Example 8: Calculate pressure drop for compressed air flow through straight pipe as isothermal compressible flow


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This is a simple fluid hydraulics problem to illustrate compressible flow in pipe - it calculates the pressure drop over a given length of straight pipe for compressed air in turbulent flow conditions without any fittings, and neglecting entrance and exit effects. There is no change in elevation between entrance and exit.

Problem Reference

Flow of Fluids through Valves, Fittings, and Pipe. 1999, Crane Co., TP410M, Page 4-9, Example 4-16

Fluid Details

Fluid : Air @ 5 barg and 40C
Flow rate : 3.0 std m/min @ MSC (*)
Phase : Gas
Density (upstream) : 6.70 kg/m
Viscosity : 0.019 centipoise

(*) MSC = Metric Standard Conditions = 15C and 101.325 kPa abs

Pipe Details

Pipe size : 1 inch Sch 40
Inside diameter : 26.6 mm (1.047")
Roughness : 0.05 mm
Length : 25 m
Fittings : None

To be Calculated

Calculate the overall pressure drop, plus the inlet and outlet velocities

Download Link

You can run this example in AioFlo by downloading and opening the data file.

Comparison of Results

Calculated Item Reference AioFlo AioFlo
Fluid model Mixed Incompressible Compressible
Reynolds Number (not given) 154 375 154 375
Flow Regime Turbulent Turbulent Turbulent
Pressure Drop (bar) 0.205 0.2065 0.2109
Inlet Velocity (m/min) 987 987 987
Outlet Velocity (m/min) 1023 987 1023


This example is a good illustration of the accuracy of the old rule of thumb which states that the incompressible model (i.e Darcy-Weisbach equation for liquids) can be used for gases if the calculated pressure drop is less than 10% of the upstream absolute pressure. The pressure drop calculated by Crane is based on a fluid of fixed density (i.e. incompressible), but they have taken the density change of the air into account in calculating the exit velocity. When the Fluid State is set to Liquid in AioFlo then the incompressible model is used and the pressure drop calculated is very close to that calculated in the published example. Changing the model to Compressible in AioFlo is accomplished by one mouse click on the Gas/Vapor option. The table above shows that the pressure drop increases very slightly when the decrease in density along the pipe is taken into account, but the difference between this answer and that obtained by Crane is only 2.9%. For an example of where this rule of thumb does not apply see Example 9.

The calculated pressure drop is about 3.5% of the upstream absolute pressure. The 2.9% difference between the pressure drops calculated by the 2 different models is probably less than the uncertainty in the piping and fluid parameters. In the old days of manual piping calculations it was a valid option to take advantage of this rule of thumb because it saved computational effort and the accuracies were acceptable, but with a program like AioFlo it takes no extra work to calculate the pressure drop rigorously using the isothermal compressible model for gas flow.

There is often confusion over what is meant by compressible or incompressible when describing the models. The usual derivation of the isothermal compressible model (and the one which is used in AioFlo) takes into account the decrease in gas density (and therefore increase in gas velocity) caused by the pressure drop as the gas travels down the pipe. However, the compressibility factor (usually designated as "Z") is assumed to be constant. Many engineers get confused by the fact that the gas is regarded as compressible, but that the compressibility factor is ignored (because it is assumed to be constant). In this example the compressibility factor (Z) of the air changes by 0.01% between the inlet and outlet of the pipe and can certainly be ignored.

In the overwhelming majority of pipe hydraulic applications for gases any changes in the compressibility factor can be safely ignored, but in extreme cases where the pressure drop is so high that the compressibility factor does change along the length of the pipe, the pipe could be broken down into sections and the compressibility factor and inlet density recalculated for each section. But in such an extreme case the assumption of isothermal expansion would probably also be violated, making these methods inappropriate.

AioFlo showing Input Data and Results for Example 8

AioFlo running Example 8 Using Uconeer to convert volumetric flow to mass flow

In AioFlo the flow rate for gases must be given in actual volumetric units at the upstream conditions or in mass units. This second screenshot shows AioFlo's sister program Uconeer being used to convert the given air flow in volumetric units at standard conditions to mass units for use in solving this problem.