I am creating a home flight simulation expansion of the Boeing 747 classic series and I have come across an interesting and hard to answer question involving the ductwork of the airplane.

The 747 uses bleed air extracted from the engines/APU or an external ground source to provide air to the various pneumatically operated devices on the airplane (L.E. flaps, air conditioning, reversers, etc.).

On the flight engineer's panel is a very important gauge showing the overall pressure in the duct lines to all of these users. The 747 has a singular circular duct, approximately 6 inches in diameter, to which all sources and users of pneumatic air are connected.

How can I calculate (or closely approximate) the pressure, in psi, in the air ducts for any given set of inputs and outputs? Here is what I know about the system:

EDIT: An important note is that, as far as I am aware, the system is not "demand based" like a lot of newer aircraft. The system supplies a constant amount of pressure to the system based either on APU or Engine RPM.

  • Highly compressed air is taken from the engines and regulated to a maximum of approximate 45-47 psi before entering the duct.
  • The pressure from the engines can be lower than this 45-47 psi figure, for example, at low thrust with the high stage bleeds open, it can be as low as 25-35 psi.
  • Each engine can supply up to 150 ppm of air.
  • The APU can supply 660 ppm at no load, 565 ppm maximum load.
  • Air conditioning packs use 200 ppm each.
  • The duct has a leak rate between 290-390 CFM at 45 psi.
  • Other needs of the pneumatic system can vary their usage.


  • $\begingroup$ What is "ppm"? Pounds per minute? $\endgroup$
    – randomhead
    Jun 23 at 0:14
  • $\begingroup$ Yes, pounds per minute. $\endgroup$ Jun 23 at 0:17
  • $\begingroup$ In our simulations of things like this, we calculated the mass in the volume of interest by summing up inflows and outflows. Knowing the volume and calculating the average gas temperature lets you use the ideal gas law to calculate the pressure. $\endgroup$ Jun 23 at 12:57
  • $\begingroup$ Could you provide an example? I feel like I am so close to understanding how to figure this out but I am getting lost in trying to translate the amounts of air into measurements of pressure. $\endgroup$ Jun 23 at 15:23
  • $\begingroup$ @ChristopherHelton - As OrganicMarble says, PV=nRT Is how you convert volumes into pressure. If you know the mass of air you can get number of moles. Then if the volume and Temp are known you can compute pressure. $\endgroup$
    – Jim
    Jun 23 at 17:22


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