Flammability Limits and Propagation Rates of Premixed Flames
Flammability Limits
Burning Velocity
Explosions, Deflagrations, and Detonations
Chemical Mechanisms of Combustion of Gases
Elementary Chemistry
Hydrogen Oxidation
Premixed Methane–Oxygen Flame Chemistry
Combustion of Larger Hydrocarbon Fuels
Specific Hazardous Gases
Hydrogen (H2)
Acetylene (C2H2)
Methane (CH4)
Ethylene (C2H4)
Ammonia (NH3)
Chapter 8
Fire Characteristics: Liquid Combustibles
Ignition of Liquids: Flash Point, Fire Point, and Autoignition Temperature
Burning Rates of Liquid Pools
Flame Spread Rates over Liquid Surfaces
Hazards of Liquid Fuel Fires
Chapter 9
Fire Characteristics: Solid Combustibles
Fire Stages and Metrics
Solids versus Gases and Liquids
Materials and Products
Pyrolysis
Ignition to Flaming Combustion
Ignition to Nonflaming Combustion
Char Formation and Melting
Mass Burning and Flame Spread
Combustible Solids
Cellulosic and Other Natural Materials
Synthetic Polymeric Materials
Fire Retardants
Composite Materials and Furnishings
Acid–Base Pairs
Metals
Exothermic Materials
Chapter 10
Combustion Products
Smoke Aerosols
General Nature
Soot Formation
Aerosol Mist Formation
Measurement of Aerosol Yields
Quantity of Smoke Particles Produced
Visibility through Smoke
Gaseous Combustion Products
CO2 and H2O
CO
Partially Oxidized Organic Molecules
Hydrogen Halides
HCN
Nitrogen Oxides
Other Combustion Gases
Smoke Alarms
Chapter 11
Smoke and Heat Hazards
Hazards of Smoke Exposure
Toxicity of Prominent Fire Gases
Carbon Monoxide
Carbon Dioxide
Hydrogen Cyanide
Hydrogen Chloride and Hydrogen Bromide
Nitrogen Oxides
Organic Irritants
Other Toxic Species
Oxygen Deficiency
Smoke Toxic Potency Measurement
Nonthermal Smoke Damage
Thermal Damage
The Limiting Hazard Concept
Chapter 12
Movement of Fire Gases
Structure of a Fire Plume in the Open Fire Plume under a Ceiling
Filling of a Fire Compartment by Smoke
Smoke Flow from a Compartment with an Opening
Smoke Movement in Buildings
Chapter 13
Fire Fighting Chemicals
Categories of Fire Suppressants
Aqueous Agents
Water
Enhanced Water
Aqueous Foams
Nonaqueous Agents
Inert Gases
Active Halogenated Agents
Dry Chemical Agents
Special Considerations for Fire Extinguishment
Extinguishment of Flowing Gas Flames
Extinguishment of a Shallow Liquid Fuel Spill Fire
Extinguishment of a Deep Tank Liquid Fuel Fire
Ultrafast Extinguishment of Fires
Chapter 14
Computational Modeling of Fires
Types of Models
Users of Models
Zone Models
The Zone Approximation
The Consolidated Model of Fire and Smoke Transport Zone Model
Field Models
Characteristics of Field Models
The Fire Dynamics Simulator
Computational Modeling and the Limiting Hazard Concept
Values and Limitations of Models
Appendix A
FESHE Correlation Guide
Appendix B
Imperial and Metric Conversions
Glossary
Index
INSTRUCTOR, STUDENT, AND TECHNOLOGY RESOURCES
Instructor Resources
Instructor’s ToolKit CD
Preparing for class is easy with the resources on this CD, including:
• PowerPoint Presentations Provides you with a powerful way to make presentations that are educational and engaging to your students. These slides can be modified and edited to meet your needs.
• Lesson Plans Provides you with complete, ready-to-use lesson plans that include all of the topics covered in the text. Offered in Word documents, the lesson plans can be modified and customized to fit your course.
