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Open resourceR01 decision: Assess pressure dependent conductance between chamber and pump.
Required asset: Conductance and effective speed example.
Depth: Flow regime; pipe geometry; valves; chamber pressure; effective speed.
Worked comparison: Compare pump speed with chamber effective speed for two lines.
Release gate: State the conductance regime before applying an equation.
1 Direct answer and engineering purpose
Vacuum line design determines how much of a pump's inlet speed is available at the chamber. Establish the gas, temperature, pressure range, actual internal geometry and valve configuration before calculating conductance. Evaluate the flow regime and solve chamber pressure, line throughput and pump inlet pressure together. A catalogue pumping speed by itself does not establish chamber performance.
The required Conductance and effective speed example compares two fictional lines serving the same fictional pump, then tests a valve, a larger pump and a different flow regime. Its numbers are not OEM ratings or universal targets.
The decision is whether the complete installed path can sustain the chamber requirement under the declared gas load and sequence. Selection requires the exact pump curve, applicable component data and installed measurements.
2 Preserve the controlled identity
This records the required correction; it does not claim an earlier Word file or production website has already been revised.
Breadcrumbs, related links and register entries must use the map rather than infer a title from subject proximity.
3 Define the chamber to pump boundary
Draw the path from the chamber pressure reference point to the pump inlet flange. Identify every pipe section, reducer, flexible connector, valve, filter, trap and instrument branch. Record where gas enters and pressure is measured. If a load enters partway along a line, upstream and downstream sections do not carry the same throughput.
Include all open branches in each operating configuration. A roughing bypass creates a different network from a high-vacuum path. A closed valve removes a path; a partially open valve needs an applicable characteristic. A position command is not proof of physical opening.
Define whether the pump curve is quoted at its bare inlet or includes a screen, separator or specified connection. Count each restriction once. A supplier assembly curve must not receive a second deduction for components already within its test boundary.
4 Set the operating states before selecting a model
A line may pass through continuum, transitional and molecular behaviour during evacuation. The model must follow pressure and geometry rather than a general label such as high vacuum. A path acceptable at final hold can still obstruct roughing or delay recovery after gas admission.
State | Conditions to record | Evidence and disposition |
|---|---|---|
Initial evacuation | Chamber and inlet pressure, temperature, valve sequence | Select applicable compressible-flow model |
Intermediate evacuation | Pressure bands and pump curve transitions | Recheck regime and effective speed |
Process hold | Gas species, load, stability | Compare chamber criterion with installed result |
Gas admission | Pulse quantity, duration, route | Assess transient response separately |
Loaded filter or trap | Deposits, temperature, service state | Use service-condition evidence |
Isolation and restart | Trapped volumes and actual valve positions | Verify sequence and recovery |
Multiple chambers | Branch states and coincident loads | Solve shared manifold and pump point |
5 Absolute pressure and throughput definitions
Use absolute pressure for chamber pressure p_c and inlet pressure p_p. Gauge vacuum and percentage vacuum are unsuitable substitutes unless converted with known ambient pressure. Name the measurement location beside each value. A pump-side gauge can indicate satisfactory vacuum while the chamber remains above its limit.
Throughput q has pressure times volume per time units, such as mbar L/s or Pa m³/s. Speed S and conductance C have volume per time units, such as L/s. At an isothermal steady state with negligible pump base-pressure effects, q = p_p S and q = C(p_c − p_p). Chamber-effective speed is S_eff = q/p_c. P1 and P2 support these relationships and their model context.
One mbar L/s equals 0.1 Pa m³/s; one m³/h equals 1/3.6 L/s. Reference flow requires reference absolute pressure and temperature. For ideal gas, throughput at temperature T is p_ref Q_ref T/T_ref. Preserve composition and any necessary compressibility correction. Compressor FAD and piston displacement are not chamber vacuum pumping speeds.
6 Establish the flow regime
Knudsen number Kn = λ/D relates mean free path λ to passage dimension D. Small Kn indicates continuum behaviour, large Kn indicates molecular behaviour, and the intervening range needs transitional treatment. Near a boundary, apply the selected correlation's validity criteria rather than treating a convenient threshold as certification. P3 supports the molecular-flow definition.
Check narrow passages and pressure extremes, not only the main tube. Pressure changes along the path, so the regime may also change spatially. The examples use an air screening approximation λp ≈ 6.7 × 10⁻³ Pa m at room temperature, supported by P4, to test whether molecular assumptions are comfortably satisfied.
In continuum flow, low Kn does not establish laminar flow. Reynolds number, pressure ratio, compressibility, entrance effects and possible choking also matter. A long-tube laminar expression is not an orifice equation and cannot represent every initial evacuation state.
7 Conductance and effective speed
For one steady throughput through an isothermal path, combine the pump and line equations to obtain:
1/S_eff = 1/S + 1/C, or S_eff = SC/(S + C).
For series restrictions carrying that same throughput, 1/C_total = Σ(1/C_i). For independent parallel paths connecting the same pressure nodes, C_total = ΣC_i. Do not combine values quoted for different gases or incompatible operating pressures. P1 supports series and effective-speed relationships; P2 supports network definitions.
If C depends on pressure, evaluate each restriction at its solved local pressures. If S changes with inlet pressure, use S(p_p). Solve q = p_p S(p_p) and q = C(p_c,p_p)(p_c − p_p) consistently. Base pressure, backstreaming, thermal gradients or species-specific pumping may require a more detailed supplier performance model.
8 Geometry that belongs in the calculation
Use actual internal diameter rather than nominal flange size. A large connection may conceal a smaller valve seat or hose tail. Verify bore through reducers and flexible sections. Record centreline length, bends, cross-sectional changes, surface condition and alternate routes.
For a sufficiently long smooth circular tube in molecular flow, air near 20 °C can be screened with C ≈ 12.1D³/L, with C in L/s and both D and L in cm. The worked tubes have L/D = 20. Short tubes and apertures need an appropriate finite-length or transmission-probability treatment. P5 provides the dimensional basis and restrictions.
For this particular model, a small relative diameter error produces about three times that relative conductance error. This derivative is a sensitivity, not a tolerance allowance. Deposits, corrugations and elbows need applicable data; they cannot silently be absorbed into the straight-tube coefficient.
9 Valves filters and traps
Request conductance for the actual gas, regime, opening and direction. A fully open molecular value cannot be applied unchanged to a throttled valve during roughing. General compressed-air flow coefficients require a valid conversion and model before use in a vacuum assessment.
Separate clean and service conditions. Filter loading or trap deposits may change available area. Preserve the protective function when comparing options: removing a trap can expose the pump to an incompatible medium. Assign responsibility for each component characteristic and the complete assembly model.
Where data are missing, mark the restriction Unknown and specify a supplier action or test. An invented equivalent length can conceal the controlling bottleneck. Record whether catalogue data cover an individual component or the whole supplied assembly to prevent double counting.
10 Continuum and transitional operation
For isothermal fully developed laminar air flow near 20 °C through a long smooth circular tube, an approximate expression is C = 135D⁴p_mean/L, where D and L are cm, p_mean = (p_c + p_p)/2 is mbar and C is L/s. Equivalently q = (135D⁴/2L)(p_c² − p_p²). These require continuum laminar validity. P5 supplies the equation basis.
The fourth-power relation belongs to that model. Turbulence, choking, substantial heating, entrance losses or complex fittings require other treatment. Transitional flow needs a validated correlation or specialist calculation for the actual geometry. Choosing whichever limiting formula gives a larger conductance is not a valid design method.
11 Gas temperature and compatibility
Record gas composition and temperatures at chamber and inlet. Molecular corrections depend on molecular mass and temperature; viscous behaviour depends on viscosity and other properties. Do not transfer a correction between regimes. Mixed gases may require species-specific analysis when pump or gauge response differs.
Vapour can condense in a cooler line, changing load and geometry. Dry-air arithmetic is not acceptance evidence for a wet or reactive process. Retain gas, material, seal, cleaning and temperature compatibility as separate release items.
Mechanical vacuum suitability, external-pressure stability, supports, thermal movement and isolation also need applicable project evidence. Conductance does not establish wall thickness or structural rating.
12 Chamber pressure and shared networks
At a continuing gas load, a restrictive path can keep chamber pressure materially above inlet pressure. Increasing pump size gives diminishing benefit as the line controls the result. Compare bore, length, valve and pump-location options at the chamber requirement, including installation constraints.
For multiple chambers, identify each branch's load and admission timing. The common manifold carries summed downstream loads, while each branch carries its own load. Parallel conductances can be added only between the same nodes. Separate chamber-effective speeds are not independent pump capacities.
Recalculate the common inlet pressure when a branch starts, vents or isolates. A single-chamber demonstration does not prove concurrency. Name the controlling branch combination and recovery condition in acceptance.
