Canonical: https://echosuite.app/guides/poiseuille/

# Poiseuille flow calculator

Explore poiseuille flow with the method’s inputs, acquisition guidance and source references. Open the calculator to enter measurements or try an illustrative worked example.

Created by [Mohammed Kamareddine, MD](https://echosuite.app/about/) · [Sources & educational scope](https://echosuite.app/about/)

[Open interactive calculator →](https://echosuite.app/calculators/#poiseuille)

## Method

Q = πr⁴ΔP/(8ηL); R = 8ηL/(πr⁴)

Use the measurement units shown below. Some fields apply only to a selected method or condition; follow the interactive tool’s method choices. The interactive tool keeps missing measurements incomplete and provides its method-specific results and reference context.

## Measurements and acquisition

### Tube radius · r  mm

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Tube length · L  cm

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Dynamic viscosity · η  mPa·s

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Pressure drop · ΔP  mmHg

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

## Sources and method context

OpenStax · Rice University · 2016 · Poiseuille flow in a circular tube · University Physics Vol. 1 §14.7 · viscosity and laminar flow

[Primary reference](https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence)

- Flow and resistance · OpenStax University Physics Vol. 1 §14.7

Q = πr⁴ΔP/(8ηL) for ideal laminar flow in a uniform tube. R = 8ηL/(πr⁴); holding flow fixed requires ΔP = QR.

- Circular velocity profile · Deville, An Introduction to the Mechanics of Incompressible Fluids (2022), §3.2.2, doi:10.1007/978-3-031-04683-4_3

The fully developed circular-pipe profile is parabolic, zero at the wall, with centreline speed twice the area-averaged speed.

- Explicit input units · NIST SP 811 Appendix B.9 · pressure and dynamic viscosity

One conventional mmHg is 133.3224 Pa. One mPa·s is 0.001 Pa·s, numerically equal to one centipoise.

Catalogue review status: Source mapped · clinical sign-off pending

These pages describe the educational tool. Interpret measurements with the complete clinical context and the method’s acquisition limitations.

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