Formula used
Vacuum conductance C relates volumetric flow to pressure difference, similar to electrical conductance.
For long, straight elements, two limiting regimes are commonly used:
- Molecular flow (long tube): C ≈ 3.81 · √(T/M) · (D³/L) in L/s, with D and L in cm.
- Molecular flow (thin aperture): C ≈ 3.64 · A · √(T/M) in L/s, with A in cm².
- Viscous laminar (isothermal Poiseuille): C = (πD⁴/(256μL)) · (P1+P2) in m³/s, converted to L/s.
- Transitional (Bosanquet): 1/C = 1/Cmol + 1/Cvisc.
- Mean free path: λ = kT /(√2·π·d²·P) and Kn = λ/Dh.
These are engineering-grade estimates for straight components. Valves, elbows, baffles, and traps are often best handled using manufacturer data or measured conductance.
How to use this calculator
- Choose the geometry that matches your vacuum restriction.
- Select the gas and set the temperature of the system.
- Enter upstream and downstream absolute pressures and units.
- Pick a regime, or keep Auto for Kn-based selection.
- Optionally enter pump speed to get effective chamber speed.
- Press Calculate, then export results using CSV or PDF.
Example data table
| Case | Element | Gas | T | P1 → P2 | Key size | Regime | Conductance (L/s) |
|---|---|---|---|---|---|---|---|
| 1 | Circular tube | Air | 20°C | 1e-3 → 1e-4 mbar | L=30 cm, D=2 cm | Auto | ~3.2 |
| 2 | Thin aperture | N₂ | 20°C | 1e-4 → 1e-6 mbar | D=1 cm | Molecular | ~9.1 |
| 3 | Rectangular duct | He | 50°C | 1 → 0.5 mbar | L=20 cm, 2×1 cm | Viscous | Varies |
Examples are illustrative; your values depend on geometry, pressure, and gas properties.
Vacuum Conductance Guide for Practical Systems
1) Why conductance matters
In vacuum engineering, conductance sets the maximum gas flow a line can pass for a given pressure drop. Even a high‑speed pump cannot outperform a restrictive tube or small orifice. This calculator helps you quantify that restriction and avoid under‑performing pumpdowns.
2) Typical unit conventions
Many laboratories use conductance in L/s, while modeling software often uses m³/s. The tool reports both. For throughput, it uses Q = C·ΔP with C in m³/s and pressure in Pa, giving Pa·m³/s, a convenient load metric for sizing pumps and traps.
3) Molecular flow data points
Molecular flow dominates when the mean free path is large compared with the line size. As a rule of thumb, at about 1 mbar the mean free path of air is on the order of 0.1 mm, while at 10−3 mbar it rises to roughly 10 cm. That shift explains why small tubes can become the main limitation in high vacuum.
4) Viscous laminar data points
Viscous conductance depends strongly on pressure and scales with the fourth power of diameter in laminar flow (D⁴). Doubling the diameter can raise viscous conductance by about 16×, while doubling the length halves conductance. This sensitivity makes short, wide connections valuable during roughing and mid‑vacuum operation.
5) Transitional behavior
Between viscous and molecular regimes, neither limit alone is accurate. A common engineering approach is the Bosanquet interpolation, treating molecular and viscous conductance as series restrictions. This calculator applies that method when you select Transitional, or when Auto detects intermediate Knudsen numbers.
6) Gas and temperature effects
In molecular flow, conductance scales with √(T/M), so lighter gases (like helium) pass more easily than heavier gases at the same temperature. Temperature also changes viscosity; the optional power‑law model estimates how conductance shifts when the system is warm, cold, or baked out.
7) Pump speed at the chamber
The effective pumping speed at a chamber equals the series combination of pump speed and line conductance. If a pump is rated 200 L/s but the line conductance is 50 L/s, the effective speed is only about 40 L/s. Enter pump speed to see this limitation instantly.
8) Interpreting the results
Use the Total conductance for quick system checks, compare the molecular and viscous limits to understand regime dependence, and watch the reported mean free path and Knudsen number when using Auto. For elbows, valves, and complex internals, treat these estimates as a baseline and validate with manufacturer conductance data.
FAQs
1) What is vacuum conductance in simple terms?
It is how easily gas flows through a vacuum component for a pressure difference. Higher conductance means less restriction and higher effective pumping speed at the chamber.
2) Should I use P1 and P2 as gauge or absolute pressure?
Use absolute pressure. Vacuum calculations rely on absolute gas density, so gauge values can distort mean free path, Knudsen number, and viscous conductance.
3) When does molecular flow apply?
Molecular flow is typical when the mean free path is comparable to or larger than the line size. In Auto mode, this is reflected by a large Knudsen number.
4) Why does diameter matter so much in viscous flow?
For laminar viscous flow in a round tube, conductance scales with diameter to the fourth power. Small diameter changes can dominate performance during roughing and mid‑vacuum.
5) What does “effective pump speed” mean?
It is the pumping speed seen at the chamber after losses in the connecting line. It is found by combining pump speed and conductance as series limitations.
6) Can I model rectangular ducts accurately?
This tool uses hydraulic diameter to approximate rectangular ducts. It is useful for first‑pass sizing, but high‑accuracy work should use detailed duct correlations or measured conductance.
7) Why is the viscous value missing for an aperture?
Short orifices in viscous flow depend strongly on thickness, edge shape, and discharge coefficients. The calculator focuses on the more robust thin‑aperture molecular conductance.