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# Effective Pumping Speed (EPS)

### What is Effective Pumping Speed?

In this explanation I will reference many other pages on our site. Yes, I know it annoying, particularly since I can't navigate you back here from there. But I'm doing this because I want to keep this explanation simple with no math. I want to show that Effective Pumping Speed is a critical number to all of life's great vacuum mysteries.

Elsewhere I note pumping speed as one of the two numbers that determine a pump's characteristics. As explained there, various methods adopted by various authorities are used by pump manufacturers. Basically, however, the pump is capped off at its inlet and gas is let in at known flow rates while the pressure at each flow is recorded. The results are published as a graph of pumping speed versus pressure. It is reasonable to call these “ideal” conditions since they certainly don't mimic a real-life pumping station at all.

In real-life, the first thing we do is connect the pump's inlet to a hose or tube that is, in turn, connected to the chamber. The tube may actually be connected to other bits and pieces before the chamber connection is made, but let's keep it simple. Consider a 500L/s high vacuum pump connected to a 4-inch (10cm) diameter and 4-inch (10cm) long pumping port on our chamber.

Elsewhere I tell you how to calculate tube conductance using Dushman's table. If you work through the numbers for the pumping port, you will find its conductance is 500L/s.

Elsewhere I show you how to combine a pumping speed with a conductance. Follow the formula and you will determine the combination of a 500L/s pump and a 500L/s port is 250L/s. And what does this last number mean? It is the Effective Pumping Speed in the chamber achieved by connecting the pump via that port. To anthropomorphize this, from the chamber's perspective the pump looks like a 250L/s pump, not a 500L/s pump at all.

In the words of one trainee meeting this vacuum concept for the first time, “Bit sickening, really.”

### EPS Units

Since EPS is a combination of conductance and pumping speed, it retains the units of volume per unit time, such as:

• liters per second: L/s
• liters per minute: L/m
• cubic feet per minute: cfm
• cubic meters per hour: m3/h

### Calculating EPS

Consider a 500 L/s high vacuum pump connected to a chamber by a pumping port 4-inch (10 cm) internal diameter × 4-inch (10 cm) long.

Calculating the port's conductance from Dushman's table gives ~500 L/s. Pumping speed and conductance are combined to give the EPS in exactly the same way two series conductances are combined.

1/EPS = 1/PS + 1/C

So a 500 L/s pump and a 500 L/s port combine as 1/500 + 1/500. That is, the EPS from the chamber is 250 L/s. The simplest connection between pump and chamber halved the pump's quoted pumping speed.

Obviously, this is a serious issue and adding a trap or valve to the connection can only further reduce the pumping speed from the chamber. Unfortunately, all too often we see connections between pump and chamber that are just plain silly. For example, a 500 L/s diffusion pump connected to a chamber by a 0.7-inch (1.8 cm) ID × 1.42-inch (3.6 cm) long tube. Dushman's table gives the tube's conductance as ~10.7 L/s. Combining this with the pump (1/500 + 1/10.7) gives an EPS of ~ 10.5 L/s.

There is no clearer illustration of the maxim: the smallest conductance rules.

### Measuring EPS

One method of measuring EPS uses the fact that in molecular flow the system follows first-order reaction kinetics:

P final = P original × e -kt

Integrating with respect to time

EPS = V/t × log e (Po/Pf)

Where V is chamber volume, t in time, and P o:
P f are the start and final pressures.
Example: a 150 L chamber has a base pressure of 1 × 10-8 Torr. Gas is injected through a valve at a rate that keeps the pressure at 4 × 10-4 Torr with the pumps operating. The valve is shut at time aero 0 s and 16 s later the chamber has reached 6 × 10-6 Torr.

EPS = 150/16 × log e (4 × 10-4)
EPS = 9.38 × log e 66.67
EPS = 9.38 × 4.2
EPS = 39 / L/sec.

Limitations to measuring the EPS this way:

• Formula only works for molecular flow conditions.
• Results are invalid if P o edges into transitional flow.
• If P f is < 50x the chamber's base pressure, wall outgassing will affect the time measurement.