I am checking the leak rate of a carbon seal installed on an aircraft engine bearing. The test cart has a reading of pounds per hour but my manual says the leakage should not be more than 0.08 cubic metres (2.5 cubic feet) per minute of free air.

Since pounds are a weight measure and cubic metres/feet are volume measures, I can't compare them directly. How do I convert the volumetric flow rate to a mass flow rate?

  • 1
    $\begingroup$ You need to be more specific here. Because the density of air changes with temperature and pressure, you need to provide more information about the state of the air. You can't make a meaningful conversion between a volumetric flow rate and a mass flow rate without knowing the density of the air. $\endgroup$
    – user16622
    May 16 '16 at 5:44

There are several pieces of additional information you need to go from units of volume/time to units of force/time.

For gasses, temperature and pressure matter. Air is mostly nitrogen and oxygen. These have atomic masses of 14 and 16 respectively. Both form diatomic molecules, so air is a mixture of gasses with molecular masses of 28 and 32. Since there is more nitrogen than oxygen, I'm going to say "air" has a molecular mass of 29. Close enough given your precision of "0.08".

At Standard Temperature and Pressure (STP; 1 atm, 0 °C), a mole of ideal gas occupies 22.4 liters. Let's say you're really asking about 21 °C. That's 294 °K as apposed to 273 °K at STP. The volume will therefore be (22.4 l)(294 °K)/(273 °K) = 24.1 l. Since that's one mole, it has a mass of 29 g. Put another way, we've decided the density of your "air" is 29 g/24.1 l.

There are 1000 liters in a cubic meter, so your 0.08 cubic meters is 80 liters, which has a mass of 96.2 g. There are 60 minutes in one hour, so we can compute the mass flow rate in your final time units, which is 5.77 kg/h.

The remaining problem is to convert kg to pounds. Kg is a unit of mass, and pounds is a unit of weight. The conversion depends on gravity. You didn't say if whether this is on the surface of the earth, on the internal space station, or somewhere else. I'll assume the surface of the earth where 1 kg of mass weighs about 2.2 pounds. (5.77 kg)(2.2 lb/kg) = 13 lb.

The final answer is therefore 0.08 cubic meter per minute of air at 1 atmosphere, 21 °C, on the surface of the earth is about 13 pounds/hour.

  • $\begingroup$ on point thank you so much i was checking the leak rate of a carbon seal installed on an aircraft engine bearing.....the test cart had a reading of pph but my manual was saying the leakage should not be more than 0.08cubic metres(2.5cubic feet) per minute of free air....so the problem was convertion from a volume rate to mass rate .... $\endgroup$
    – godfrey
    May 16 '16 at 12:59
  • $\begingroup$ @god: If this is in a aircraft engine, the pressure can be quite different from 1 atmosphere, and the temperature quite different from the 294K I used in the example. You really need to get more specifics. $\endgroup$ May 16 '16 at 13:18
  • $\begingroup$ the testing is done before installation on the engine so the conditions of which we are interested with are those on the ground that is the standard pressure and temperature as you rightfully pointed out ..... $\endgroup$
    – godfrey
    May 17 '16 at 8:56
  • $\begingroup$ Unless otherwise specified, volumetric flow rates for gases should be in Standard Cubic Feet per unit time. e.g. SCF/min. (en.wikipedia.org/wiki/Standard_cubic_feet_per_minute). Mass flow is a better tool in my experience for measuring seal leakage. $\endgroup$
    – DLS3141
    May 17 '16 at 12:32

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