Poiseuille flow rate formulas and interpretation
The Hagen–Poiseuille equation describes steady laminar flow of a Newtonian fluid through a straight circular pipe.
The migrated interface keeps the original four inputs while using a lighter responsive layout.
How to use the Poiseuille flow rate calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Flow rate increases with pressure drop and radius to the fourth power, and decreases with viscosity and pipe length.
Q = πΔPr⁴/(8μL)- Q — Flow rate
- Volumetric flow (m³/s)
- ΔP — Pressure drop
- Pressure difference along pipe (Pa)
- r — Radius
- Internal pipe radius (m)
- μ — Dynamic viscosity
- Fluid resistance to shear (Pa·s)
- L — Length
- Pipe length (m)
Small pipe example
A 1000 Pa drop drives water-like fluid through a 0.01 m radius, 1 m pipe.
- Pressure drop
- 1000 Pa
- Radius
- 0.01 m
- Viscosity
- 0.001 Pa·s
- Length
- 1 m
- Q = π × 1000 × 0.01⁴ /(8 × 0.001 × 1)
- Q ≈ 0.00393 m³/s
Result: Ideal laminar flow is about 3.93 L/s.
Confirm laminar conditions before relying on the result.
Understanding your results
Interpreting the result
Because radius is raised to the fourth power, small diameter errors cause large flow errors.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.