OPERATIONS TRAINING PROGRAM
STUDENT TEXT
Rev. 0
FLUID FLOW
OPERATIONS TRAINING PROGRAM
Contents:
Table of Contents:
NOTICE: If you plan to use this material in a classroom setting, then please purchase
the exam bank and answer key from the Scribd store for $4.99 or visit
marathonjohnb at Scribd. The exam is given at the end of the course and has
specific questions for each chapter ii
Contents: iii
Chapter 1 INTRODUCTION TO FLUIDS 12
Introduction 12
Description of Fluids 13
Humidity 14
Relative Humidity 14
Density () and Specific Volume () 14
Density Differences for Non-Mixable (Non-Miscible) Fluids 15
Specific Gravity 18
Pressure (p) 21
Pressure Measurements 23
Absolute, Gage, and Vacuum Pressure Relations 30
Buoyancy 32
Hydrostatic Pressure 34
Pascal's Law (the law of hydraulics) 39
Pressure Difference for Fluid Flow 41
Chapter 1 Summary 43
Chapter 2 Compression of Fluids 45
Compressibility 45
The Combined Gas Law 45

Effects of Pressure Changes on Confined Fluids 47
Effects of Temperature Changes on Confined Fluids 48
Filling and Venting 48
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Chapter 2 Summary 51
Chapter 3 NATURAL CIRCULATION FLOW 53
Natural Circulation 53
Conditions Required For Natural Circulation 54
Chapter 3 Summary 56
Chapter 4 VOLUMETRIC AND MASS FLOW RATE 57
Volume (V) 57
Volumetric Flow Rate () 59
Mass, Density, and Specific Volume 64
Mass Flow Rate () 66
The Steady Flow Condition 68
Continuity of Flow 68
Chapter 4 Summary 75
Chapter 5 TYPES OF FLOW 77
Laminar Flow 77
Turbulent Flow 77
Factors Influencing Type of Flow 78
Ideal Fluid 79
Noise Level and Flow Rate 79
Chapter 5 Summary 80
Chapter 6 FORMS OF ENERGY &THE GENERAL ENERGY EQUATION 81
General Energy Equation 81
Potential Energy (PE) 83
Kinetic Energy (KE) 84

Flow Energy (FE) 84
Internal Energy (U) 87
Heat, as an operator controlled input or output (Q) 88
Work, as an operator controlled input or output (W) 89
General Energy Equation 89
A Special Case of the General Energy Equation: Bernoulli's Principle 92
Simplified Bernoulli's Equation 94
Specific Energies 96
Chapter 6 Summary: 98
ENERGY CONVERSIONS IN IDEAL FLUID SYSTEMS 99
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Energy Conversions in Ideal Fluid Systems 99
Energy Conversions for Changes in Cross-Sectional Area (Flow Area) 99
Energy Conversions for Changes in Elevation 102
Chapter 7 Summary: 105
Chapter 7 Energy Conversions in Real Fluid Systems 107
Friction 107
Fluid Friction 107
Viscosity 108
Energy Conversion by Fluid Friction in Real Fluids 108
Energy Conversion by Fluid Friction 110
Open versus Closed Fluid Flow Systems 116
Energy Conversions in Closed Systems 116
_Head_ 120
Head Loss due to Friction 125
Throttling 126
Overcoming Head Losses 127
Centrifugal Pump Operation 128

Positive Displacement Pump Operation 129
Using the General Energy Equation to Analyse Real Fluids 130
Specific Rules Using Arrow Analysis 135
The General Energy Equation and Diagnosis using Arrow Analysis 137
Chapter 8 Summary: 149
Chapter 8 Fluid Flow Measurement 151
Flow Measuring Devices 151
Differential Pressure Meters 151
Orifice Plates 151
Flow Nozzles 153
Venturi Tubes 153
Other Applications of the Venturi Principle 154
Chapter 9 Summary: 157
Water Hammer and Pipe Whip 159
Mechanisms of Water Hammer 159
Occurrence of Water Hammer (and Steam Hammer) 159
Cavitation 165
Cavitation in Centrifugal Pumps 165
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Net Positive Suction Head (NPSH) 167
Conditions Causing Cavitation 168
Minimizing Gas Formation in Liquid Piping Systems 170
Other Pump Problems 170
Possible Results of Water Hammer 171
Methods of Water (and Steam) Hammer/ Pipe Jet & Pipe Whip Prevention 174
Chapter 10 Summary 176
Chapter 9 Unintended Siphoning 177
Introduction 177