• Test Bank Contains multiple-choice questions, and allows you to create tailor-made classroom tests and quizzes quickly and easily by selecting, editing, organizing, and printing a test along with an answer key, including page references to the text.
• Image and Table Bank Provides you with a selection of the most important images and tables found in the textbook. You can use them to incorporate more images into the PowerPoint presentations, make hand outs, or enlarge a specific image for further discussion.
Technology Resources
Navigate Course Manager
Combining our robust teaching and learning materials with an intuitive and customizable learning platform, Navigate Course Manager gives you the tools to
build a solid, knowledgeable foundation with world-class content. With Navigate Course Manager, learning is no longer confined to the four walls of the classroom. Now you can learn anytime and anywhere, when it is ideal for you.
World-class content joins instructionally sound design in a user-friendly online interface to give students a truly interactive, engaging learning experience with:
• eFolio, an engaging eBook that offers study advantages far beyond the print textbook. With anytime access to complete textbook content, interactive eBooks allow students the flexibility to navigate between the text and enhanced activities for greater understanding of core concepts.
• Course Management tools that simplify the management and delivery of curriculum and assessments to students enabling anytime, anywhere access to learning. Instructors can track real-time progress, manage assignments, and view results in the grade book.
ACKNOWLEDGMENTS
Over the course of my career in fire science, I have benefited from numerous collaborations, initially with colleagues at the U.S. Naval Research Laboratory, mostly at the National Institute of Standards and Technology (formerly the National Bureau of Standards), and continuously from interactions with fire professionals both in the United States and around the world. Special thanks to Rick Peacock for his assistance with resources for computer modeling. Preparing the latest edition of this book was a pleasure due to the quality of Ray Friedman’s earlier edition. During the preparation of this manuscript (and the years preceding it), I have benefited from the patience, love, and support of my wife, Debbie Gann.
Richard G. Gann, PhD Montgomery Village, MD September 2013
Reviewers and Contributors Brian Bagwell, Psy.D.
Metropolitan State University of Denver Denver, Colorado
Timothy W. Baker
Lansing Community College
Lansing, Michigan
David A. Budde
EMS & Fire Science Technology Director
Lake Land College
Mattoon, Illinois
Melvin Byrne
Virginia Department of Fire Programs
Fairfax, Virginia
Kevin L. Hammons
IRIS Fire Investigations
Englewood, Colorado
Gary Johnson
Central Ohio Technical College
Newark, Ohio
Sherry LaQua-Hanchett Portland Community College Portland, Oregon
Stephen S. Malley
Weatherford College Public
Safety Professions
Weatherford, Texas
Byron Matthews
Cheyenne Fire and Rescue
Cheyenne, Wyoming
Larry Perez, Program Director New Mexico State University at Dona Ana Las Cruces, New Mexico
Mike Richardson
St Matthews Fire Department
Louisville, Kentucky
Christopher M. Riley
Portsmouth Fire, Rescue, and Emergency Services
Portsmouth, Virginia
John Shafer
Green Maltese
Greencastle Fire Department Greencastle, Indiana
Douglas Smith
Portland Community College
Portland, Oregon
Robert Solomon, PE
NFPA
Quincy, Massachusetts
Kenneth Staelgraeve
Macomb Community College
Clinton Township, Michigan
Peter J. Struble
Practitioner in Residence
Fire Science Program Wallingford, Connecticut
Michael Wolever
Toledo Fire and Rescue (ret.)
Bowling Green State University Bowling Green, Ohio
INTRODUCTION
How Do Chemistry and Physics Relate to Fire Protection?
The Evolution of Fire and Fire Science
Personal and public safety is enhanced by familiarity with the science of how fires start, grow, and are controlled. This is the premise of this book. Over the millennia of human existence, the evolution of this understanding has curtailed the impact of unwanted fire on a societal scale. Our application of this knowledge today can reduce the threat to our own lives and possessions. As recently as 1985, unwanted fires in the United States cost 6200 lives, 28,400 injuries, and $14.8 billion in property damage. Modern fire science has reduced these numbers, but in 2010, unwanted fires in the United States still cost 3100 lives, 17,700 civilian injuries, 72,000 fire fighter injuries, $11.6 billion in property damage, and 10,000 square miles of burned forests and wildlands [1, 2]. The total cost to the economy was a staggering $350 billion.
Fire is older than civilization. The first fuels, in the form of vegetation, appeared on our planet some 500 million years ago, and the first wildfires were ignited by lightning and volcanoes. Our first hominid ancestors appeared approximately 5 million years ago. These nomadic creatures lived through great destruction from the uncontrolled spread of fires. They also learned by observation that rain falling on a fire could limit harm to them and ignition of the surrounding plant life [3, 4].
It was not until about 400,000 years ago that our forebears learned how to get hold of something burning. They found great value in controlled fire: it provided warmth, made food easier to eat, and kept away wild animals. They still did not know how to start a fire, so skill at keeping a fire burning at all times was schooled and valued, and someone who allowed a fire to go out was subject to punishment.
Less than 1000 generations ago, the species we refer to as Cro-Magnon had begun living in established clusters and locations. Within their small enclaves,
they raised crops and engaged in hunting and gathering. More importantly, they had learned how to start fires. Fire was used to clear land for farming, to capture and keep livestock, and to bake clay and work metal. The development of more permanent homes and greater possessions also meant these early humans now had more to lose from a fire.
As the centuries passed, the number of large, dense, urban centers grew; being constructed of wood and other flammable or combustible materials, these nascent cities were especially vulnerable to fire. In what is now Europe, more than 40 recorded conflagrations occurred between 31 BC and 410 AD. Successive cultures developed penal codes to deter arson, building codes to mitigate large fires, and permanent water supplies and fire brigades to fight fires.
And yet, inexorably, as recently as the beginning of the 20th century, conflagrations continued to destroy large portions of cities, such as Baltimore (Figure I-1) and Chicago. Rapid fire growth in single buildings, such as the 1911 Triangle Waist Company in New York, continued to claim many lives.
The latter part of the 19th century had seen the emergence of modern chemistry as a science that could be used to explain many natural phenomena. By this time, Newton’s 17th-century formulation of the basic laws of physics had also been expanded greatly. The field of combustion science was born, and fuel-burning engines were developed to provide power to cities and motorized transport.
At this point in human history, it was realized that fire is a form of combustion. As such, fire is a chemical process that behaves according to the laws of physics. It follows that understanding of the pertinent chemical and physical principles provides the basis for preventing and controlling fire.
Figure I-1 Map of the Baltimore, Maryland, area destroyed by the 1904 fire [5].
Map courtesy of the University of Texas Libraries, The University of Texas at Austin
The chemistry of fire encompasses the chemical make-up of the items that burn, the chemical reactions that give rise to flames and other fire products, the chemical reactions that retard or suppress burning, and the harmful chemical reactions of the fire products with people and property. Certain physical principles are also important in the understanding of fire. Notably, the laws governing momentum and energy apply. They underlie the rate of mixing of air into the flames, the buoyant rise of the fire gases to the ceiling and the subsequent motion under the ceiling, the escape of smoke from a burning room into connecting compartments, and the rate at which heat is transferred from the flames to not yet ignited material or to people trying to escape the fire.
The Role and Contents of This Book
This text introduces the scientific concepts and principles needed to understand fire and its consequences, and how it is controlled. In essence, it provides the basics of what could be called fire literacy. The text is directed at people who are embarking on a fire science curriculum and at those who would simply like to learn more about this fascinating, yet threatening, phenomenon. It is intended to stimulate thinking about such questions as these:
• What is a fire?
• How do fires start, grow, and go out?
• Which fire hazards are of concern?
• What can a computer model of a fire do?
Principles of Fire Behavior and Combustion, Fourth Edition is a highly expanded and updated successor to Principles of Fire Protection Chemistry and Physics, Third Edition. It addresses all the course objectives and learning outcomes for the National Fire Academy FESHE Model Curriculum Associate’s (Core) course called Fire Behavior and Combustion.
