Pressure after the pumping time
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Pump-down curve
Vacuum system
Gas load at the pumping time
Results
Pumping lines
Pump selection
Pump types whose working range covers the target pressure (chapter 4 tables). The working range ends 5 to 10 times above the ultimate pressure.
Wall strength under atmospheric pressure
Step-by-step calculation
Outgassing and seal library
Typical values from the book (figures 10.1–10.3, tables 10.1–10.2, appendix D). Real rates depend on cleaning, history and pumping time; measure for critical systems.
Screening other materials? NASA's outgassing database lists TML and CVCM (ASTM E595: 24 h at 125 °C in vacuum) for thousands of polymers, adhesives and cables. A common acceptance limit is TML ≤ 1 % and CVCM ≤ 0.1 %. These are mass-loss percentages, not outgassing rates, so use them to choose materials and take the rates for the calculator from the table above or from measurements.
Gas library
Method, assumptions & sources
- Source. Formulas and data from Vacuum Science and Technology (Suurmeijer, Mulder, Verhoeven): kinetic gas theory (ch. 1), gas flow and conductance (ch. 3), pumps and pumping systems (ch. 4), seals (ch. 9), materials, outgassing and permeation (ch. 10, appendix D). The calculator reproduces the worked example of §3.17 and exercises 3-1, 3-2, 3-3, 4-5, 4-6, 4-8 and 4-17 (see the tests in the repository).
- Conductance. Molecular flow: orifice (3.97), short tubes with the Clausing factor 4d/(4d + 3l) (3.109–3.110), long tubes (3.107), rectangular ducts (3.112–3.114), annular gaps (3.105, 3.116) and bends as extra length α·d (3.118). Viscous flow: Poiseuille (3.89, 3.91, 3.93). Transition: the empirical f(d·p) of (3.123) written in d/λ so it applies to every gas; orifices are interpolated between molecular and choked flow (assumption). Conductances scale with √(T/M) (3.120).
- Gas loads. Metals: q = q₁ₕ·(1 h/t) with 10⁻⁶, 10⁻⁵ or 10⁻⁴ Pa·m³/(s·m²) at 1 h (figure 10.1, table 10.1); polymers and ceramics per figure 10.2 (≈1/t^0.6–0.85); after bakeout the values of appendix D. Permeation through O-rings Q = P(T)·Δp·F·πD with the Arrhenius fit of figure 10.3 and a seal geometry factor F = 2, which reproduces the Viton example of §4.11.1 and exercise 4-8. A double O-ring with pumped interspace sees only the interspace pressure (§9.2.1).
- Pump-down. V·dp/dt = Q(t) − S_eff·(p − p_u), integrated with exponential steps (7.4, 7.7); pump speed falls as S₀·(1 − p_u/p) (7.8), the throughput is limited by choked flow through the narrowest section of the line, an optional Roots pump takes over below its switch-on pressure, and the high-vacuum pump at the crossover pressure. The 1/t outgassing law is extrapolated beyond its tens of hours of validity with a warning.
- Pumps. Ultimate pressures, working ranges and typical speeds from the tables of chapter 4; the working range ends 5 to 10 times above the ultimate pressure. Backing pump: S_b ≥ Q_max/p_b,max (exercises 4-3, 4-6).
- Wall strength (not in the book). Cylinders: Windenburg–Trilling elastic buckling with the long-cylinder limit 2E/(1−ν²)·(t/D)³; spheres: 0.25·E·(t/Rₒ)², a lower bound that, with the default safety factor 4, equals the elastic allowable pressure of ASME VIII-1 UG-28(d); flat plates under 1 atm: Roark's formulas for clamped or simply supported rectangular and circular plates. Ports, flanges, welds and stiffeners need a separate check to the applicable pressure-vessel code.
- Not included. Gas mixtures and partial pressures, pump speed curves from data sheets, compression ratio of turbo pumps, desorption peaks during bakeout, diffusion-limited outgassing, virtual leaks, conductance of complex geometries (use a fixed conductance element), thermal transpiration.
- Verification against other sources. Besides the book examples, the tests compare the calculator with standard handbook values for air at 20 °C (orifice 11.6 L/s per cm², long tube 12.1·d³/l, Poiseuille 135·d⁴·p̄/l, choked orifice ≈ 20 L/s per cm²; d and l in cm, p̄ in mbar): all agree within 1 %. Cylinder buckling agrees within 5 % with the von Mises formula of EN 13445-3. Known deviation: the book's short-tube factor 4d/(4d + 3l) is up to about 11 % higher than the exact Clausing values, so short-tube conductances are slightly optimistic.