F.J. Callahan discusses the leakage formula and the cost of leakage.

The content below is an excerpt from the Swagelok Tube Fitter's Manual. In it, F.J. Callahan discusses the leakage formula and the cost of leakage.

What is leakage?

It is unwanted flow out of or into a fluid system.

How is it expressed?

Leakage is expressed as a flow—a volume per unit of time, cm3/minute, gallons/day etc. The system fluid is the leakage vehicle. Therefore, costs of a given amount of leakage will vary greatly depending on what is leaking. In vacuum systems, leakage is into the system, rather than out of the system. Leakage into a vacuum system is usually expressed in cm3/sec Helium at a 1 atmosphere pressure (atmospheric pressure outside the system, no pressure in the system). Thus a leak rate might be expressed as less than 4  10-9 atmosphere cm3/sec He. This means that no leakage was detectable when the Helium Leak Detector was set to a sensitivity able to detect a leak of 4/1 000 000 000 of a cubic centimeter per second of helium at a one atmosphere pressure differential.

What causes leakage?

The making of metal-to-metal highly reliable seals is a difficult task. Perhaps the clearest study of what causes leakage was developed by the Engineering Standards Committee on Control Valves of the Fluid Controls Institute. This was published in the August 1966 edition of Instruments and Control Systems Magazine.* They found that “zero leakage” was an inaccurate and misleading term, and they set out to more accurately study leakage and how it occurs. 

Leakage formula

Using the data developed for control valve seating and applying it to the two seals of the Swagelok tube fitting (front ferrule to tube and front ferrule to body), we find that leakage depends on the following five factors:

1. “*P” or differential pressure. A 1000 psi (68 bar) system will normally show about 10 times the leakage of a 100 psi (6.8 bar) system.
2. “H” or height of gap between two surfaces. In the formula shown, “H” is cubed. Therefore if leakage is directly proportional to the cube of the gap height, then an improvement in the surface finish of 50 % will result in an 800 % improvement in seal integrity.
3. “W” or width of leakage area. The diameter of the seal will affect leakage—smaller sizes are easier to seal than larger sizes. A 1 in. OD tube is four times more likely to leak than a 1/4 in. OD tube.
4. “U” or absolute viscosity. Fluid viscosity affects leakage rate. The more viscous the fluid, the less leakage will occur.
5. “L” or length of seal. The longer the intimate contact between sealing members, the less leakage will occur.

Swagelok tube fittings take advantage of good design principles and superb manufacturing quality control to make a product that has a long smooth seal and that will perform properly in a very wide range of customer applications. The Gap (H) and Length (L) are the only factors in the formula we can control. Gap can be a problem if tubing surface finish is poor. Since we cannot control operating pressure, seal diameter, or fluid viscosity, we must work within the parameters of gap and length of seal to make good, reliable, repeatable seals. Swagelok tube fittings are often chosen for applications where the costs or consequences of leakage are expensive, inconvenient, or dangerous.

Actual costs (of leakage)

Compressed air costs money! The raw material is free, but the equipment, the energy used to compress it, and the piping system to transport it make up the cost of using (or wasting) air. 

The table below shows the approximate volumes of air leaking from a small orifice at given pressures. Various cost studies on compressed air normally use this “equivalent leak size” to show how costs mount up when a number of small air leaks total the leak from a given orifice size (1/32, 1/16, and 1/8 in.). It doesn’t take long for air leaks in a small system to total up to the equivalent of a 1/32 or 1/16 in. orifice.

* “Should a Control Valve Leak,” Hans Baumann, Instruments and Control Systems, August, 1966.

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