The first five chapters of this text are an elementary review of the formalism and fundamentals of chemistry and physics that govern fire behavior. Effort has been made to show the relevance of what might appear, at first glance, to be esoteric material. Many of the specialized words in the text are defined in the glossaries at the end of each chapter and again at the end of the text. Even if you are already well versed in chemistry and physics, you should at least skim this
material; it will both serve as a refresher and establish a common basis for the material to follow. If you have never taken courses in chemistry or physics, you might benefit from obtaining an introductory textbook on chemistry (e.g., C. H. Corwin’s Introductory Chemistry: Concepts and Critical Thinking, sixth edition, Pearson Prentice Hall, 2010) and physics (e.g., D. Halliday, R. Resnick, and J. J. Walker’s Fundamentals of Physics Extended, ninth edition, Wiley, New York, 2010). I also found that a web search was useful in filling in some gaps.
The subsequent nine chapters of this text describe combustion; the fire characteristics of materials (gases, liquids, and solids); the properties, movement, and effects of combustion products (temperature, smoke, toxicity, and corrosivity); and fire extinguishing agents and procedures. The principles behind the hardware and tactics of firefighting are included, but the applications are left to other references, examples of which are cited. The text provides information on special situations that might confront the fire fighter or be of interest to the fire protection engineer (e.g., spontaneous ignition, exothermic materials, and fires in abnormal environments) and on the computer modeling of fires.
In the new edition, the text has been changed to be friendlier to the reader who is encountering many of these subjects for the first time. Each chapter contains introductory material that identifies the importance and context of the chapter content, as well as the capabilities the reader will develop from that content. There are new examples relevant to fires, additional data and figures to reinforce the text, and extensive references for those who might want to learn more about any of the subjects.
Compared to the third edition, the fourth edition contains new material throughout.
• This introduction outlines the history of fire and its role in society, the early realization that fire is a chemical phenomenon, and indicates how the understanding of fire principles leads to enhanced ability to prevent and control unwanted fires.
• Chapter 1, “Fire Measurement and the SI System of Units” now explains how different sets of units arose, why it is important to be able to convert among alternate units for the same property, how to report and use numbers to the degree of precision that is appropriate; and why fires are characterized by enthalpy rather than energy.
• Chapter 2, “Chemical Elements and Compounds: Atoms and Molecules,” now explains how the molecules in common materials are named and
shows the different ways that molecules can be portrayed, depending on the properties that the viewer needs to see.
• Chapter 3, “Physical and Chemical Change,” has additional information on the states of matter; explanations of how molecular behavior leads to the material properties we sense; extended descriptions of phase changes, with examples related to fires; and presentation of the equivalence ratio, which determines the heat generation and the nature of combustion products from a fire.
• Chapter 4, “Flow of Fluids,” now contains an expanded presentation of Newton’s laws of motion and gravitation; calculation of pressure drops in a standpipe and a stairwell; and a revised discussion of viscosity, buoyancy, and turbulence, including their roles in fires.
• Chapter 5, “Heat Transfer,” now contains expanded presentations of conduction, convection, and thermal radiation; and a new section on burn and structural hazards.
• Chapter 6, “Combustion, Fire, and Flammability,” is a new chapter. It presents the National Fire Incident Reporting System (NFIRS) and how it enables identifying the most common and the most dangerous fire types; the fire tetrahedron; the definitions of combustion and flammability; the stages of fires; and the concepts of fire initiation, spread, ventilation, backdraft, extinguishment, hazard, and risk. It includes two examples of room fires that demonstrate the progression from a small flame to room flashover.
• Chapter 7, “Fire Characteristics: Gaseous Combustibles,” now relates fire stages to generic types of flames and contains an enhanced presentation of ignition.
• Chapter 8, “Fire Characteristics: Liquid Combustibles,” contains expanded text relating vapor pressure and temperature to ignitability and flammability hazard, as well as enhanced text regarding boilover and its hazards.
• Chapter 9, “Fire Characteristics: Solid Combustibles,” now contains differentiation between the burning of solid fuels and other fuel states; explanation of the difference between materials and products; their testing and evaluation, including the expanding use of heat release rate; and expanded description of the types of pyrolysis, gasification, and ignition. There are also sections on smoldering combustion, ignition of secondary burning items, commercial uses of different types of synthetic polymers,
and the rationale for the use of fire retardants and the current public debate that is leading to re-examination of the benefits and proper use of these additives.
• The splitting of the presentation on combustion products into two chapters, Chapters 10 and 11, “Combustion Products” and “Smoke and Heat Hazards,” respectively, reflects the major advances in the knowledge of fire smoke and its hazards. There is a new section on the importance of smoke aerosols, additional text on the measurement and characterization of aerosols, presentation of different criteria for visibility through smoke, and an expansion and update on the principles of smoke alarms. New sections on smoke toxicity include discussion of the incapacitating effects of smoke components on people, the way these effects are measured and quantified for use in fire safety assessments, a brief introduction to thermostructural damage, and the concept of the limiting fire hazard.
• Chapter 12, “Movement of Fire Gases” contains expanded text on the filling of rooms by fire smoke, the flow of smoke from a room, and the physics that governs smoke movement throughout a building.
• Chapter 13, “Fire Fighting Chemicals” now contains an expanded section on terminology, a new section on the response of automatic sprinklers to a fire, and additional text on the mechanisms of fire suppression using water. Environmental impacts have completely changed the landscape for non-aqueous fire suppression. The phenomenology of the global environmental effects is explained, and new extensive sections describe the migration to different gaseous fire suppressants. There is expanded discussion of flame extinguishment using water mist and dry chemical powders, and a new section on ultrafast flame suppression.
• Chapter 14: “Computational Modeling of Fires” reflects the transition from innovative research to tools that have become the norm for engineering practice. New text includes the elements of a fire model, whether it be a simple equation or complex mathematics requiring a computer for solution and a section on the uses and users of such models. There are also sections on CFAST and FDS, the two most commonly used computer models, each of which can be downloaded at no charge.
Additional
Throughout this book, you will find citations to two references to which every student of fire science should have access: the NFPA’s Fire Protection Handbook (two volumes), now in its 20th edition, and the SFPE Handbook of Fire Protection Engineering, now in its fourth edition. These are the “go to” resources for dealing with fire safety matters where more complexity is evident or suspected. While each successive edition has improved significantly over the prior edition, any edition of these references provides background material and detailed exposition on the components of fire protection science, as well as graphs and tables of supporting data. D. Drysdale’s An Introduction to Fire Dynamics (third edition, John Wiley, New York, 2011) is also a solid resource.
The provision of fire safety is a mission in motion. In a few short decades, the advances have been remarkable. Smoke alarms once an expensive curiosity are now installed in nearly all homes. Automatic sprinklers are the norm in commercial buildings. Less fire-prone cigarettes and ground-fault circuit interrupters are decreasing the number of ignitions from these sources. Oxygen consumption calorimetry is enabling the commercialization of products, such as mattresses, that do not burn as vigorously as the versions they replace. Computational fire models are facilitating innovative building designs that are newly functional, yet still safe. Our fire incidence data system and its analysis have grown in content and credibility; this system shows that our national fire problem is decreasing and identifies our substantial cost savings as a result of this trend.
All of these achievements have been accomplished in the presence of headwinds. Our growing affluence over the past decades has increased the combustible fire load in our homes and in those structures where we work and play. New materials that may be superior in other ways are ignited more readily and burn more vigorously. Recognition of health hazards has forced replacement of PCBs and asbestos, two families of materials that had been providing fire safety benefits. Most recently, new understanding of our global environment has altered our perception of fire safety, which has traditionally been provided locally or regionally. Notably, the threats of ozone depletion and global warning have led to restrictions being placed on the use of the highly effective halogenated fire suppressants.
Old fire problems are solved; new ones emerge. Fire morphs, but it remains a bane of our world. What is not changing is the need for an intellectually curious, practically oriented fire safety community, ready to protect an evolving society.
References
1. Karter, M. J. Jr. (2011). Fire Loss in the United States during 2010. Quincy, MA: National Fire Protection Association.
