Method & Equations
The volumetric flow rate for steady, incompressible, fully developed laminar flow of a Newtonian fluid in a circular pipe is given by the Hagen–Poiseuille law:
Q = (π ΔP r⁴) / (8 μ L)
, where Q
is flow rate, ΔP
is pressure drop, r
the pipe radius, μ
the dynamic viscosity, and L
the pipe length.
Average velocity is v = Q / (π r²)
. With optional density ρ
, the Reynolds number is Re = ρ v D / μ
where D = 2r
.
Validity: This correlation applies when Re ≲ 2,000
and entrance/exit and compressibility effects are negligible.
Results
Enter inputs and press Calculate to see results here.
Assumptions
- Newtonian fluid; properties evaluated at a uniform temperature.
- Steady, incompressible, fully developed internal flow in a straight, circular pipe.
- No roughness or minor losses (entrance/exit) included.
- Laminar regime recommended (Re < 2000).
Frequently Asked Questions
1) Which equation does this tool use?
It uses the Hagen–Poiseuille relation for laminar flow in a circular pipe: Q = (π ΔP r⁴) / (8 μ L)
. Average velocity and the Reynolds number are also reported when density is provided.
2) When is this method valid?
It is valid for steady, incompressible, fully developed laminar flow of a Newtonian fluid in a straight circular pipe, typically when the Reynolds number is below about 2,000.
3) What units can I enter?
You can mix units: pressure (Pa, kPa, MPa, bar, psi), length/diameter (m, mm, cm, in, ft), viscosity (Pa·s, mPa·s/cP, lb/(ft·s)). Results appear in SI and common practical units such as L/s and gpm.
4) Does pipe roughness or fittings matter?
This calculator ignores wall roughness and minor losses, which mainly affect turbulent or developing flows. For laminar conditions, roughness has little influence; for turbulent cases, use friction-factor correlations.
5) Can I use it for non-circular ducts?
No. The closed-form relation here assumes a circular cross-section. Non-circular ducts require hydraulic-diameter adaptations or different analytical solutions.
6) Which fluid properties are needed?
Dynamic viscosity is required. Density is optional and only needed for computing the Reynolds number. Both properties vary with temperature, so use values appropriate to your process conditions.
7) Why do my results differ from experiments?
Differences often come from incorrect units, inaccurate viscosity values, temperature variations, entrance effects on short pipes, or operation outside the laminar regime. Ensure your inputs reflect actual conditions.