## This content will become publicly available on June 7, 2020

# 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 constant-area 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:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluids Engineering

- Additional Journal Information:
- Journal Volume: 141; Journal Issue: 12; Journal ID: ISSN 0098-2202

- 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. doi:10.1115/1.4043717.
```

```
Kirkland, William M. A Polytropic Approximation of Compressible Flow in Pipes With Friction. United States. doi:10.1115/1.4043717.
```

```
Kirkland, William M. Fri .
"A Polytropic Approximation of Compressible Flow in Pipes With Friction". United States. doi:10.1115/1.4043717.
```

```
@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 constant-area 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 Turbo-Blower

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, Yi-Wei
- Journal of Fluids Engineering, Vol. 132, Issue 1