A Polytropic Approximation of Compressible Flow in Pipes With Friction
Abstract
This paper demonstrates the usefulness of treating subsonic Fanno flow (adiabatic flow, with friction, of a perfect gas in a constantarea pipe) as a polytropic process. It is shown that the polytropic model allows an explicit equation for mass flow rate to be developed. The concept of the energy transfer ratio is used to develop a close approximation to the polytropic index. Explicit equations for mass flow rate and net expansion factor in terms of upstream properties and pressure ratio are developed for Fanno and isothermal flows. An approximation for choked flow is also presented. Here, the deviation of the results of this polytropic approximation from the values obtained from a traditional gas dynamics analysis of subsonic Fanno flow is quantified and discussed, and a typical design engineering problem is analyzed using the new method.
 Authors:

 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1524879
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluids Engineering
 Additional Journal Information:
 Journal Volume: 141; Journal Issue: 12; Journal ID: ISSN 00982202
 Publisher:
 ASME
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
Citation Formats
Kirkland, William M. A Polytropic Approximation of Compressible Flow in Pipes With Friction. United States: N. p., 2019.
Web. https://doi.org/10.1115/1.4043717.
Kirkland, William M. A Polytropic Approximation of Compressible Flow in Pipes With Friction. United States. https://doi.org/10.1115/1.4043717
Kirkland, William M. Fri .
"A Polytropic Approximation of Compressible Flow in Pipes With Friction". United States. https://doi.org/10.1115/1.4043717. https://www.osti.gov/servlets/purl/1524879.
@article{osti_1524879,
title = {A Polytropic Approximation of Compressible Flow in Pipes With Friction},
author = {Kirkland, William M.},
abstractNote = {This paper demonstrates the usefulness of treating subsonic Fanno flow (adiabatic flow, with friction, of a perfect gas in a constantarea pipe) as a polytropic process. It is shown that the polytropic model allows an explicit equation for mass flow rate to be developed. The concept of the energy transfer ratio is used to develop a close approximation to the polytropic index. Explicit equations for mass flow rate and net expansion factor in terms of upstream properties and pressure ratio are developed for Fanno and isothermal flows. An approximation for choked flow is also presented. Here, the deviation of the results of this polytropic approximation from the values obtained from a traditional gas dynamics analysis of subsonic Fanno flow is quantified and discussed, and a typical design engineering problem is analyzed using the new method.},
doi = {10.1115/1.4043717},
journal = {Journal of Fluids Engineering},
number = 12,
volume = 141,
place = {United States},
year = {2019},
month = {6}
}
Works referenced in this record:
Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio
journal, January 2012
 Christians, Joseph
 International Journal of Mechanical Engineering Education, Vol. 40, Issue 1
Estimating sonic gas flow rates in pipelines
journal, March 2005
 Keith, Jason M.; Crowl, Daniel A.
 Journal of Loss Prevention in the Process Industries, Vol. 18, Issue 2
Flow Analysis and Assessment of Loss Models in the Symmetric Volute of a TurboBlower
journal, January 2012
 Kim, Semi; Park, Junyoung; Choi, Bumseok
 Journal of Fluids Engineering, Vol. 134, Issue 1
A flow rate equation for subsonic Fanno flow
journal, March 2013
 Urata, Eizo
 Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 227, Issue 12
Single Phase Compressible Steady Flow in Pipes
journal, January 2010
 Hullender, David; Woods, Robert; Huang, YiWei
 Journal of Fluids Engineering, Vol. 132, Issue 1
A Novel Adiabatic Pipe Flow Equation for Ideal Gases
journal, January 2012
 Seob Kim, Jung; Radheshyam Singh, Navneet
 Journal of Fluids Engineering, Vol. 134, Issue 1