Using Moody Plots to Estimate
Pressure Loss in Pipe Flow
Prepared for Louise C Mallory, Chemical Engineering, Queen’s University
Chee 218: Laboratory Projects I
Thursday January 31, 2002
Author:
John Stephenson, Team K
Lab group members: Jenny Du, Team K
Rebecca McWalters, Team K
Kyra Hillier, Team P
Andrew Munro, Team P
Andrew Wilcox, Team P
Abstract
The use of a Moody diagram, a correlation between friction factor and Reynolds number
has been extensively used to design piping system. In this report, the validity of the
Moody diagram was examined by constructing an appropriate experiment. The apparatus
consisted of a long length of brass pipe carrying water, a flow valve, a rotameter and
various pressure gauges. The flow rate of water was varied and the pressure drop was
recorded. This data was then fit onto a Moody diagram, and found to fit closely with the
data in the literature. Indeed, Moody diagrams can be used to design piping systems.
[make reference to specific information, ~200 words]
Introduction
The Moody diagram is old-fashioned graphical method of estimating pressure drops in
pipes. Newer computational methods such as the Colebrook equation, which requires
iterative solving, and more recently the Wood’s approximation that can be directly solved
for have largely replaced the application of the Moody diagram for routine calculations.
However, Piranha Consulting has used the Moody diagram for the layout of a multibillion-dollar chemical plant which uses water to cool its heat exchangers. Due to the
small number of calculations, the relative ease of using a Moody diagram became
apparent. The water will be quickly flowing through a small 1” brass pipe in these units.
The new project engineer overseeing our design of the chemical plant has expressed
doubt in the validity of using a Moody diagram to design these heat exchangers, and if
the Moody diagram fails to hold, the entire design of the heat exchangers (present
throughout the plant) will have to be scraped, and redone at a great expense.
The purpose of this report is to verify that the Moody diagram can be used to estimate
friction factor values for water flowing through pipes that are typical in the design of the
plant. A simple apparatus consisting of 1” brass pipe in the basement of Dupuis Hall was
rented and used to collect experimental data. The data was then graphically analyzed
using Microsoft Excel.
Theory
The Moody diagram is simply a plot of Reynolds number versus friction factor for
varying relative roughness of pipes.
Reynolds number (Re) is a dimensionless quantity that is calculated from the diameter of
the pipe (D), the average fluid velocity (V), the fluid density () and the fluid viscosity
(). (eqn 1)
Re 
DV

(Equation 1)
Reynolds found that when this dimensionless quantity was below 2000, laminar flow
occurs. When a fluid flow is said to be laminar, it flows in thin layers. In between a
Reynolds number of 2000 and 4000 there is a transition region which consists of shifts
between laminar and turbulent flow. Beyond 4000, the fluid is considered to be turbulent
for the purposes of fluid mechanics. Turbulent flow is a fast and chaotic motion of the
fluid.
When fluid flows through a pipe, various resistances to the fluid flow are encountered.
Mathematically chemical engineers use a friction term (F) to account for energy losses in
flow. (eqn 2)
F
 P

(Equation 2)
The friction term is based on a number of variables and has found to be: (eqn 3)
xV 2
F  2f
D
(Equation 3)
Setting equation 2 and equation 3 equal, we can solve for the friction factor (f) in terms of
pressure drop (-P), fluid velocity (V), density (), and length (x) and diameter (D) of
the pipe. (eqn 4)
f 
 PD
2  V 2 x
(Equation 4)
For turbulent flow, friction factor (f) also depends on the relative roughness of the inner
surface of the pipe. This relatively roughness is simply c/D, where c is the surface
roughness of the material.
Some equations have been formulated to allow c/D, f and Re to be all correlated,
including Wood’s approximation. (eqn 5)
f  a  b Re c
a  0.0235(c / D)
b  22(c / D)
(Equation 5)
0.225
 0.1325(c / D)
0.44
c  1.62(c / D) 0.134
(Wood, 1966)
Experimental Procedure
Figure 1. Photograph of Equipment (courtesy of Steve Hodgson)
The equipment used for this report is located in the basement of Dupuis Hall (fig. 1). It
consists of 1” brass pipe with a variety of pressure taps to measure pressure drops at any
points using the digital pressure meters. The flow rate can be varied using a valve, and
read off of the rotameter shown in the upper left The equipment empties water on the
bottom left to a drain.
Outline of Procedure
1. A 55 gallon bucket was tared on a scale
2. Flow was turned to 20% and the bucket was filled for 2 minutes.
3. The bucket was weighed again, now containing the water
4. The pressure valves were opened to the atmosphere, and the pressure gauge tared,
the valves were then closed.
5. A 0.70m section of pipe was selected and the two appropriate pressure taps were
opened to the digital pressure meter.
6. Nine random flow rates were selected, and one data point was collected for each
point. The measurements were then repeated for the nine points.
7. Steps 4-6 were repeated with another section of pipe 1.20m in length
Safety
 Safety helmets and safety goggles were worn at all times by all members of both
teams.
 Permission to use the equipment was obtained from the lab supervisor.
 All experimental work was supervised
 Fire exits were noted
 No materials (e.g. toxic, flammable, corrosive) or equipment requiring other
safety precautions were handled.
Results & Discussion
Results, which should guide the reader through your experimental results in an
orderly fashion. This
is where your plots and data tables should go -- but beware of significant figures
and improper
plots!
Present your case
Conclusions and Recommendations
The Conclusions section should briefly summarize the major conclusions drawn in
the Body and present
the conclusions in order of importance (most important first). New information or
arguments should not be
presented here.
The Recommendations section (if presented separately) should indicate further work
that needs to be
done. Your recommendation(s) should be written in strong and convincing prose,
relying on material that was presented in the Body. Your first priority is to complete the
task set, i.e. to meet the objectives. However, this is seldom all that there is to an
engineering job. Ask yourself how the analysis or the experimental work can be
extended and what additional contributions can be made within the time deadline of the
job.
References
Noel De Nevers, Fluid Mechanics for chemical engineers, 2nd Edition, McGraw Hill,
1991
Paula Klink, "Energy losses in pipe flow",
http://info.chee.queensu.ca/CHEE218/Labs/Pipes%20and%20Fittings/pipes.htm,
2001.
Don J. Wood, “An explicit friction factor relationship,” Civil. Eng. 36(12): 60-61, 1966
Appendices
Team K and P, the teams representing the primary source of data for this report, was
composed of:
Team K:
Jenny Du
Rebecca McWatters
John Stephenson
Team P:
Kyra Hillier
Andrew Munro
Andrew Wilcox
Other teams worked in pairs and contributed to the data found in this report:
Team
Team Leader
A&B
Felix Yuen
C&D
Joshua Zeifman-Zeelenberg
E&F
Michael Lankin
G&H
Erin Longworth
J&I
Julia Mackenzie
L&M
Kristen Galea
N&O
Michael Westby