How to Calculate Velocity of a Fluid from Pressure (Bernoulli)

Fluid Velocity Formula:

\[ V = \sqrt{\frac{2 \times \Delta P}{\rho}} \]

Fluid Velocity (V): m/s

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Fluid Velocity from Pressure?

Definition: This calculator determines the velocity of a fluid based on pressure difference and fluid density using Bernoulli's principle.

Purpose: It helps engineers and physicists analyze fluid flow in pipes, nozzles, and other systems where pressure changes occur.

2. How Does the Calculator Work?

The calculator uses the Bernoulli-derived formula:

\[ V = \sqrt{\frac{2 \times \Delta P}{\rho}} \]

Where:

\( V \) — Fluid velocity (meters/second)
\( \Delta P \) — Pressure difference (Pascals)
\( \rho \) — Fluid density (kilograms/cubic meter)

Explanation: The formula relates the kinetic energy of the fluid (velocity) to the pressure energy, assuming incompressible, inviscid flow along a streamline.

3. Importance of Fluid Velocity Calculation

Details: Understanding fluid velocity helps in designing efficient piping systems, predicting flow rates, and analyzing energy losses in fluid systems.

4. Using the Calculator

Tips: Enter the pressure difference in Pascals and fluid density in kg/m³ (default 1000 for water). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does this formula make?
A: It assumes steady, incompressible, frictionless flow along a streamline with no height changes.

Q2: What's a typical density for water?
A: Water at 4°C has a density of 1000 kg/m³. For other fluids, check reference tables.

Q3: When is this formula not applicable?
A: For compressible flows, viscous flows, or when significant elevation changes occur.

Q4: How do I measure pressure difference?
A: Use pressure gauges at two points in the flow or calculate from known system parameters.

Q5: What units should I use?
A: Use Pascals for pressure and kg/m³ for density to get velocity in m/s.