is my velocity result showing as an error?

If solving for velocity produces a negative value under the square root, it means the energy balance is physically impossible with the given inputs. Check that your pressure and elevation values are consistent with the direction of flow.

What is the standard density for water and air?

Water at 20°C has a density of approximately 998 kg/m³ (commonly rounded to 1000). Air at sea level and 20°C is approximately 1.204 kg/m³.

How is Bernoulli's equation written?

P1 + ½ρv1² + ρgh1 = P2 + ½ρv2² + ρgh2, where P is static pressure, ρ is fluid density, v is flow velocity, g is gravitational acceleration (9.80665 m/s²), and h is elevation above a reference datum.

Can I use this for compressible gases?

Only at low Mach numbers (below ~0.3) where compressibility effects are negligible. For high-speed gas flows, a compressible flow equation (e.g., isentropic relations) should be used instead.

Bernoulli Equation Calculator

Name: Bernoulli Equation Calculator
Availability: InStock
Author: Nham Vu

Enter known fluid flow conditions at two points and solve for the unknown pressure, velocity, or elevation using Bernoulli's equation.

Fluid Parameters

All values in SI units (Pa, m/s, m, kg/m³).

Fluid Density ρ (kg/m³)

Solve for at Point 2

Pressure P₂ (Pa) Velocity v₂ (m/s) Elevation h₂ (m)

1 Point 1 (all three required)

P₁ (Pa)

v₁ (m/s)

h₁ (m)

2 Point 2 (two known, one unknown)

P₂ (Pa)

v₂ (m/s)

h₂ (m)

Bernoulli's Equation

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

P = static pressure (Pa) ρ = fluid density (kg/m³) v = flow velocity (m/s) g = 9.80665 m/s² h = elevation (m) ½ρv² = dynamic pressure

Result

Fill in the inputs and click Calculate.

Summary

Enter known fluid flow conditions at two points and solve for the unknown pressure, velocity, or elevation using Bernoulli's equation.

How it works

Select which variable at Point 2 you want to solve for: pressure, velocity, or elevation.
Enter the fluid density (kg/m³) — default is water at 1000 kg/m³.
Fill in all known values at Point 1: pressure (Pa), velocity (m/s), and elevation (m).
Fill in the two known values at Point 2 (the third is the unknown being solved).
Click Calculate to apply Bernoulli's equation and view the result.

Use cases

Calculate pressure drop along a pipe with changing diameter.
Find fluid velocity at a constriction (Venturi effect).
Determine pressure at a nozzle exit given inlet conditions.
Analyze flow over an airfoil to estimate lift pressure difference.
Solve hydraulic engineering problems involving open channels.
Estimate velocity from a tank orifice at a given depth (Torricelli's theorem).
Check flow conditions in HVAC duct systems.
Educational demonstrations of conservation of energy in fluids.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu