Stored gas and continuing gas load
A pump-down has two parts. First the pump removes the gas already in the vessel, piping and connected equipment. At the same time, more gas keeps arriving: air leaking through seals and joints, gas released from surfaces and product, and water or solvent vapour boiling off as pressure falls.
At high pressure the stored gas dominates and the pressure falls quickly. At low pressure the stored gas is nearly gone and the continuing gas load controls the result. If that load is large enough, the vessel never reaches the target pressure however long the pump runs. Most disagreements over pump-down time come from ignoring this second part.
The ideal pump-down equation
For a clean, leak-free vessel and a pump with constant speed, the pressure falls exponentially:
t = (V / Seff) × ln(p0 / p1)
- t: time, in hours if speed is in m³/h
- V: total evacuated volume in m³, including piping, filters, condensers and connected equipment
- Seff: effective pumping speed at the vessel, m³/h
- p0: starting absolute pressure, normally about 1,013 mbar(a) at sea level and lower at altitude
- p1: target absolute pressure
This is a useful first estimate, not a selection basis. Real pumps lose speed at low pressure, and real vessels have gas loads.
Worked example: ideal and loaded vessel
Take a 2 m³ vessel including its pipework, a pump giving an effective speed of 100 m³/h at the vessel, and a target of 10 mbar(a) from 1,013 mbar(a).
- Pressure ratio: 1,013 / 10 = about 101.
- ln(101) = about 4.62.
- V / Seff = 2 / 100 = 0.02 h.
- t = 0.02 × 4.62 = about 0.092 h, or roughly 5.5 minutes.
Now add a continuing gas load. Gas load Q is expressed as pressure times volume flow, for example mbar·m³/h. The lowest pressure the pump can hold is roughly p = Q / Seff. If leakage and outgassing total 200 mbar·m³/h, the floor at 100 m³/h is about 2 mbar(a). The vessel can still reach 10 mbar(a), but the last part of the pump-down slows sharply as pressure nears that floor.
If the load were 1,000 mbar·m³/h, perhaps from wet product releasing vapour, the floor would be about 10 mbar(a), and the target would never be reached with that pump. More pump speed, a condenser or a drier product would be needed. These figures are illustrative; your own volume, pump curve and gas load decide the answer.
Effective pumping speed and the connecting line
The speed printed for a pump is at its inlet flange. What the vessel sees is lower because the pipe, valves, filters and bends resist flow. Their combined ability to pass gas is called conductance, C. The effective speed is:
1 / Seff = 1 / Spump + 1 / C
If a pump of 100 m³/h is connected through a line with a conductance of 100 m³/h, the vessel sees only 50 m³/h. In rough vacuum conductance is fairly high, but it falls as pressure drops into the medium-vacuum range, where a long narrow line can waste most of the pump. Keep lines short and wide, with few bends. See vacuum conductance and line design.
Using the real pump curve
Most vacuum pumps have a speed curve that is fairly flat over part of the range and falls towards the ultimate pressure. A Roots booster combination has a curve that rises steeply once the booster cuts in. Using one average speed for the whole pump-down can be badly wrong.
The reliable method is to split the pressure range into bands, read the speed in each band from the curve, correct it for conductance, and calculate the time in each band:
| Step | What to do |
|---|---|
| 1. Choose bands | For example 1,013–500, 500–100, 100–30, 30–10 mbar(a) |
| 2. Read pump speed | Average speed in each band from the supplier’s curve |
| 3. Correct for the line | Apply conductance to get effective speed in each band |
| 4. Subtract gas load | Net removal rate falls as pressure approaches Q / Seff |
| 5. Calculate band time | Use the equation for each band and add the times |
| 6. Compare with need | Check against the process cycle and add margin for wear and fouling |
Smaller bands give a more accurate answer, especially where the curve changes quickly.
Where does the gas load come from?
- Leaks: door seals, flanges, valve stems, sight glasses, instrument fittings and hoses.
- Outgassing: gas and moisture adsorbed on metal surfaces, gaskets, insulation and paint, released slowly under vacuum.
- Process vapour: water or solvent evaporating from product, especially in drying, distillation and degassing.
- Process gas: gas released by reactions, or purge and bleed gas deliberately admitted.
- Temperature: warm vessels and product release vapour faster; cooling during pump-down changes the load.
Vapour load is often the largest item in process vacuum. Removing it with a condenser before the pump can be far cheaper than buying a much larger pump. See vacuum condensable vapour handling.
How to measure gas load: the rate-of-rise test
On an existing vessel, pump down to a stable low pressure, close the isolation valve to the pump and record pressure against time. The gas load is approximately the vessel volume multiplied by the rate of pressure rise:
Q ≈ V × (Δp / Δt)
A straight-line rise suggests a real leak; a rise that slows and levels off suggests outgassing or vapour. Repeat with the vessel empty and loaded to separate equipment leakage from product load. Our vacuum leak and outgassing diagnosis page explains the test in more detail.
Common mistakes in pump-down sizing
| Mistake | Consequence |
|---|---|
| Counting only the vessel volume | Pipework, condensers and filters add volume and time |
| Using the pump’s maximum catalogue speed | Pump-down calculated too short at low pressure |
| Ignoring line conductance | Large pump, poor result at the vessel |
| Ignoring vapour from wet product | Target never reached, oil contamination in oil-sealed pumps |
| Gauge pressure instead of absolute | Wrong pressure ratio, especially at altitude |
| No margin for wear | Cycle time drifts out of specification after months of service |
Choosing a margin for selection
A calculation gives the time for a new, clean system. In service, pumps wear, oil degrades, filters load and seals harden, so the real time grows. Rather than adding a fixed percentage, test the result against realistic changes: a lower pump speed, a higher leak rate and a wetter product. If the cycle still fits, the selection is robust. If a small change pushes the time outside the process window, a larger pump, a booster or a condenser is worth considering.
For critical batch processes, record pump-down time and ultimate pressure at commissioning and check them at each service. A drift in either is the earliest sign that the system needs attention.
How Reddy Compressors helps
We have worked with industrial air and gas systems since 2002, from our office at Tarnaka, Secunderabad. We sell new and used/refurbished vacuum pumps, rent them, service them and supply their spares, across makes, as an independent multi-brand specialist, not an authorised dealer. We have tie-ups with all major and reputed brands. We work through the pump-down and gas-load calculation with you before recommending a pump. Where a Roots booster or blower forms part of the system, we cover that equipment in the same way.
Our team of over 20 service engineers and technicians works across Telangana and Andhra Pradesh, and we supply equipment and spares across India. On existing systems we can help set up rate-of-rise tests and record baselines so that later changes in performance are easy to spot.
What to send us
- Vessel and connected-equipment volume, or drawings
- Starting and target pressures in absolute units
- Required pump-down time and cycle pattern
- Product, moisture or solvent content, and process temperature
- Line size, length and fittings between vessel and pump
- Existing pump nameplate and any rate-of-rise or pressure readings
Frequently asked questions
How do I calculate vacuum pump-down time?
For a first estimate, use t = (V / S) × ln(p0 / p1), with V in m³, S as effective speed in m³/h and pressures in absolute units. Then refine it by splitting the pressure range into bands, reading the real pump curve in each band, correcting for line conductance and allowing for leaks, outgassing and vapour. The banded result is the one to rely on.
Why does my vessel take longer to pump down than calculated?
Usual reasons are a higher gas load than assumed, from leaks or wet product, a pump that has lost speed through wear or contaminated oil, a restrictive line or blocked filter, extra connected volume, or a calculation based on catalogue maximum speed. A rate-of-rise test and a check of pump ultimate pressure on its own will usually show which cause applies.
What is effective pumping speed?
It is the speed actually available at the vessel after the losses of the connecting pipe, valves, filters and condensers. It is found from 1 / Seff = 1 / Spump + 1 / C, where C is the line conductance. A restrictive line can halve the benefit of a pump, so line design deserves the same attention as pump size.
How do I measure the leak rate of a vacuum vessel?
Pump the vessel down, isolate it from the pump and record pressure over time. Multiplying the vessel volume by the rate of pressure rise gives the gas load. A steady straight-line rise points to a leak, while a curve that levels off points to outgassing or vapour. Test empty and loaded to separate the two, then locate leaks with a suitable detection method.
Is a bigger vacuum pump always the answer to slow pump-down?
No. If the line is restrictive, a bigger pump gives little gain at the vessel. If vapour dominates, a condenser upstream may be more effective. If leaks are the cause, fixing them is cheaper and permanent. Work out where the time is being lost, at high pressure or near the target, before choosing extra pump capacity or a Roots booster.
Can you help size a vacuum pump for our vessel?
Yes. Send us the volume, pressures, cycle time and process details. We carry out the pump-down estimate, compare options across makes, and can then sell or rent the selected vacuum pump or Roots booster, new or used/refurbished, service it and supply spares.
Related pages
Calculators and worked examples
These tools give indicative figures for screening, comparison and for preparing an enquiry. They run in your browser and send nothing. No prices or tariffs are assumed: enter your own to see costs. Efficiencies and other figures shown are example values: replace them with your own. Results are not a performance guarantee or a design certificate; final selection is confirmed by a service engineer against the machine data sheet and the site.
Vacuum pump-down time and required pumping speed
Estimate how long a pump takes to bring a vessel from one absolute pressure to another, what the connecting line costs in speed, the lowest pressure a continuing gas load allows, and the speed needed for a target time.
The worked example below shows the method with fixed numbers. Turn on JavaScript to change the inputs.
Worked example
Inputs
- Evacuated volume incl. piping and connected equipment (unit below): 2
- Volume unit: m³
- Start pressure (mbar a): 1013
- Target pressure (mbar a): 10
- Pump speed at its inlet, average over the range from the curve (unit below): 100
- Line conductance, same unit as the speed (0 = no line loss): 0
- Speed and conductance unit: m³/h
- Continuing gas load: leaks + outgassing + vapour (0 = none): 0
- Gas load unit: mbar·m³/h
- Required pump-down time, for the speed check (min; 0 = skip): 0
- Liquid water in the vessel or product?: No (dry)
- Temperature of that water or wet product (°C): 20
Result
- Evacuated volume: 2 m³ = 2,000 litres
- Effective speed at the vessel: 100 m³/h = 27.78 L/s (no line loss entered)
- Pressure ratio p₀ ÷ p₁: 101.3 ln = 4.618
- Ideal pump-down time (no gas load): 5.54 min (333 s, 0.0924 h)
Method. Ideal pump-down: t = (V ÷ S_eff) × ln(p₀ ÷ p₁), with V the whole evacuated volume (vessel, piping, filters, condensers), absolute pressures and S_eff the average effective speed over the range. Effective speed through a line: 1/S_eff = 1/S_pump + 1/C. A continuing gas load Q (leaks, outgassing, vapour, as pressure × volume flow) sets a floor p_floor = Q ÷ S_eff; with that load the time becomes t = (V ÷ S_eff) × ln((p₀ − p_floor) ÷ (p₁ − p_floor)), and a target at or below the floor is never reached. Holding duty: the effective speed needed to hold a pressure p against Q is Q ÷ p. Required speed for a target time: S_eff = V × ln(p₀ ÷ p₁) ÷ t (solved numerically when there is a gas load), then the pump speed that gives it through the line. Units: 1 L/s = 3.6 m³/h; 1 mbar·L/s = 3.6 mbar·m³/h. Water boils when the pressure falls below its vapour pressure (Magnus formula: about 23 mbar at 20 °C, 42 mbar at 30 °C). Constant speed is assumed: real pumps lose speed towards their ultimate pressure, so treat the result as a lower bound and check the maker’s curve, or use the banded tool.
What to take from it. If the target is near the floor Q ÷ S_eff, find and cut the gas load (leaks, wet product, a condenser) before buying a bigger pump; if the line conductance is close to the pump speed, fix the line first.
Technical content reviewed by D. Srinivas Reddy, Managing Partner and service engineer, Reddy Compressors. Last updated 17 October 2026. How our engineering content is reviewed.
Banded pump-down time from the pump curve
Split the pressure range into bands, enter the average pump speed in each band from the curve and the line conductance, and add the band times, with a continuing gas load if there is one.
The worked example below shows the method with fixed numbers. Turn on JavaScript to change the inputs.
Worked example
Inputs
- Evacuated volume incl. piping and connected equipment (m³): 2
- Band boundary pressures, start to target (mbar a): 1013, 500, 100, 30, 10
- Average pump speed in each band, from the curve (m³/h): 100, 100, 100, 100
- Line conductance: one value for all bands or one per band (m³/h; 0 = no line loss): 0
- Continuing gas load (mbar·m³/h; 0 = none): 0
Result
- Band 1: 1,013 → 500 mbar a: 50.8 s (0.847 min, 0.01412 h); S_eff 100 m³/h
- Band 2: 500 → 100 mbar a: 115.9 s (1.931 min, 0.03219 h); S_eff 100 m³/h
- Band 3: 100 → 30 mbar a: 86.7 s (1.445 min, 0.02408 h); S_eff 100 m³/h
- Band 4: 30 → 10 mbar a: 79.1 s (1.318 min, 0.02197 h); S_eff 100 m³/h
- Total pump-down time: 5.54 min (333 s, 0.0924 h)
- Slowest band: Band 2 35% of the total time
Method. For each band from pₐ down to p_b: S_eff = 1 ÷ (1/S + 1/C), floor p_f = Q ÷ S_eff, t = (V ÷ S_eff) × ln((pₐ − p_f) ÷ (p_b − p_f)) (with Q = 0 this is the ideal V/S × ln(pₐ/p_b)). The band times are added. If a band end is at or below its floor, the pump-down stops there. Smaller bands give a better answer where the curve changes quickly. Enter one conductance for all bands, or one per band (conductance falls at lower pressure in viscous flow).
What to take from it. The band that takes longest shows where the time goes: near the target it is usually the gas load or the line, not the pump size.
Vacuum rate-of-rise gas load
Turn an isolation test (pressure rise over time with the pump valved off) into the gas load entering the system, compare a later interval to see whether it is a leak or outgassing, and find the speed needed to hold a working pressure.
The worked example below shows the method with fixed numbers. Turn on JavaScript to change the inputs.
Worked example
Inputs
- Isolated volume incl. pipework (litres): 500
- Pressure at isolation (mbar a): 0.1
- Pressure at the end of the interval (mbar a): 0.6
- Interval (s): 100
- Later interval of the same test: pressure rise (mbar; 0 = not measured): 0
- Later interval: duration (s): 100
- Working pressure for the pumping-speed check (mbar a; 0 = skip): 0
Result
- Rate of rise: 0.005 mbar/s = 0.3 mbar/min
- Gas load Q = V × Δp ÷ Δt: 2.5 mbar·L/s = 9 mbar·m³/h = 0.25 Pa·m³/s
- As air at 20 °C: 10.7 g/h = 0.148 litres per minute of atmospheric air
Method. Q = V × Δp ÷ Δt, with V in litres, Δp in mbar and Δt in s, gives Q in mbar·L/s (× 3.6 = mbar·m³/h; × 0.1 = Pa·m³/s). Mass of air at 20 °C: 1 mbar·L/s ≈ 4.28 g/h. Curve shape (screening values used by this tool): a later interval rising at 80% or more of the first rate points to a real leak; 50% or less points to outgassing or vapour levelling off; between, a mixture. Required effective speed to hold a working pressure p: S = Q ÷ p. The isolated volume must include every pipe up to the closed valve; record temperature, because a warming vessel shows a rise of its own. A leak from atmosphere stays roughly constant only while the inside pressure is well below about half an atmosphere.
What to take from it. The number gives the size of the gas load, the curve shape gives its cause: test empty and loaded, and repeat after more pumping, before replacing seals.