# Compressible Pipe Flow Calculator Spreadsheet

## Background for Compressible Pipe Flow Calculator Spreadsheet

Compressible pipe flow calculations are needed for gas flow if the density of the gas changes during the flow through the pipe.  The fanno flow equations shown below can be used for calculations with a gas flow that has no heat transfer with surroundings.  Frictional losses are taken into account.  The fanno flow equations are shown below.

Example Compressible Pipe Flow Calculator Spreadsheet

An example compressible pipe flow calculator spreadsheet is partially shown in the image below.  This Excel spreadsheet can be used to calculate the frictional pressure drop, or the gas flow rate, or the required minimum pipe diameter.  This Excel spreadsheet, as well as others for pipe flow calculations, is available for both U.S. or S.I. units for a very reasonable price in our spreadsheet store.

References

1.  Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

2. Darcy Weisbach equation history – http://biosystems.okstate.edu/darcy/DarcyWeisbach/Darcy-WeisbachHistory.htm

3. Bengtson, Harlan H.  Fanno Compressible Flow Calculator Spreadsheet,  An online blog article.

4. Bengtson, H.H., Pipe Flow/Friction Factor Calculations with Excel, an online continuing education course for Professional Engineers.

# A Spreadsheet for Choked Air Flow Calculation

## Conditions for Choked Air Flow Calculation with a Fanno Flow Excel Spreadsheet

For flow of air in a pipe with the frictional pressure drop less than 20% of the inlet air pressure, satisfactory results can be obtained using incompressible flow calculations with the Darcy-Weisbach equation.  For background information on that type of calculation, see the article, “Pipe Flow-Friction Factor Calculations with Excel Spreadsheets.”  If the frictional pressure drop is more than 20% of the incoming air pressure, then Fanno Flow equations should be used, as discussed here using a Fanno Flow Excel spreadsheet.

With adiabatic compressible flow conditions, the maximum air flow rate that can pass through a pipe is that which occurs when the exit Mach number is 1.0.  This is referred to as “choked flow.”

## Equations for Choked Air Flow Calculations with a Fanno Flow Excel Spreadsheet

Shown below are the primary equations used in the fanno flow excel spreadsheet being discussed here for compressible flow of air in a pipe.  These equations are for compressible pipe flow with negligible heat transfer with the surroundings, but including effects of friction in the flow.

The parameters in these fanno flow equations are as follows:

• f = Moody friction factor
• L = pipe length
• D = pipe diameter
• k = adiabatic constant for the flowing air
• M = mach number
• T = air temperature
• P = air pressure
• ρ = air density

Parameters with an asterisk refer to conditions at the “choke point” in the pipe, where the Mach number is 1.

## Screenshot for a Choked Air Flow Calculation Spreadsheet Using Fanno Flow Equations

The screenshot below shows part of a fanno flow excel spreadsheet for making compressible air flow calculations.  These calculations are for air flow in a pipe, in S.I. units. This Excel spreadsheet and others for compressible pipe flow calculations in a fanno flow excel spreadsheet are available in either U.S. or S.I. units at a very reasonable cost  in our spreadsheet store.

Reference:

Bengtson, Harlan H.,  “Compressible Flow Pressure Drop Calculator Spreadsheet,” an online blog article