Example 12: Calculate nitrogen flow rate for known pressure drop comparing adiabatic and isothermal models


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In this example Rennels and Hudson tackle a typical plant nitrogen reticulation problem. In their solution they illustrate a novel method of employing the adiabatic model for compressible flow. However, the AioFlo solution using the isothermal compressible model shows that for normal plant pipe sizing work with the pressure drops and velocities typically encountered in reticulation piping the adiabatic and isothermal models give virtually identical results.

Problem Reference

Rennels and Hudson, Pipe Flow - A Practical and Comprehensive Guide, 2012, Page 43, Example 4.5

Fluid Details

Fluid : Nitrogen @ 100 psia, 530R
Phase : Gas (Compressible)
Density (upstream) : 0.4941 lb/ft
Viscosity : 0.018 cP

Pipe Details

Pipe size : 4 inch Sch 40
Pipe ID : 4.026 inch
Roughness : 0.0018 inch
Length : 100 ft
Pressure drop : 15.944 psi
Elevation change : nil
Fittings : incl. as equiv. length

To be Calculated

Calculate the flow rate of nitrogen that would match the given pressure drop

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 Adiabatic Isothermal Incompressible
Reynolds Number (not given) 3 135 661 3 383 665
Friction Factor (Moody) 0.016466 0.01647 0.01646
Flow rate (lb/s) 10.00002 9.994 10.78


The flow rates calculated with the two compressible models differ by only 0.06%. This difference is much less than the typical uncertainties in pipe design regarding the physical properties of the fluids and the dimensions of the piping. The high degree of agreement between these two calculations is put into perspective when the result in the last column above is considered. In this last column the nitrogen is regarded as incompressible (i.e. a liquid) and this introduces an error of almost 8%.

In general, the flow rate calculated with the isothermal model will be slightly less than that calculated with the adiabatic model and this is usually the conservative view. The isothermal model has the advantage of requiring less information than the adiabatic model, and the amount of computation required is significantly less. While the isothermal model is suitable for normal reticulation piping involving typical velocities and pressure drops, the adiabatic model should be used for very high flow rates and pressure drops such as in high pressure vent lines.

AioFlo showing Input Data and Results for Example 12

AioFlo running Example 12