What this calculator does
Poiseuille's Law works out volumetric flow rate of a viscous fluid through a cylindrical pipe under laminar flow. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaQ = πΔP·r⁴ / (8ηL)
The inputs explained
| Field | What to enter |
|---|---|
| Pressure difference (Pa) | A number, measured in Pa. Starts at 1000. |
| Pipe radius (m) | A number, measured in m. Starts at 0.01. |
| Dynamic viscosity (water ≈ 0.001) (Pa·s) | A number, measured in Pa·s. Starts at 0.001. |
| Pipe length (m) | A number, measured in m. Starts at 1. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with pressure difference
Every other input is held at the calculator’s starting values while pressure difference varies. Select any row to load that scenario into the calculator.
How the answer changes with pressure difference
| Pressure difference (Pa) | Volumetric flow rate | Volumetric flow rate | Average flow velocity |
|---|---|---|---|
| 500 | 0.001963 m³/s | 1.963 L/s | 6.250 m/s |
| 750 | 0.002945 m³/s | 2.945 L/s | 9.375 m/s |
| 1,000 | 0.003927 m³/s | 3.927 L/s | 12.500 m/s |
| 1,500 | 0.005890 m³/s | 5.890 L/s | 18.750 m/s |
| 2,000 | 0.007854 m³/s | 7.854 L/s | 25.000 m/s |
| 3,000 | 0.011781 m³/s | 11.781 L/s | 37.500 m/s |