13 Link the line model to pump down
Pump-down is transient. Chamber and line volumes, changing load, pump curve and valve timing can all matter. A final-pressure S_eff is not necessarily valid across evacuation.
Use justified pressure bands or a dynamic model. A pipe modification changes volume as well as conductance; account for both when assessing time. A percentage increase in effective speed must not be presented as an equal percentage reduction in full process cycle time.
14 Measurement methodology
Provide suitable absolute-pressure measurements at the chamber and inlet, documenting taps and connecting capillaries. Record calibration, zero checks, gas correction, response time and uncertainty. A slow gauge connection can hide a pulse even when data collection is fast.
For a steady test, establish known throughput, hold the defined valve configuration and record both pressures and temperature. Calculate C = q/(p_c − p_p) only when steady state and gas accounting justify it. Metered additional gas may not equal total throughput: measure or account for background load.
Repeat across relevant pressure bands and service states. Retain raw readings, timestamps, instruments, pump controls and anomalies. A tiny pressure difference with large relative uncertainty may not resolve conductance meaningfully. Define the stability window from the process and instrument response, not a generic interval.
15 Diagnostic method
Observation | Evidence to examine | Bounded next step |
|---|---|---|
Chamber high while inlet low | Calibrated gauges and throughput | Investigate path restriction |
Both pressures rise | Curve, pump controls, exhaust and total load | Reconcile operating point before resizing pipe |
Difference grows with service | Filter, trap, temperature and deposits | Compare matched clean and service states |
Slow response after command | Actual valve travel and time traces | Separate opening delay from restriction |
Gas change alters reading | Gauge correction and gas properties | Verify instrument and model applicability |
Pressure rises after isolation | Thermal state and gas release | |
Concurrent operation fails | Branch sequence and manifold pressure | Repeat the defined combination |
These observations guide investigation without proving a mechanism. Preserve what the data exclude as well as what they suggest. A repeat test after a documented change is more informative than assigning all poor vacuum to either leakage or the pump.
16 Hypothetical comparison basis
All following values are fictional training inputs, not equipment ratings or customer results. The gas is dry air near 20 °C. The assumed pump provides S = 100 L/s across the narrow inlet-pressure band, with negligible base-pressure contribution. Selection still requires the actual curve.
Continuing chamber throughput is q = 0.001 mbar L/s. Both candidate lines are smooth straight tubes with no valve, bend, filter or distributed gas source initially included. Line A has D = 5 cm and L = 100 cm. Line B has D = 10 cm and L = 200 cm. Both have L/D = 20. The fictional screening target is chamber pressure at or below 4.0 × 10⁻⁵ mbar absolute at that load.
17 Worked case A Compare two molecular lines
Regime and method: apply the long-tube molecular expression C = 12.1D³/L, then S_eff = SC/(S + C), p_p = q/S and p_c = q/S_eff. Check the resulting highest pressure for molecular validity. Dimensions are centimetres; conductance and speed are L/s.
Quantity | Line A | Line B |
|---|---|---|
Internal diameter and length | 5 cm and 100 cm | 10 cm and 200 cm |
Tube conductance | 15.125 L/s | 60.500 L/s |
Pump inlet speed | 100.000 L/s | 100.000 L/s |
Chamber effective speed | 13.138 L/s | 37.695 L/s |
Pump inlet pressure | 1.000 × 10⁻⁵ mbar abs | 1.000 × 10⁻⁵ mbar abs |
Chamber pressure | 7.612 × 10⁻⁵ mbar abs | 2.653 × 10⁻⁵ mbar abs |
Fictional target result | Fails screen | Passes screen only |
Line A conductance is 12.1 × 5³/100 = 15.125 L/s. Its S_eff is 100 × 15.125/115.125 = 13.138 L/s. The same method gives Line B's results. The pump and load are identical; only the declared connection geometry changes.
Regime check: Line A's maximum pressure is 0.007612 Pa. Using λp ≈ 6.7 × 10⁻³ Pa m gives λ ≈ 0.880 m and Kn ≈ 17.6 for its 0.05 m bore. Line B gives Kn ≈ 25.3 at its chamber end. Both support molecular treatment in this example. Lower downstream pressure increases mean free path. This check does not establish a universal pressure threshold.
Interpretation: Line B has four times the tube conductance despite being twice as long and approximately 2.87 times the chamber-effective speed. Its screen pass is not final acceptance. Fittings, service conditions, exact curve and measurement uncertainty remain to be included.
18 Worked case B Add a valve
Assumptions: retain Line B and add a fictional fully open valve with molecular conductance 40 L/s for the same gas and pressure band. No other restriction is present. Retain the 100 L/s pump and 0.001 mbar L/s load.
Method: C_total = 1/(1/60.5 + 1/40) = 24.080 L/s. Then S_eff = 1/(1/100 + 1/24.080) = 19.407 L/s. Chamber pressure becomes 0.001/19.407 = 5.153 × 10⁻⁵ mbar absolute.
Result: the assumed assembly fails the fictional 4.0 × 10⁻⁵ mbar target although the bare line passed. Component evidence changes the disposition. This demonstrates why the asset must include every restriction. No real valve rating is inferred from the invented 40 L/s input.
19 Worked case C Increase the pump speed
Assumptions: return to the two bare molecular lines. Increase fictional pump inlet speed from 100 to 200 L/s without changing gas, geometry or load. Assume that speed is sustained at the new inlet pressure.
Method: apply S_eff = SC/(S + C). Line A rises from 13.138 to 14.062 L/s, approximately 7.0 percent. Line B rises from 37.695 to 46.449 L/s, approximately 23.2 percent. As pump speed becomes very large, the respective path limits are 15.125 and 60.5 L/s.
Interpretation: doubling inlet speed does not double chamber speed in either fictional arrangement. This identifies a design comparison, not an energy, cost or productivity benefit. Equipment suitability, installation constraints and measured duty remain necessary for an investment decision.
20 Worked case D Solve a laminar operating point
Assumptions: this is a separate continuum case. Dry air near 20 °C flows in a smooth tube of D = 2 cm and L = 200 cm. Fictional pump speed is 5 L/s and throughput is 10 mbar L/s. Assume isothermal, fully developed laminar flow, negligible entrance losses and no accessories.
Method: p_p = q/S = 2 mbar absolute. The coefficient 135D⁴/(2L) is 5.4 L/(s mbar). Solve 10 = 5.4(p_c² − 2²), giving p_c ≈ 2.419 mbar absolute. Mean pressure is approximately 2.210 mbar, C ≈ 23.863 L/s and S_eff ≈ 4.134 L/s.
Validity screen: at the lower pressure of 200 Pa, λ ≈ 3.35 × 10⁻⁵ m and Kn ≈ 0.00168 for the 0.02 m bore. Using room-temperature air properties, mass-flow Reynolds number is approximately 42, supporting laminar treatment. L/D = 100 and the modest pressure ratio support this bounded long-tube screen. Different starting pressures, fittings or temperature conditions still need separate analysis.
Interpretation: conductance here depends on mean pressure. The molecular equation would return only 0.484 L/s and a misleading operating point because its regime is invalid. Recalculate at a new throughput; do not treat 23.863 L/s as constant throughout pump-down.
21 Worked case E Infer conductance from a test
Assumptions: a fictional steady dry-air molecular test records total q = 0.001 mbar L/s, p_c = 8.0 × 10⁻⁵ mbar and p_p = 1.0 × 10⁻⁵ mbar. Background load is included. Temperature, gauge corrections and stability are assumed valid.
Method: C = 0.001/(8.0 × 10⁻⁵ − 1.0 × 10⁻⁵) = 14.286 L/s. Apparent inlet speed is 100 L/s and chamber-effective speed is 12.5 L/s. The reciprocal-speed equation returns the same result, providing an arithmetic cross-check.
For illustration, independent relative standard uncertainties of 3 percent in q and 5 percent in each pressure give approximately 5.8 percent relative uncertainty in the difference and 6.5 percent in inferred C by root-sum-square propagation. These are fictional uncertainty inputs, not instrument specifications. Correlated gauge errors need different propagation. Compare prediction and observation with their uncertainties before declaring a restriction defective.
22 Required asset Conductance and effective speed example
Complete one record per candidate path and operating state. Duplicate it for both lines and every relevant pressure band. Numeric entries require units, evidence revision and status: Measured, Supplier confirmed, Calculated, Assumed or Unknown. Unknown inputs remain open actions. Never preload the worked-case values as production defaults.
A Boundary and duty
Input or evidence field | Project entry | Source status and disposition |
|---|---|---|
Project chamber process and owner | [Enter] | [Evidence and revision] |
Drawing boundary and pressure reference points | [Enter] | [Verified or action] |
Gas composition and temperature | [Enter] | [Basis and applicability] |
Chamber target and permitted variation | [Absolute units] | [Requirement owner] |
Throughput by state and background load | [Units and basis] | [Included loads and exclusions] |
Concurrent branches and valve sequence | [Enter] | [Controlling state] |
Required response or pump-down case | [Enter] |
B Geometry and components
Component input | Project entry | Evidence and disposition |
|---|---|---|
Line A bore length and condition | [Enter] | [Drawing or measured] |
Line B bore length and condition | [Enter] | [Drawing or measured] |
Bends reducers hoses and restrictions | [Each component ID] | [Applicable model] |
Valve opening direction and conductance | [Enter] | [Gas regime and revision] |
Filter trap and service state | [Enter] | [Clean and service evidence] |
Pump curve boundary and fitted accessories | [Enter] | [No duplicate deductions] |
Intermediate sources and alternate paths | [Enter] | [Network accounting] |
C Calculation and measurement
Calculation field | Project entry | Evidence and disposition |
|---|---|---|
Pressure band and regime check | [Kn and continuum checks] | [Validity decision] |
Selected equation units and limitations | [Enter] | [Reference and reviewer] |
Individual and total conductance | [L/s by state] | [Calculation record] |
Inlet pressure and pump curve speed | [Enter] | [Curve revision] |
Chamber effective speed and pressure | [A versus B] | [Comparison result] |
Gas temperature and base-pressure effects | [Correct or justify omission] | [Owner] |
Sensitivity and uncertainty | [Enter] | [Controlling input] |
Throughput and both pressure traces | [Attach reference] | [Calibration and configuration] |
Predicted versus measured result | [Enter] | [Deviation and closure] |
D Release disposition
Release requirement | Evidence or result | Status owner and closeout |
|---|---|---|
Regime stated before applying equation | [Enter] | [Pass Hold or Fail] |
Geometry and accessories reconciled | [Enter] | [Reviewer and date] |
Curve applies at solved inlet pressure | [Enter] | [Reviewer and date] |
Chamber target met at agreed gas load | [Enter] | [Test reference] |
Service state and concurrency covered | [Enter] | [Test or limitation] |
Model and instrument uncertainty acceptable | [Enter] | [Requirement basis] |
Compatibility and mechanical evidence | [Enter] | [Responsible discipline] |
Open actions and operating restrictions | [Enter] | [Owner and due date] |
Technical release | [Name date and conditions] | [Approved Conditional or Hold] |
23 Commissioning and acceptance
Reconcile the as-built route with the calculation before testing. Confirm bore, length, component identity, valve travel, bypass state and cleanliness. Record pump and control configuration. Verify instruments and use the site's approved operating and isolation arrangements.
Test the named gas and throughput conditions. Record chamber and inlet pressures simultaneously over the agreed stability period, including relevant startup, recovery and concurrent states. If a service filter or trap condition controls duty, show how it is represented or retain an explicit limitation. A clean test cannot close an untested service-state requirement.
Accept against a named chamber target, gas load, configuration and operating state. Record acceptance authority and restrictions. A favourable pump-side gauge reading does not replace chamber evidence.
When prediction and test differ materially, examine instruments, load accounting, actual valve position, component data and pump curve before changing the model. Preserve the original calculation and raw data. Revised assumptions require evidence, not values chosen only to reproduce a desired result.
24 Frequently asked questions
Is nominal pump speed available at the chamber
Only the assembled calculation and test establish chamber-effective speed. Finite conductance reduces the speed available under the simplified steady model. Use the relevant inlet pressure, gas and pump configuration.
Can one conductance cover the whole range
Usually it cannot. Conductance can vary with pressure and regime, and each fitting may have its own limits. State the range for every value and reassess it as evacuation or process conditions change.
Does a larger pipe always solve poor vacuum
A larger pipe may help when the path is the controlling restriction. Gas load, pump capability, component condition and instrumentation also matter. The two-pressure test and reconciled throughput support the decision about which change to investigate.
Can compressed air loss tables be used
Only if their physical model, gas, pressure range, geometry and units apply. They are not molecular conductance data. Retain validity limits beside any converted result.
Does a pressure difference establish a leak
No. A pressure difference during flow is consistent with a restriction and does not identify the gas source.
What should an enquiry contain
Provide the chamber criterion, throughput basis, gas and temperature, pressure band, route drawing, component identities, valve sequence, pump curve and pressure traces. Mark missing evidence explicitly so a supplier can address the actual design gap.