Viscous Flow Pipe Conductance Calculator (Poiseuille)
Tube Conductance Calculator
Results
Conductance: — L/s
or — m³/s
Formula: (π · D⁴ · P_avg) ÷ (128 · η · L)
Results are for preliminary estimation only, not a substitute for review by a qualified/licensed engineer.
Introduction
For vacuum system designers sizing roughing and foreline pipework in UHV systems, this calculator provides a defensible first-pass conductance number for a straight tube before committing to a pump or a line diameter. It accurately applies the Poiseuille equation for viscous flow, a model strictly valid for Knudsen numbers (Kn) less than 0.01.
Understanding tube conductance is critical for optimizing system performance, ensuring efficient gas transport, and minimizing pump-down times. This tool helps engineers quickly assess the impact of various pipe dimensions and operating pressures on gas flow in the viscous regime.
How to Use This Calculator
- Enter the tube's internal diameter in mm.
- Enter the tube length in metres.
- Enter the average pressure in Pa, computed as (P_inlet + P_outlet) ÷ 2.
- Enter the gas dynamic viscosity in Pa·s and read the conductance in L/s; check that the regime badge has not flagged Kn > 0.01.
FAQ
Q: Which pressure do I enter — inlet, outlet, or average?
A: Average: P_avg = (P_inlet + P_outlet) ÷ 2. Viscous conductance scales linearly with the average pressure in the tube, so entering the higher inlet pressure alone inflates the result.
Q: Why does the calculator say my result is outside the viscous-flow regime?
A: Because the Poiseuille equation applies strictly only while the Knudsen number Kn < 0.01; above that, gas–wall collisions matter and the viscous assumption no longer holds, so the number should not be used as-is.
Q: Does tube conductance depend on pressure?
A: In viscous flow, yes — the computed conductance is proportional to P_avg, so doubling the average pressure doubles the result. That pressure dependence is exactly why the Kn < 0.01 check is built in.
Q: What happens if I enter a small diameter error?
A: It is amplified: diameter enters the formula to the fourth power, so a 2× diameter mistake produces a 16× change in conductance — enter the true internal bore in mm, not the outside diameter.