2. National Interagency Fire Center. www.nifc.gov.
3. Goudsblom, J. (1992). Fire and Civilization. New York, NY: Penguin Press.
4. Grun, B. (1982). The Timetables of History. New York, NY: Simon and Schuster.
5. Lyons, P. R. (1976). Fire in America! Quincy, MA: National Fire Protection Association.
CHAPTER 1
Fire Measurement and the SI System of
Units
OBJECTIVES
After studying this chapter, you should be able to:
• Explain the importance of measurement in understanding fire behavior.
• Name the basic SI units of measurement and covert between values in SI units and English units.
• Understand the precision of a measurement and the reduced precision used in estimations.
• Explain the differences between mass and weight and among energy, heat, and enthalpy.
Introduction
In 1999, the Mars Climate Orbiter miscalculated the distance to the planet’s surface and disintegrated in the planetary atmosphere. The cause was human error. The spacecraft was programmed with English units, but NASA used metric units. The difference in measuring units led to the incorrect transfer of the navigational information between the spacecraft’s manufacturer team in Denver, Colorado, and the flight team in Pasadena, California and the ultimate destruction of the spacecraft. Input data for engineering calculations can be tabulated in a variety of units. To avoid serious consequences, it is critical that the input data, the calculation method, and the calculated values all use a consistent set of units.
About Measurement
Measurement is the key to understanding fire phenomena and to translating that understanding into fire safety practice. To help understand the phenomena, it is important to ask when the fire started, how rapidly it grew, how hot it became,
and how severe the threat to the population was. The answers to all of these (and many other) questions are rooted in an ability to quantify. The meaning of relative terms, such as “fast moving” or “big,” varies widely depending on people’s experiences and perceptions. To a gardener, a big fire may involve a large pile of leaves; in contrast, to an insurance company, a big fire may be one that destroys a house.
Given the many different languages of the world, it is not surprising that the early cultures made up their own methods to measure objects, frequently cast in terms of properties of the human body. (That way, you always had your “yardstick” with you.) The units of measurement varied from region to region and often from person to person. For example, the Chinese measured length using the bu (about 1.67 m), the Anglo-Saxons used the ell (about 1.14 m), and the Spaniards used the vara (about 0.86 m). As cultures expanded to the point of geographical contiguity, and as trade among multiple cultures began to prosper, the need for a common set of measurements grew.
The current international measurement system, also known as the metric system, was introduced in France by Napoleon at the beginning of the 19th century. It was refined further in the 1960s, and certain units, referred to as SI units, were agreed upon. SI comes from the French name Système International d’Unités.
All industrialized countries, with the exception of the United States and to some extent the United Kingdom, have chosen SI units to express mass, length, time, electrical current, temperature, and other measures. Adoption of the SI system facilitates the following:
• Quantitative communication regarding nearly everything, from the weather to the multitudinous forms of life.
• Exchange of manufactured products among countries.
• Computations, due to the use of factors of 10 for each unit. Instead of 12 inches in 1 foot and 5280 feet in a mile, SI uses 1000 millimeters in 1 meter and 1000 meters in 1 kilometer.
In the United States, the primary users of SI units today are scientists and engineers. In other countries, both scientists and ordinary citizens primarily use SI units or are in the process of changing over to their use. Because the data compiled in different engineering references are in either SI or English units, it is important that the U.S. reader learn to convert between the two systems.1
When a quantity is measured, there is a limit to the precision of the value
that is obtained. If a length measurement is performed with an inexpensive ruler, it may be possible to read only the nearest millimeter marking. A value might then be reported as 147 mm, in which case the length is represented by three significant figures. With a more meticulously marked ruler and a magnifying glass, it would be possible to estimate the length more precisely and report the value to four significant figures for example, 147.3 mm. One should report a value to the number of significant figures. Using an electronic measuring device with a 10-digit display does not increase the number of significant figures. Similarly, entering a number into a computer spreadsheet in which the cells are set to display 10 digits does not increase the number of significant figures in the value.
When estimating a calculated value, it is acceptable to speed the calculation by using fewer than the actual number of significant figures. Thus, in estimating the total surface area of the Earth, one might assume that the planet is a perfect sphere with a radius of about 6000 km. The surface area is given by the formula 4πr2 (where r = the planet’s radius), and the value of π is close to 3. The magnitude of the surface area can then be estimated at approximately 500,000,000 km2 , reported to one significant figure.
Length, Area, and Volume Units
The basic SI unit of length is the meter (m). Originally, the meter was selected as 1/10,000,000 of the distance from the Earth’s equator to the North Pole. Toward the end of the 19th century, however, it was redefined as the distance between two lines on a standard bar composed of an alloy of 90 percent platinum and 10 percent iridium, measured when the bar is at the melting temperature of ice. The meter is currently defined as the length of the path traveled by light in 1/299,792,458 of 1 second.
Table 1-1 shows various SI “meter” units as they relate to the English equivalents. References [1] and [2] at the end of the chapter contain more conversions among length (and other) units.
Table 1-1 SI Length Units as Related to the Meter, with English Equivalents
Notice that “in.” is the abbreviation for inches. The period is included to distinguish it from the preposition “in”; it is the only abbreviation that is followed by a period.
Formally, SI dimensions are given in multiples of 1000 (km, m, mm, and so on). Nevertheless, some intermediate factors of 10 (e.g., cm, dm) are widely used.
Area is two-dimensional and, for a rectangular flat surface, is the length of the surface times its width. In the SI system, small areas can be expressed in square meters (m²), square centimeters (cm²), and so on. In the English system, areas of similar size are expressed in square inches (in.2) or square feet (ft2). Larger areas, such as tracts of land, are expressed in hectares (ha) in the metric system; 1 hectare is 10,000 m². The English equivalent of one hectare is 2.47 acres. In fire dynamics, the cross-sectional area of a vent is used to calculate the flow through the vent, and the area of a hot surface is used to calculate the heat transferred to a colder object.
Volume is three-dimensional. For a rectangular space, such as a room, it is the length times the width times the height. Volume can be expressed in cubic meters (m³), cubic centimeters (cm³), and so on. The liter (L) is commonly used as a unit of liquid and gas volume, and is the same as 1 cubic decimeter (dm³) or 1000 cubic centimeters (1000 cm³). One liter is equivalent to 0.264 U.S. gallon or 1.056 quarts.
Mass and Density Units
The basic SI unit of mass is the kilogram (kg). The kilogram was selected because it is approximately the mass of 1 liter of water. (The mass of a volume of water varies because water expands or contracts slightly as its temperature changes.) The gram (g), also widely used, is 1/1000 of a kilogram, and is approximately the mass of 1 cubic centimeter (cc) of water. Table 1-2 shows the
relationship of various mass units to the kilogram (with their English equivalents). To convert from metric units to English units, multiply the metric value by the number in the right column. To convert from English units to metric units, divide the English value by the number in the right column.
Table 1-2 SI Mass Units as Related to the Gram, with English Equivalents
The concepts of mass and weight are often confused. The mass of an object is a fundamental property of the object, representing the quantity of matter in the object. An object’s mass is invariant (except in a nuclear bomb explosion, when mass changes into energy). By comparison, weight refers to the force acting on an object because of gravity attraction and is a convenient way to measure mass on Earth at sea level. If an object were on the moon, its weight would be only about one-sixth of its weight on Earth, and if the same object were in an orbiting space station; it would be nearly weightless. However, its mass would be the same in all three cases.
Density is the mass of a substance in a unit volume. It is generally is expressed in grams per cubic centimeter (g/cm³), kilograms per cubic meter (kg/m³) or, in English units, pounds per cubic foot (lb/ft3). The term specific gravity refers to the ratio of the density of a substance to that of a reference substance. For liquids and solids, the reference substance is usually water; for gases, the reference substance is air. Especially for gases and liquids, the temperature and pressure must also be specified, because the densities of the substance of interest and the reference substance depend on the temperature and pressure (Table 1-3). The densities of most solids are less sensitive to temperature and pressure.
Table 1-3 Densities of Selected Materials [2]
For mixtures of two or more substances, there are multiple ways of denoting the relative prevalence of each component.
• Concentration: the mass of a component per unit volume.
• Volume fraction (gases): the ratio of the volume that a gas in the mixture would occupy (at standard temperature and pressure) to the total volume of the system. This is sometimes multiplied by 100 to obtain the volume percent. Thus the volume fraction of oxygen in dry air is 0.209, and the volume percent of oxygen in dry air is 20.9 percent. (There is more on the composition of air in the Physical and Chemical Change chapter.)
• Mass fraction: the ratio of the mass of a component in a mixture to the total mass of the mixture. This can also be multiplied by 100 to obtain the mass percent. Thus, for dry air, the mass fraction of oxygen is 0.233 and the mass percent is 23.3 percent.
Note
Historically, there has been extensive use of units like ppm (parts per million), such as to indicate a concentration of a toxic gas in fire smoke, or pph (parts per hundred), such as to indicate the amount of fire retardant added to a plastic material. There is a critical ambiguity in these units: “ppm” might refer to 1 g of material X in 1000 kg material Y or 1 cm3 of material X in 1000 L of material Y. As a result, the use of these types of units is
discouraged. The units to be used instead of ppm are µL/L for volume fractions and mg/kg for mass fractions. These are numerically identical: 1 mg/kg = 1 ppm by mass.
Units for time are the same in the SI system and the English system. The basic unit is the second (s). Table 1-4 shows abbreviations for related time units.
Speed is the rate at which an object is moving, with typical metric units being m/s or km/h. Velocity is speed in a chosen direction. Thus, if a train is moving to the northeast at a speed of 150 km/h, its velocity in the east direction is 106 km/h (150/√2). (An alternative wording is that the train is moving eastward at 106 km/h.) Colloquially, when the speaker and the audience both understand the direction of movement, the terms may be used synonymously.
Table 1-4 Time Units (SI and English) Time
Acceleration is the rate of change of speed. Typical metric units are m/s2 and km/h.
Note
SI units named for a person are abbreviated using a capital letter. When the unit is spelled out, it begins with a lowercase letter except when it appears at the beginning of a sentence or in a title.
The basic unit of force in the SI system is the newton (N). A newton is the force needed to accelerate a mass of 1 kg at the rate of 1 m/s2 . In the English system, 1 lb of force is the force that will accelerate 1 lb of mass at the rate of 32.2 ft/s2 . This definition was selected so that 1 lb of mass at sea level would feel a gravitational attraction of 1 lb of force. (Note the use of the same term, lb, to denote two different types of units.)
From the relation between the pound of mass and the kilogram, and the relation between the foot and the meter, it is easy to show that 1 newton is equal to 0.224 pound of force. The gravitational force on 1 kg at sea level is 9.81 N.
Pressure is force per unit area. The basic SI unit of pressure is the pascal (Pa), which is 1 N/m². One Pa is a very low pressure, so a unit called the bar is also used. A bar is defined as 100,000 Pa or 100 kilopascals (kPa). One bar is only 1.3 percent greater than normal atmospheric pressure at sea level (101.3 kPa); therefore, for approximate calculations, 1 bar is often equated to 1 atmosphere (atm).
Several English units of pressure arose out of convenience in particular applications. The following describes the more common ones:
• Testing of the fracture or deformation condition for materials gave rise to the unit of pounds per square inch (psi). The pressure of compressed gases in their storage cylinders is commonly monitored in psig, where the “g” stands for “gauge.” This is the pressure above atmospheric pressure. Pressures in psig are 14.7 psi lower than pressures in psia, where “a” stands for “absolute.”
• Manometers (glass U-shaped tubes filled with a fluid) were frequently used to measure pressure differences or absolute atmospheric pressure. When using a manometer, the measured height of the liquid column is proportional to the gas pressure. The two commonly used fluids were mercury (Hg) and water (H2O). The conversion factors from SI units are as follows:
101 kPa = 760 mm Hg (also referred to as torr)
101 kPa = 4020 in. H2O
The latter units are often used to measure the small pressure differences