Siphoning 177
Chapter 11 Summary 180
List of Figures:
Figure 1-1 Example of non-miscible fluids 15
Figure 1-2 Pressure caused by Molecules 22
Figure 1-3 Force versus Pressure 22
Figure 1-4 Pressure Scales 24
Figure 1-5 Typical Pressure Gage 24
Figure 1-6 Liquid Supported by Atmospheric Pressure 25
Figure 1-7 Buoyancy Forces on an Object 33
Figure 1-8 Relationship between Liquid Level and Pressure 34
Figure 1-9 Pressure Versus Height 35
Figure 1-10 Static Head versus Pressure 36
Figure 1-11 Head and Pressure Illustration 38
Figure 1-12 Pressurizing a 40
Figure 1-13 Hydraulic System Forces 40
Figure 1-14 A Simple Hydraulic System 41
Figure 3-15 Air Baloon Buoyancy 53
Figure 3-16 Heat Source / Heat Sink 54
Figure 4-17 Volume of an Object 57
Figure 4-18 Volume of Pipe Section A 58
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Figure 4-19 Volume of Pipe Section B 58
Figure 4-20 Volumetric flow Rate Visual 59
Figure 4-21 Volumetric Flow rate Between Two Points 60
Figure 4-22 Volumetric Flow Rate Example 1 61
Figure 4-23 Volumetric Flow Rate Example 2 63
Figure 4-24 Mass Flow Rate Example 67

Figure 4-25 Continuity of Flow 68
Figure 4-26 Continuity Example 2 71
Figure 5-27 The Two Basic Types of Fluid Flow 78
Figure 6-28 A Visual of Potential Energy 83
Figure 6-29 Visual of Kinetic Energy 84
Figure 6-30 Flow Energy in Compressing Piston 85
Figure 6-31 Flow Energy in Fluid Flow through a Pipe 85
Figure 6-32 Visual of Flow Energy 86
Figure 6-33 Visual of Internal Energy 87
Figure 6-34 Visual of Heat Energy 88
Figure 6-35 Visual of Work Energy 89
Figure 6-36 Fluid Energies 'IN' versus 'OUT' 90
Figure 6-37 Energies Added versus Energies Removed 90
Figure 6-38 Visual of the General Energy Equation 91
Figure 6-39 Bernoulli's Principle 92
Figure 6-40 Ping Pong Ball Floating in Air Stream 93
Figure 6-41 Air Passing Above and Below Airplane Wing 93
Figure 6-42 Air Passing by a Thrown Baseball 94
Figure 7-43 Pipe Section with a Reduction in Area 101
Figure 7-44 Pipe Section With Increase in Area 101
Figure 7-45 Pipe Section with Increasing Elevation 103
Figure 7-46 Pipe Section with Decreasing Elevation 103
Figure 8-47 Straight Pipe Section 109
Figure 8-48 Pipe Section with Changes in size and Elevation 109
Figure 8-49 The Pressure Drop from a 1°F Temperature Rise 111
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Figure 8-50 Pressure Drop and Fluid Friction 114
Figure 8-51 Energy Conversions in a Closed System 117

