Enter Pipe and Fluid Data
Plotly Velocity Profile
The curve is parabolic for laminar Poiseuille flow in a circular pipe.
Formula Used
Volumetric flow rate: Q = (π × ΔP × r⁴) / (8 × μ × L)
Average velocity: v̄ = Q / (πr²)
Maximum centerline velocity: vmax = 2v̄
Wall shear stress: τw = (ΔP × r) / (2L)
Reynolds number: Re = (ρ × v̄ × 2r) / μ
Poiseuille flow describes steady, incompressible, Newtonian, fully developed laminar flow through a straight circular pipe.
The radius term is raised to the fourth power, so small radius changes strongly affect the final flow rate.
How to Use This Calculator
- Enter the pressure drop across the pipe section.
- Select the matching pressure, length, radius, viscosity, and density units.
- Provide the pipe length and the internal radius.
- Enter the dynamic viscosity of the working fluid.
- Add fluid density to estimate Reynolds number and flow regime.
- Press Calculate Flow Rate to show results above the form.
- Review the velocity profile, resistance, and laminar validity note.
- Use the export buttons to save a CSV summary or PDF report.
Example Data Table
| Case | ΔP (Pa) | μ (Pa·s) | L (m) | r (m) | Q (L/s) | Average Velocity (m/s) |
|---|---|---|---|---|---|---|
| Water test line | 2000 | 0.001 | 2.5 | 0.003 | 0.025447 | 0.9 |
| Light oil pipe | 12000 | 0.08 | 10 | 0.01 | 0.058905 | 0.1875 |
| Glycerin tube | 9000 | 1.2 | 1 | 0.0025 | 0.000115 | 0.005859 |
| Lab capillary | 3000 | 0.0035 | 0.4 | 0.0012 | 0.001745 | 0.385714 |
These examples assume laminar, fully developed, Newtonian flow in straight circular pipes.
Frequently Asked Questions
1) What does Poiseuille flow mean?
It describes laminar flow in a straight circular pipe when the fluid is Newtonian, incompressible, and fully developed. The velocity profile is parabolic, with the fastest motion at the centerline.
2) When is this calculator valid?
Use it when the pipe is circular, the flow is steady, and the Reynolds number stays in the laminar range. It is most reliable when entrance effects and strong temperature changes are small.
3) Why does radius affect flow so strongly?
The formula contains r⁴, so radius changes have a fourth-power effect. Doubling radius increases ideal laminar flow by sixteen times if every other input stays unchanged.
4) Which viscosity value should I enter?
Enter dynamic viscosity, not kinematic viscosity. Common units are Pa·s, mPa·s, and cP. Water near room temperature is close to 1 mPa·s or 1 cP.
5) Why is Reynolds number included?
Reynolds number helps judge whether laminar assumptions are reasonable. If it rises too high, the flow may become transitional or turbulent, and Poiseuille predictions lose validity.
6) Can I use diameter instead of radius?
Yes. Convert diameter to radius before entry by dividing it by two. The calculator then computes area, average velocity, and Reynolds number from that radius.
7) What happens if pressure drop doubles?
For ideal Poiseuille conditions, flow rate doubles because Q is directly proportional to pressure drop. Average velocity, maximum velocity, and wall shear stress also double.
8) Why might measured flow differ from this result?
Real systems can include fittings, entrance losses, roughness, non-Newtonian behavior, temperature shifts, or developing flow. Those factors can change pressure losses and reduce agreement with the ideal equation.