Flow Measurement · Free Calculator
Laminar Flow Element and Capillary Flow Calculator
Calculate flow through a capillary tube or laminar flow element, where DP is directly proportional to flow, using the Hagen Poiseuille law, and check that the flow is really laminar.
Hagen PoiseuilleCapillaryLinear DPLow flow
qty
Total flow813.6 mL/min (0.8136 L/min)
Flow per capillary813.6 mL/min
Velocity17.27 m/s
Reynolds number1,145
How this result was calculated
- Q = π d⁴ ΔP ÷ (128 µ L) = 813.6 mL/min per capillary
- Re = ρ v d ÷ µ = 1,145 (laminar)
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Hagen Poiseuille Law
Q = π × d⁴ × ΔP ÷ (128 × µ × L)
Re = ρ × v × d ÷ µ (laminar below about 2000)
Re = ρ × v × d ÷ µ (laminar below about 2000)
d is the capillary inside diameter, L its length, ΔP the pressure drop, µ the dynamic viscosity and ρ the density. The law holds for fully developed laminar flow; real laminar flow elements are calibrated because entrance effects and viscosity changes with temperature matter.
Worked example
Air (µ = 0.0181 cP) through a 1 mm × 100 mm capillary at 10 mbar flows about 0.81 L/min with Re ≈ 1,150 (laminar). At 50 mbar the formula would give 4.1 L/min, but Re ≈ 5,700 is no longer laminar.
Key insight: because DP is linear with flow, laminar flow elements give good turndown and are used for small gas flows, purge rotameter checks and leak test standards; they are very sensitive to viscosity, so temperature must be measured.
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Frequently Asked Questions
What is a laminar flow element?
A bundle of small passages in which flow stays laminar, so the pressure drop is proportional to flow rather than to its square.
Why does viscosity matter so much?
In laminar flow the pressure drop comes from viscous friction, so flow is inversely proportional to viscosity.
What Reynolds number is laminar?
In pipes, below about 2000 the flow is laminar.
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