Figure 8-52 A Simple Closed Loop System 119
Figure 8-53 Closed Loop Example 119
Figure 8-54 Pressure is Proportional to Column Height 120
Figure 8-55 Pressures Within a Fluid Flow System (exaggerated) 123
Figure 8-56 Total Static Head Examples 125
Figure 8-57 Typical Valve 127
Figure 8-58 A Centrifugal Pump 128
Figure 8-59 Pressures Within a Centrifugal Pump 129
Figure 8-60 Positive Displacement Pump 130
Figure 8-61 General Energy Equation in Mental Form 130
Figure 9-62 A Simple Orifice Plate 152
Figure 9-63 A Simple Flow Nozzle 153
Figure 9-64 Simple Venturi Tube 154
Figure 9-65 Auto Carburetor Uses Venturi Principle 154
Figure 9-66 A Typical Steam Jet 155
Figure 9-67 A Simple Eductor 156
Figure 10-68 Case 1 Valve Quickly Closed 162
Figure 10-69 Case 2 Valve Quickly Opened 162
Figure 10-70 Case 3: Cold Condensate in Steam Line 163
Figure 10-71 Case 4: Hot Condensate in Steam Line 163
Figure 10-72 Case 5: Boiling 164
Figure 10-73 Cavitation in a Centrifugal Pump 166
Figure 10-74 Cavitation and the Collapsing Bubble 167
Figure 10-75 Pump Runout 168
Figure 10-76 Low Suction Pressure 169
Figure 10-77 Pipe Rocket / Pipe Jet 172
Figure 10-78 Pipe Whip 173
Figure 11-79 Example of a Siphon 178
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List of Tables:
Table 1-1 Densities of Common Materials 15
Table 1-2 Densities of Common Fluids 21
Table 1-3 Common Pressure Units 26
Table 1-4 Absolute, Gage and Vacuum Pressure 30
List of Terminal Objectives:
TO 1.0Given the necessary fluid system parameters, SOLVE for unknown fluid
parameter values as system conditions are varied 12
TO 2.0Given the necessary fluid system parameters and using the Combined Ideal
Gas Law, DESCRIBE the compressibility or incompressibility of a fluid when a
pressure is exerted 45
TO 3.0For any natural circulation fluid system, DESCRIBE the mechanism that
allows for fluid flow 53
TO 4.0Using fluid system volumetric and mass flow rates, SOLVE for unknown fluid
parameters values to predict fluid system characteristics 57
TO 5.0Given the necessary fluid system parameters, DETERMINE the fluid flow type
and the flow characteristics of that fluid system 77
TO 6.0Given a fluid system, IDENTIFY the forms of energy using the General Energy
Equation 81
TO 7.0GIVEN an Ideal fluid system where no heat is transferred in or out, and no
work is performed on or by the fluid, EXPLAIN the energy conversions that
occur 99
TO 8.0GIVEN a Real fluid system, DESCRIBE the effects of fluid friction to predict
energy conversions 107
TO 9.0EXPLAIN the energy conversions that occur as fluid flows through the Venturi
tube, flow nozzle, and orifice plate flow measuring devices 151
TO 10.0IDENTIFY the conditions and prevention methods for both "water hammer"
and "pipe whip" in fluid systems 159
TO 11.0IDENTIFY the conditions and prevention methods of a fluid siphon for a fluid

system 177
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References:
ARITHMETIC: Student Text, TTFGMAPA.H0102, rev. 2 / Westinghouse Savannah River Company, Aiken, SC
MATHEMATICS: Student Text, TTFGMA1A.H0104, rev. 4 / Westinghouse Savannah River Company, Aiken, SC
Bay, Denise and Horton, Robert B., Macmillan Physical Science, Teacher's Edition, Macmillan Publishing Co., New
York, (1988).
Cline, John W., Thermodynamics, Heat Transfer, and Fluid Flow, Westinghouse Savannah River Company HLW
Fundamentals Training Program, (1993).
Driskell, Les., Control Valve Selection and Sizing, Instrument Society of America, North Carolina, (1983).
Driskell, Les, Control-Valve Selection and Sizing, Independent Learning Module, Instrument Society of America,
Publishers Creative Services Inc., Research Triangle Park, North Carolina, (1983).
Durham, Franklin P., Thermodynamics, 2nd ed., Prentice-Hall, Inc., New Jersey, (1959).
Freeman, Ira M., Physics Made Simple, Revised Edition, Bantan Doubleday Dell Publishing Group, Inc., New York,
(1990).
Giancoli, Douglas C., Physics, 3rd ed, Prentice Hall, New Jersey, (1991).
Glasstone, Samuel and Sesonske, Alexander, Nuclear Reactor Engineering, 3rd ed., Van Nostrand Reinhold Co.,
New York, (1981).
Heimler, Charles H. and Price, Jack S., Focus on Physical Science, Teacher's Edition, Charles E. Merrill Publishing
Co., Ohio (1984).
Hewitt, Paul G., Conceptual Physics a new introduction to your environment, 3rd ed., Little Brown and Company,
Inc., Boston, (1977).
Holman, J. P., Thermodynamics, 4th ed., McGraw Hill, Inc., New York, (1988).
Julty, Sam, How Your Car Works, Book Division, Times Mirror Magazines, Inc., New York (1974).
Murphy, James T., Zizewitz, Paul W., and Hollon, James Max, Physics Principles & Problems, Charles E. Merrill
Publishing Co., Ohio, (1986).
Serway, Raymond A. and Faughn, Jerry S., College Physics, 2nd ed., Saunders College Publishing, Philadelphia,
(1989).

U.S. Department of Energy, DOE Fundamentals Handbook, Thermodynamics, Heat Transfer, and Fluid Flow,
Vols. 1 through 3, U.S. Department of Energy, (1992).
Wiedner, Richard T. and Sells, Robert L., Elementary Classical Physics, College Physics Series, Vol. 1, Allyn and
Bacon, Inc, Boston, (1965).
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Chapter 1 INTRODUCTION TO FLUIDS
This chapter introduces various terms used to describe the characteristics of a fluid and some basic flow
characteristics of given fluids in a typical application. It also presents the relationship between
various parameters within a given fluid system under various conditions
TO 1.0 Given the necessary fluid system parameters, SOLVE for unknown
fluid parameter values as system conditions are varied
EO 1.1 DEFINE the following Fluid Flow terms to include their
typical units: specific volume, density, and specific gravity
EO 1.2 EXPLAIN what will occur when two non-mixable fluids are
placed in the same container
EO 1.3 CALCULATE a fluid’s density, specific volume, or specific
gravity when given any one of the other quantities
EO 1.4 DEFINE the Fluid Flow term “Pressure” to include units
EO 1.5 Given the necessary fluid parameters,
CALCULATE/CONVERT absolute pressure, gage pressure,
feet of head, or vacuum pressure for a fluid system
EO 1.6 EXPLAIN Archimede’s Principle and relate it to the term
“Buoyancy”

EO 1.7 DESCRIBE the relationship between the pressure in a fluid
column and the density and depth of the fluid
EO 1.8 DEFINE the Fluid Flow term “Head” to include units
EO 1.9 EXPLAIN the concept of Pascal’s law, including its
applications.
Introduction
Fluid flow is an important part of most industrial processes; especially those involving the transfer of
heat. Frequently, when it is desired to remove heat from the point at which it is generated, some type of
fluid is involved in the heat transfer process. Examples of this are the cooling water circulated through a
gasoline or diesel engine, the air flow past the windings of a motor, and the flow of water through the
core of a nuclear reactor. Fluid flow systems are also commonly used to provide lubrication.
Fluid flow in the nuclear field can be complex and is not always subject to rigorous mathematical
analysis. Unlike solids, the particles of fluids move through piping and components at different velocities
and are often subjected to different accelerations.
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Even though a detailed analysis of fluid flow can be extremely difficult, the basic concepts involved in
fluid flow problems are fairly straightforward. These basic concepts can be applied in solving fluid flow
problems through the use of simplifying assumptions and average values, where appropriate. Even though
this type of analysis would not be sufficient in the engineering design of systems, it is very useful in
understanding the operation of systems and predicting the approximate response of fluid systems to
changes in operating parameters.
The basic principles of fluid flow include three concepts or principles; the first two of which the student
has been exposed to in previous manuals. The first is the principle of momentum (leading to equations
of fluid forces) which was covered in the manual on Classical Physics. The second is the conservation of
energy (leading to the First Law of Thermodynamics) which was studied in thermodynamics (Heat
Transfer). The third is the conservation of mass (leading to the continuity equation) which will be
explained in this module.

Description of Fluids
A fluid is any substance that flows. The molecules of fluids are not rigidly attached to each other.
Essentially, fluids are materials which have no repeating crystalline structure. Fluids include both liquids
and gases. Liquids are fluids which have a definite volume and take the shape of their container. Gases
also take the shape of their container; however, they will expand to completely fill the container thus they
do not have a definite volume.
Several properties of fluids are discussed in the Heat Transfer course. These include temperature,
pressure, mass, specific volume and density.
Temperature is defined as the relative measure of how hot or cold a material is. It can be used to
predict the direction that heat will be transferred.
Pressure is defined as the force per unit area. Common units for pressure are pounds force per
square inch (psi).
Mass is defined as the quantity of matter contained in a body and is to be distinguished from
weight, which is measured by the pull of gravity on a body.
The specific volume of a substance is the volume per unit mass of the substance. Typical units
are ft
3
/lbm.
Density, on the other hand, is the mass of a substance per unit volume. Typical units are lbm/ ft
3

