What is Bernoulli's equation?

Bernoulli's equation states that for a steady, incompressible, inviscid fluid flow along a streamline, the total mechanical energy per unit volume is constant: P + ½ρv² + ρgh = constant, where P is static pressure, ρ is fluid density, v is flow velocity, g is gravitational acceleration, and h is elevation.

What fluids can this calculator handle?

Any Newtonian fluid where viscosity effects are negligible. Presets include water (1000 kg/m³), seawater (1025 kg/m³), air at sea level (1.225 kg/m³), and gasoline (720 kg/m³). You can also enter a custom density.

What are the assumptions behind the calculation?

The fluid is incompressible, the flow is steady and inviscid (frictionless), and both points lie on the same streamline. Results become less accurate at high flow speeds where compressibility or viscous losses matter.

Why does velocity increase when a pipe narrows?

The continuity equation requires mass flow rate to be conserved. When the pipe cross-section shrinks, velocity must increase. Bernoulli's equation then shows that this velocity increase comes at the cost of lower static pressure.

What units does this calculator use?

Pressure can be displayed in Pascals (Pa), kilopascals (kPa), atmospheres (atm), or PSI. Internally all calculations use SI units (Pa, m/s, m, kg/m³). Results are then converted to your selected display unit.

Bernoulli Pressure Calculator

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

Solve Bernoulli's equation for pressure, velocity, or elevation at any two points in a steady, incompressible fluid flow.

Fluid

Fluid density ρ (kg/m³)

Solve For

P₂ Pressure 2 v₂ Velocity 2 h₂ Height 2

Point 1 (upstream / known)

Pressure P₁

Velocity v₁ (m/s)

Elevation h₁ (m)

Point 2 (downstream / target)

Pressure P₂ (solving for this)

— calculated —

Velocity v₂ (m/s)

Elevation h₂ (m)

Fill in the inputs and click Calculate.

Result

—

Equation Breakdown

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Point Comparison

Quantity	Point 1	Point 2

Summary

Solve Bernoulli's equation for pressure, velocity, or elevation at any two points in a steady, incompressible fluid flow.

How it works

Select the fluid type or enter a custom density (kg/m³).
Choose which quantity to solve for: P2, v2, or h2.
Enter all known values for Point 1 and Point 2.
Click Calculate to get the result with the full equation breakdown.
Switch units between Pa, kPa, atm, and PSI as needed.

Use cases

Determine outlet pressure in a pipe narrowing from a wide to a narrow section.
Calculate velocity increase when fluid flows from a large tank into a smaller pipe.
Find the elevation change needed to match a target downstream pressure.
Verify venturi meter readings in engineering lab assignments.
Estimate lift-related pressure differences in simplified aerodynamics problems.
Solve hydraulics homework problems step by step.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu