Pumping Speed Calculator: Effective Speed, Throughput & Pumpdown Time

simulator intermediate ~10 min
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Seff = 83.3 L/s — conductance limits pump to 17% of rated speed

A 500 L/s pump connected through a 100 L/s conductance pipe delivers only 83.3 L/s effective speed — the pipe is the bottleneck, reducing usable pumping to 17% of capacity.

Formula

Seff = Sp × C / (Sp + C)
Q = Seff × P (throughput)
t = (V / Seff) × ln(P₀ / Pf)

The Conductance Bottleneck

A vacuum pump's nameplate speed tells only half the story. The pipe connecting pump to chamber has a finite conductance — its ability to pass gas molecules — and the effective pumping speed at the chamber is always less than the rated pump speed. This series combination, Seff = Sp × C / (Sp + C), is the most important equation in practical vacuum system design. Doubling the pump speed helps little if the pipe remains the bottleneck.

Throughput and Gas Load

Throughput Q = Seff × P represents the volumetric flow rate of gas at a given pressure. In steady state, throughput equals the total gas load from outgassing, leaks, and process gas. Understanding throughput helps size pumps correctly — you need enough throughput to handle all gas sources while maintaining the target pressure.

Pumpdown Dynamics

Evacuating a chamber from atmospheric pressure follows an exponential decay: pressure drops as P(t) = P₀ × exp(−Seff × t / V). The time constant V/Seff determines how fast pressure falls. Below about 0.01 mbar, outgassing from chamber walls typically becomes the dominant gas source, and pumpdown slows dramatically compared to the ideal exponential model.

Practical System Design

Experienced vacuum engineers follow the rule: make the pipe as short and wide as possible. Conductance scales as the cube of diameter in molecular flow, so doubling pipe diameter increases conductance eightfold. This simulation visualizes the pump-pipe-chamber system and shows how conductance limitation affects your actual pumping performance in real time.

FAQ

What is effective pumping speed?

Effective pumping speed is the actual rate at which gas is removed from the chamber, accounting for the conductance limitation of the connecting pipe. It is always less than the rated pump speed: Seff = Sp × C / (Sp + C), where Sp is the pump speed and C is the conductance.

What is conductance in vacuum systems?

Conductance measures how easily gas flows through a pipe or restriction, analogous to electrical conductance. For molecular flow, pipe conductance depends on diameter cubed and inversely on length. Low conductance 'chokes' the pump, drastically reducing effective speed.

How do you calculate pumpdown time?

For an ideal system in the viscous/transition regime, pumpdown time t = (V/Seff) × ln(P0/Pf), where V is chamber volume, P0 is starting pressure, and Pf is target pressure. Real systems take longer due to outgassing and leaks.

Why is my pump slower than rated?

The most common reason is conductance limitation — the connecting pipe restricts gas flow. Even a 2000 L/s pump delivers only 50 L/s through a 50 L/s conductance pipe. Maximizing pipe diameter and minimizing length solves this.

Sources

Embed

<iframe src="https://homo-deus.com/lab/vacuum-science/pump-speed/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub