What is the Hagen-Poiseuille equation?

It describes steady, laminar flow of a Newtonian fluid (like water) through a straight cylindrical pipe: Q = (π × r⁴ × ΔP) / (8 × μ × L), where Q is volumetric flow, r is pipe radius, ΔP is pressure difference, μ is dynamic viscosity, and L is pipe length.

When is this equation valid?

It applies when flow is laminar — typically when the Reynolds number is below 2,300. At higher velocities or larger pipes, flow becomes turbulent and the equation underestimates pressure loss. The calculator shows Re so you can check.

What fluid properties does this assume?

Water at 20 °C (68 °F) with dynamic viscosity 0.001002 Pa·s (1.002 cP) and density 998 kg/m³. At higher temperatures the viscosity drops and flow rate increases; for precise work, adjust for temperature.

Why does flow rate scale with the 4th power of diameter?

A pipe twice as wide has four times the cross-section but flow also speeds up more near the center, producing 2⁴ = 16 times the flow. This makes diameter the most powerful lever: doubling the pipe size increases flow 16×.

Can I use this for gases or oils?

The equation works for any Newtonian fluid, but this tool is set up for water. For oils, change the viscosity; for gases, compressibility effects matter and a different equation is needed.

Flow Rate from Pressure Calculator

Name: Flow Rate from Pressure Calculator
Availability: InStock
Author: Nham Vu

Enter pipe dimensions and inlet pressure to calculate water flow rate using the Hagen-Poiseuille equation for laminar flow.

Pipe & Pressure Inputs

Unit System

Inlet Pressure (psi)

Pipe Inner Diameter (inches)

Pipe Length (feet)

Results

Enter values and press Calculate

Equation Reference

Pressure Difference

Gauge pressure at the inlet (assuming outlet at atmospheric). Higher pressure → proportionally more flow.

Pipe Radius (4th Power)

Q scales with r⁴. Doubling the pipe diameter increases flow 16×. Diameter is the dominant factor.

Pipe Length & Viscosity

Flow is inversely proportional to both length and viscosity. Longer pipe or thicker fluid → less flow.

Q = (π × r&sup4; × ΔP) / (8 × μ × L)

Summary

Enter pipe dimensions and inlet pressure to calculate water flow rate using the Hagen-Poiseuille equation for laminar flow.

How it works

Select your unit system: imperial (psi, inches, feet, GPM) or metric (kPa, mm, m, L/min).
Enter the inlet pressure (gauge pressure driving the flow).
Enter the pipe inner diameter and pipe length.
The calculator applies the Hagen-Poiseuille equation for laminar, viscous flow.
Results show volumetric flow rate, velocity, and Reynolds number to verify the laminar assumption.

Use cases

Estimating water flow from a garden hose or irrigation line.
Sizing residential supply pipes for fixture demand.
Checking whether a copper or PVC pipe is large enough for a planned flow.
Troubleshooting low water pressure by identifying flow bottlenecks.
Classroom demonstration of the Hagen-Poiseuille principle.
Verifying laminar flow conditions before applying the equation.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu