Hagen-Poiseuille Equation Calculator

Formula first

Overview

This equation describes laminar flow conditions where the fluid moves in parallel layers with no disruption between them. It relates the pressure drop across the length of a pipe to the radius of the pipe and the viscosity of the fluid. The result provides the rate at which the fluid volume passes through the cross-section per unit time.

Symbols

Variables

Q = Volumetric Flow Rate, R = Pipe Radius, $\mu$ = Dynamic Viscosity, $\mathcal{P}$_1 = Inlet Pressure, $\mathcal{P}$_2 = Outlet Pressure

Apply it well

When To Use

When to use: Use this equation when analyzing laminar flow of a viscous, incompressible Newtonian fluid through a pipe with a constant circular cross-section.

Why it matters: It is essential for understanding blood flow in the circulatory system, designing lubrication systems, and analyzing flow in microfluidic devices.

Avoid these traps

Common Mistakes

• Applying the equation to turbulent flow conditions, where it is no longer valid.
• Confusing the radius of the pipe with the diameter.
• Failing to convert units for viscosity, resulting in incorrect pressure or flow values.

One free problem

Practice Problem

Calculate the flow rate Q ($m^3$/s) for a fluid with dynamic viscosity 0.001 Pa·s, a pipe radius of 0.01 m, a length of 2 m, and a pressure difference of 100 Pa.

Solve for: $Q$

Hint: Ensure the pressure difference is calculated as (P1 - P2) and units are in SI.

The full worked solution stays in the interactive walkthrough.

References

Sources

1. White, F. M. (2016). Fluid Mechanics. McGraw-Hill Education.
2. Munson, B. R., Young, D. F., & Okiishi, T. H. (2013). Fundamentals of Fluid Mechanics. Wiley.
3. NIST CODATA
4. IUPAC Gold Book
5. Wikipedia: Hagen–Poiseuille equation
6. White, Frank M. Fluid Mechanics. 8th ed., McGraw-Hill Education, 2016.
7. Britannica - Hagen-Poiseuille equation
8. Wikipedia - Hagen–Poiseuille equation