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

Background

The examples provide a comparison of AioFlo results with published data from well known and respected references that are generally accessible to engineers. This will allow prospective AioFlo users to validate its accuracy against a range of typical calculations. The worked examples can also be run by new users as part of their learning process. To learn more about AioFlo click on "Home" in the menu above.

Description

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, 530°R Phase : Gas (Compressible) Density (upstream) : 0.4941 lb/ft³ 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

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

Discussion

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.