Density and specific volume are the inverse of one another. Both density and specific volume are
dependant on the temperature and somewhat on the pressure of the fluid. As the temperature of
the fluid increases, the density decreases, and the specific volume increases. Since liquids are
considered incompressible, an increase in pressure will result in no change in density or specific
volume of the liquid. In actuality, liquids can be slightly compressed at high pressures, resulting
in a slight increase in density and a slight decrease in specific volume of the liquid.
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Humidity
Humidity is the amount of liquid vapor suspended in a gas (or the amount of water in air). The units of
humidity are grains per cubic foot. (A grain is the weight of a wheat seed.)
Relative Humidity
Relative humidity is the percentage of liquid that a gas contains compared to being 100% saturated,
(where it can hold no additional liquid). Units are percent.
Relative humidity is a percentage measurement of humidity up to and including saturation at 100% at any
particular temperature. Since air holds more water when it is at a higher temperature, air that is saturated
and then heated will have the capacity to hold more water and will no longer be termed "saturated". The
relative humidity of air will then be less than 100% if it's temperature is increased. As a result, without
changing the amount of liquid suspended within a gas, and by only changing the temperature, the relative
humidity can vary from saturated at 100% relative humidity to something considerably less than
saturated.
A gas can not contain more than 100% of its liquid holding capacity. If the temperature of a 100%
saturated gas is decreased then its capacity to hold moisture decreases and the liquid precipitates. This is
why dew accumulates on leaves and grass when the temperature goes down in the early morning hours.
Density (
ρ
) and Specific Volume (
υ
)
Density,
ρ
, is the amount of mass contained in one cubic foot of space; units are mass per unit Volume.
Specific volume,
υ
, is the amount of space occupied by one pound mass (the force of one pound
converted to mass by dividing by
g

c
); units are Volume per unit mass.
Specific volume is the inverse of density;
υ
=
1
ρ
&
ρ
=
1
υ
.
Where:
ρ
= Density (Greek letter rho), lbm/ft
3
or kg/m
3
, etc.
m = mass, lbm or kg, etc.
V = Volume, ft
3
or m
3
, etc.
υ
= Specific volume, ft
3
/lbm or m

3
/kg , etc.
Both density and specific volume measure the same property: how close the molecules or atoms of a
substance are to each other.
Volume (V) is the amount of space occupied by a three-dimensional figure. Volume is represented by
length units cubed
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
( ft
3
, in
3
, m
3
, etc.).
The specific volume is the amount of space occupied by a unit of mass. Specific volume is the total
volume V divided by the total mass m of an object.
υ =
V
m
Where:
υ
= specific volume, ft
3
/lbm
V = volume, ft
3
m = mass, lbm

A low value of density (or high value of specific volume)
means the molecules or atoms in the substance are relatively
far apart. This is true of gases (hydrogen, oxygen) and for
vapors such as steam. Conversely, a high value of density (or
low value of specific volume) means that the molecules or
atoms are relatively close together. This is true of liquids
(such as water) and solids such as ice.
The density of a material will govern the way it behaves
when put in contact with other materials. Table 1-1 lists the
densities of some common materials. If a material that is
very dense is placed into a container containing a less-dense
liquid, the material will sink. For example, if a piece of iron
is placed into a container of water, the iron will sink because
it is more dense than water.
If, however, that same piece of iron is placed in a liquid that
is more dense, such as mercury, the iron will float. Even
though iron is relatively dense, it is not as dense as the
mercury.
Density Differences for Non-Mixable (Non-Miscible) Fluids
Miscibility is the property of two substances, which
makes them "mixable". Salt and water are miscible so
when they are mixed together they make salt water and
stay mixed until separated by evaporation. But when
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Densities of Some Common Materials:
Material
Density, g/cm
3
hydrogen

9.0 x 10
-5
helium
2 x 10
-4
air
1.3 x 10
-3
Styrofoam 0.1
wood 0.7
alcohol 0.8
ice 0.92
water 1.0
sea water 1.03
aluminum 2.7
rock 3
iron 7
mercury 13.6
Table 1-1 Densities of Common Materials

Figure 1-1 Example of non-miscible fluids
OPERATIONS TRAINING PROGRAM
Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
two substances are non-miscible (not mixable), like oil and water, the water, being the highest density
liquid sinks to the bottom of the container, and the oil being less dense rises to the top. They "unmix"
themselves very quickly. Oil and vinegar salad dressing is an example of this.
Why do some fluids "unmix" themselves? Vinegar is more dense than olive oil; therefore, under the
attraction of gravity the vinegar moves to the bottom of the container. The object with greater mass
creates a greater pressure around itself than an object with a smaller mass. As a result, the lighter objects
get “pushed” out of the way. This pressure then forces the lighter oil molecules out of the lowest regions

