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A Tutorial on Pipe Flow Equations
by
Donald W. Schroeder, Jr.

Stoner Associates, Inc.
P.O. Box 86
Carlisle, Pennsylvania 17013-0086
August 16, 2001

Preface and Dedication
This paper is a form of plagiarism for it contains few new thoughts! The author is extremely
indebted to the following two groups of engineers for developing its concepts fully:
Samuel I. Hyman, Brooklyn Union GasCompany, Brooklyn, New York
Michael A. Stoner, Stoner Associates, Inc, Carlisle, Pennsylvania
, Michael A. Karnitz, Stoner Associates, Inc, Carlisle, Pennsylvania
Gas Flow Formulas – Strengths, Weaknesses and Practical Applications
published in the 1975 AGA Distribution Conference Proceedings
and republished as
Gas Flow Formulas – An Evaluation
in Pipeline and Gas Journal, December1975 andJanuary 1976
J. Christopher Finch, Natural Gas Pipeline Company of America
David W. Ko, Natural Gas Pipeline Company of America
Tutorial – Fluid Flow Formulas
published in the 1988 PSIG Conference Proceedings
In addition, the subject of explicit friction factor equations was definitively covered by:
Garry A. Gregory, Neotechnology Consultants, Ltd., Calgary, Alberta, Canada
Maria Fogarasi,University of Calgary., Calgary, Alberta, Canada
Alternate to Standard Friction Factor Equation
Published in Oil and Gas Journal, April 1, 1985.

They said it all (or mostly all considering some exciting new work published in the year 2000).

Abstract:
The purpose of this paper is to describe the equations which govern the flow of compressible fluids
through pipes. Particular emphasis isplaced on those used within the natural gas industry in hopes that
engineers within that industry can make knowledgeable decisions on how to model pipes. Its thesis is that
all practical equations were created to solve intense numerical problems and have been made obsolete by
advancing computing technology. It further discusses a new flow formula proposed by the GERG
Research project 1.19A Note Concerning Units:
These equations have generally been published in the English system of units. Where appropriate, the
alternate equations in metric units have been included, with the names of the metric units being shown in
italic type. Since the Pole, Spitzglass, and Weymouth equations are included only for historical interest,
only their original published form is presentedBiographical Sketch:
Don Schroeder, whose present title is Director, Technical Affairs, has been employed by Stoner
Associates, Inc. of Carlisle Pennsylvania in various capacities over the past 23 years. During this time he
has served as principal author of SAI's gas steady-state and transient offerings as well as being heavily
involved in their optimization efforts. Prior to joining StonerAssociates, he worked for the former
Columbia Gas System for 12 years: 5 in various engineering capacities within their Pittsburgh Group
Companies, and 7 in their Service Corporation's Operations Research Department. Don's academic
background includes a Bachelor of Science in Chemical Engineering degree from Carnegie Institute of
Technology in its "pre-Melon" days. Don served as secretary of PSIG(Pipeline Simulation Interest
Group) from 1971 to 1973, chairman from 1973 to 1975, and has been the immediate past-chairman ever
since (this is the longest he ever held a job). He also has served as PSIG treasurer since 1989.

Table of Contents
I.
II.
III.
IV.
Appendix A.
Appendix B.

The Fundamental Equation
The Friction Factor
The “Practical” Equations
Some Conclusions andObservations
Nomenclature and Units
Bibliography

Page 1
Page 3
Page 7
Page 13
Page 14
Page 15

I. The Fundamental Equation
During the almost two centuries that the natural gas industry has been in existence there has always been
a need for workable equations to relate the flow of gas through a pipe to the properties of both the pipe
and the gas and to the operating conditions such as...
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