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Laminar Pipe Flow by Hagen–Poiseuille — result sheet
Estimate flow rate, mean speed, and Reynolds number for a pressure-driven Newtonian fluid in a circular pipe.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Q = πD⁴ΔP/(128μL); v̄ = Q/(πD²/4); Re = ρv̄D/μ.
Hagen–Poiseuille flow describes steady, fully developed, laminar flow of a Newtonian fluid through a long circular pipe. The fourth-power diameter term makes small changes in diameter especially important, so the calculator also reports Reynolds number as a model check.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Pressure drop — Pa; minimum 1.0E-6; maximum 1000000000000
- Inside diameter — m; minimum 1.0E-6; maximum 1000
- Pipe length — m; minimum 1.0E-6; maximum 1000000000
- Dynamic viscosity — Pa·s; minimum 1.0E-12; maximum 1000000
- Fluid density — kg/m³; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Pressure drop | 100 |
| Inside diameter | 0.01 |
| Pipe length | 10 |
| Dynamic viscosity | 0.001 |
| Fluid density | 1000 |
2.454 × 10⁻⁶ m³/s, 0.03125 m/s, Re = 312.5
Assumptions and limits
- The fluid is incompressible and Newtonian, the pipe is straight and circular, and the flow is steady and fully developed.
- The pressure drop is along the stated pipe length and wall slip, roughness, fittings, elevation, and entrance effects are ignored.
- A Reynolds number above the laminar range means this formula should not be used as a turbulent-flow prediction.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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