and upward where the pressure is lower. A layering effect is created in a salad dressing bottle where the
denser vinegar, under the influence of earth’s gravitation, occupies the bottom of a container while the
less dense olive oil is forced to rest on top.
Some gases do not mix well with other gases. As an example, certain subterranean bunkers that
contained poisonous chlorine gas used during the Second World War is still a potential health hazard for
Europeans. Chlorine gas is a nerve agent and is heavier than air so it tends to pool in the lowest areas. It
does not deteriorate nor dissipate, so it remains active, ready to permanently destroy the nervous system
of anyone who may step into it. In this example it is good for one to know his or her density
fundamentals. In industries today, there are an abundance of chemicals in fluid form (liquid or gas) that
can be equally as dangerous to their surrounding areas.
Like chlorine gas, phosgene gas and carbon monoxide are also heavier than air. Phosgene gas both
suffocates and creates hydrochloric acid in the lungs. It is created in many industrial processes where
foods may rot, or even where an animal decomposes near a confined space. It has the odor of new mown
hay or green corn. Phosgene gas has killed and caused pneumonia in workers who entered unventilated
confined spaces without wearing self contained breathing devices. Carbon monoxide exits from the
exhaust pipe of a vehicle and migrates downward into confined spaces where it displaces the air. It
suffocates a victim by displacing the oxygen in red blood cells.
Radioactive tritium gas is a heavy form of hydrogen gas (an isotope). Tritium is many times lighter than
air so it escapes upward when released. Gas bubbles of tritium in air act like bubbles of air rising from
the bottom of a fish tank. This light gas rises to occupy a thin layer in the highest regions of the gas
envelope that covers the earth.
A comparison of the densities of two (non-mixable) items will allow us to predict which item will float
and which will sink. Consider the following examples:
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Example:
Using information from Table 1-1, Densities of Common Materials, calculate the specific volume
of mercury.

ρ =
1
υ
υ
=
1
ρ
υ =
1
13.6
g
3
cm
υ
= 0.0735
cm
3
g
Example:
An unknown material has a specific volume of
0 37
3
.
cm
g
calculate its density.
ρ =
1
υ
ρ

=
1
0 37
3
.
cm
g
ρ
= 2 703
3
.
g
cm

Example:
An unknown material has a specific volume of
0 0200
3
.
ft
lbm
calculate its density.
ρ =
1
υ
ρ
=
1
00200
3

.
ft
lbm
ρ
= 50
3
lb
ft
m
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Specific Gravity
Specific gravity is the ratio of the density of a fluid or solid to the density of a standard fluid. Water is the
standard of comparison for liquids and solids, and air is the standard of comparison for gases.
For a liquid the ratio
ρ
liquid
ρ
water
is the specific gravity.
For a gas the ratio
ρ
gas
ρ
air
is the specific gravity.
Specific gravity units are a dimensionless number and can be reported without units. When specific
gravity is calculated to be a number greater than the number 1.0 (one) the liquid or gas is more dense than

its standard so may tend to drop to the bottom of a container. When specific gravity is calculated to be a
number smaller than the number 1.0 (one) the liquid or gas is less dense than its standard and may tend to
rise to the top of the container.
Specific gravity is a measure of the relative density of a substance compared to the density of water. It is
the density of the substance divided by the density of water. The density of pure water at standard
temperature and pressure (32
o
F and 14.7 psi) is approximately 62.4 lbm/ft
3
. Knowing the specific gravity
of the substance provides a quick way of determining if the substance will float or sink when put in water.
Specific gravity is a unitless quantity since it is the ratio of two quantities having the same units.
The equation for specific gravity SG is stated as follows:
standard
substance
ρ
ρ
=
SG

Where:
SG = specific gravity of substance
ρ
substance
= density of substance, lbm/ft
3
ρ
standard
= density of the standard. For a liquid the standard is water at 0
o

C and
1 atmosphere of pressure, (the average pressure at sea level). For a gas
the standard is air at 0
o
C and 1 atmosphere of pressure.
water
3 3
lb
ft
1
g
cm
= 1
kg
= 1,000
kg
m
ρ
= 62.4
m
=
3

If the specific gravity of a liquid is greater than 1, it will sink in water. If the specific gravity is less than
1, it will float in water. Also, if the specific gravity of a gas is greater than 1, it will sink in air and
occupy low regions, and if it is less than 1 it will rise in air until it reaches an equilibrium height where
the density of air is equal to its own density. Consider the following examples:
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
Example:
Given:
ρ
water
= density of water, 1.0
g/cm
3
ρ
oil
= density of oil, 0.083
g/cm
3
Calculate the specific gravity
of oil.
water
oil
SG
ρ
ρ
=

3
3
0.1
83.0
cm
g
cm
g

SG
=

0.1
83.0
=
SG

SG = 0.83
Since the specific gravity is less
than 1, the oil will float.
Example
Given:
ρ
water
= density of water, 1.0
g/cm
3
ρ
mercury
= density of mercury,
13.6 g/cm
3
Calculate the specific gravity
of mercury.
water
mercury
SG
ρ
ρ

=

3
3
0.1
6.13
cm
g
cm
g
SG
=

0.1
6.13
=
SG

SG = 13.6
Since the specific gravity is
greater than 1, the mercury will
sink.
Example
Given:
ρ
water
= density of
water, 62.4 lbm/ft
3
υ

ice
= specific volume
of ice, 0.0174
ft
lb
3
m
Calculate the specific
gravity of ice.
ρ =
1
υ
ρ
=
1
00174
3
.
ft
lbm
ρ
= 57 4
3
.
lb
ft
m
SG =
ρ
ice

ρ
water
3
3
ft
lb
62.4
ft
lb
4.57
m
m
SG
=

4.62
4.57
=
SG
SG = 0.92
Since this is less than 1 it will
float.
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids

*Note: Gases are compared to the density of air and not to the density of water.
The standard of comparison for all liquids is water, and the standard for all gases is air. Table 1-2
compares the densities of common fluids, both liquids and gases
Densities of Common Fluids
Fluid Density lbm/ft
3
Acetone 49.421
Air (at 1 atmosphere, 0
°
C) 0.0805
Alcohol (methyl) 50.544
Benzene 56.098
Bromine 198.869
Carbon tetrachloride 99.466
Chlorine (gas) 0.2005
Coconut oil 57.72
Sulfuric acid (fuming) 114.70
Gasoline 42.432
Glycerin 78.624
Helium (at 1 atmosphere, 0
°
C) 0.0112
Hydrogen (at 1 atmosphere, 0
°
C) 0.00561
Kerosene 50.544
Mercury 848.64
Milk 64.272
Water (fresh) 62.4
Water (sea) 63.96

Table 1-2 Densities of Common Fluids
Pressure ( p )
All substances are made of molecules. A molecule is a chemically bonded group of atoms (or elements).
Molecules account for the general characteristics of all fluids, and knowing these characteristics is a
requirement of this course. The key to understanding of these general characteristics of a fluid is found in
comprehending just three things about a fluid:
1) - mass;
2) - the internal energy of a molecule, and
3) - the attraction of each molecule for every other molecule.
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OPERATIONS TRAINING PROGRAM
Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
These key characteristics either alone or taken together explain all of the other characteristic of fluids of
interest in this course. Stated another way; these three characteristics are the major source of the other
general characteristics of every fluid! Therefore, knowing the mass, the internal energy of a molecule,
and the attraction of molecule for molecule explains, viscosity, fluid friction, compression and
decompression pressures, atmospheric pressure, temperature, “head” pressure, buoyancy, hydraulic
pressure, condensation and boiling, and several other fluid characteristics.
Pressure is caused by the
collisions of the molecules of a
fluid with the walls of its
container (See Figure 1.2).
Except at absolute zero
temperature, where by definition
all internal energy is zero and all
movement is stopped, the
molecules of any substance are
constantly moving. In a solid,
the molecules are tightly bound

so that they only vibrate and
rotate. In a liquid or a gas, they also have freedom to translate (move around). The molecules are
continuously colliding with each other and with the walls of their container. As billions of molecules in
each cubic inch of a fluid collide billions of times each second with the walls, they exert forces that push
the walls outward. The forces resulting from these repeated collisions by these molecules add up to the
pressure exerted by a gas on itself and on its surroundings.
Pressure is "the force per unit of area” that a substance exerts on itself and on its surroundings. In a
confined fluid, pressure is always exerted equally in all directions. We use the lower case p for pressure.
pressure =
force
area

p =
F
A
We need to draw a careful
distinction between force and
pressure. Consider the example in
Figure 1.3. Two rectangular
blocks, each with dimensions of 2
by 10 by 20 inches, and each
weighing 500 lbf, are placed on a
table. Each block exerts a
downward force of 500 lbf on the
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Figure 1-2 Pressure caused by Molecules
A
B

10 in
2 in
20 in
2 in
20 in
10 in
Figure 1-3 Force versus Pressure
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
surface of the table, but because they apply that force over different areas, the pressures they exert on the
table are different.
Block A applies 500 lbf over an area of 200 in
2
. It will exert a pressure given by:
p
A
=
500lbf
20 in • 10 in
p
A
= 2.5
lbf
in
2
= 2.5 psi
Block B applies 500 lbf over an area of 20 in
2
. It will exert a pressure given by:
p

B
=
500lbf
2 in • 10 in
p
B
= 25
lbf
in
2
= 25 psi
The pressure exerted by Block B is ten times that exerted by block A even though the applied force is the
same. This is because the weight of block A is distributed over a larger area.
Pressure ≠ Force
Pressure Measurements
Pressure is a force divided by an area.

In the English system, we measure pressure in pounds per square inch. In SI, the pressure unit is the
pascal. These two units are given as follows:
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
1
1
1
2
=
f


2
psi
lb
in
1 Pa =
1 N
m
kg
m s
2
=
•
There are two standard methods used to measure pressure:
• The amount of pressure above a perfect vacuum (absolute), and
• The amount of pressure above or below atmospheric pressure, (gage).
Pressures referenced to a perfect vacuum are called absolute pressures. In the United States, we use psi
for our pressure measurements. An absolute pressure then has the unit "pounds per square inch -
absolute" or psia. The letter "a" is not a unit; it is a label. It simply tells us what the reference pressure is.
Zero pressure on the absolute scale is the absence of all pressure. Outer space is nearly a perfect vacuum.
Achieving a nearly perfect vacuum on earth is not difficult. The space above the mercury column in a
barometer is a nearly perfect vacuum. Atmospheric pressure is the amount of pressure exerted on the
earth's surface by the weight of the air molecules in the atmosphere. The atmospheric pressure at sea
level is 14.7 psia.
Pressure referenced to the earth's atmospheric pressure is called gage pressure, and is given as "pounds
per square inch - gage" or psig. Again, the "g" is simply a label telling us what the reference pressure is.
Figure 1.4 shows the relationships between absolute pressure measurements and gage pressure
measurements. In doing problems, psig will cancel with psia since the units are psi even though the
references are different.
From Figure 1.4 the following relationship can be determined:
p

absolute
= p
atm
+ p
gage
A pressure gage is an instrument which measures pressure. To clear up any confusion; a pressure gage is
a piece of hardware; a gage pressure is a pressure referenced to atmospheric pressure. Pressure gages
indicate the amount of pressure sensed
relative to a reference pressure.
Figure 1.5 shows a typical bellows type
pressure detector.
Other types of pressure detectors use
similar arrangements to measure the
difference between an unknown pressure
and the reference pressure. Pressure
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TY P ICA L P R E S SU R E GAGE
M EASURED P R ES SURE
BELL O W
S
R EF ER ENCE
PRESSUR E
IN DIC A TED
P R E S S U R E
I S
DIF FER EN C E B E TW EE N
M EAS UR ED PRESSUR E
R EF ER EN C E PRESSUR E and
Figure 1-5 Typical Pressure Gage


Figure 1-4 Pressure Scales
OPERATIONS TRAINING PROGRAM
Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
gages referenced to atmospheric pressure indicate the amount of pressure above or below atmospheric
pressure. The units for these pressure gages are psig (lbf/in
2
gage) for pressure above atmospheric and
psiv (lbf/in
2
vacuum) for pressure or vacuum below atmospheric.
Finally, pressures and
vacuums may be expressed
in terms of the height of a
liquid column the pressure
will support. These include
inches of water, feet of
water, and inches of
mercury. Millimeters of
mercury is also a common
unit for measuring pressure.
Millimeters of mercury is
also given the name torr.
One torr equals one
millimeter of mercury.
Figure 1.6 shows that
atmospheric pressure at sea level, 14.7 psia, would support a mercury column 29.92 inches high or a
water column 34.0 feet high (408 inches).
Table 1-3 compares some of the common pressure units to atmospheric pressure. Unless otherwise stated
each of these pressure units is assumed to be an absolute pressure.

1 atm 14.7 psia
1 atm
408 in. of H
2
O
1 atm 29.92 in Hg
1 atm 760 mm Hg
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Figure 1-6 Liquid Supported by Atmospheric Pressure
1.6 Liquid Supported By Atmospheric Pressure
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Student Guide: Fluid Flow Chapter 1: Introduction to Fluids
1 atm 760 torr
1 atm
101 10
5
. ×
Pa
Table 1-3 Common Pressure Units
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