Thoroughly updated with the latest codes, technologies, and
practices, this all-in-one resource provides details, calculations,
and specifications for designing efficient and effective residential,
commercial, and industrial HVAC systems.
HVAC Systems Design Handbook, Fifth Edition, features new
information on energy conservation and computer usage for
design and control, as well as the most recent International Code
Council (ICC) Mechanical Code requirements. Detailed illustrations,
tables, and essential HVAC equations are also included. This
comprehensive guide contains everything you need to design,
operate, and maintain peak-performing HVAC systems.
Coverage includes:
• Load calculations
• Air- and fluid-handling systems
• Central plants
• Automatic controls
• Equipment for cooling, heating, and air handling
• Electrical features of HVAC systems
•D
esign documentation—
drawings and specifications
• Construction through operation
• Technical report writing
•Engineering fundamentals—fluid mechanics,
thermodynamics, heat transfer, psychrometrics,
sound and vibration
• Indoor air quality (IAQ)
• Sustainable HVAC systems
• Smoke management
ISBN 978-0-07-162297-4
MHID 0-07-162297-7
5 9 9 9 9>
CONSTRUCTION
Cover Design: Mary McKeon
HVAC Systems
Design Handbook
A complete, fully revised
HVAC design reference
fifth edition
HVAC
Systems
Design
Handbook
Fifth Edition
Haines
Myers
Roger W. Haines and Michael E. Myers
9 780071 622974
HVAC Systems
Design
Handbook
Roger W. Haines, P.E.
Michael E. Myers, P.E., LEED AP
Fifth Edition
New York Chicago San Francisco
Lisbon London Madrid Mexico City
Milan New Delhi San Juan
Seoul Singapore Sydney Toronto
HVAC_book.indb i
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Cataloging-in-Publication Data is on file with the Library of Congress
Copyright © 2010, 2003, 1998, 1994, 1988 by The McGraw-Hill Companies, Inc. All
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services are required, the assistance of an appropriate professional should be sought.
HVAC_book.indb ii
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Contents
Preface
ix
Acknowledgments
Introduction
xiii
xi
Chapter 1. HVAC Engineering Equations for Daily Use
1.1
Introduction
Part 1—Frequently Used HVAC Equations
1.2 Air Side Equations
1.3 Fan Laws
1.4 Heat Transfer Equations
1.5 Fluid Handling
1.6 Power and Energy
1.7 Steam Equations
Part 2—Infrequently Used HVAC Equations
1.8 Air Side Equations
1.9 Fluid Handling
1.10 Smoke Management
Chapter 2. HVAC Engineering Fundamentals: Part 1
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
Introduction
Problem Solving
Value Engineering
Codes, Regulations and Standards
Fluid Mechanics
Thermodynamics
Heat Transfer
Psychrometrics
Sound and Vibration
Energy Conservation
Summary
Chapter 3. HVAC Engineering Fundamentals: Part 2
3.1 Introduction
3.2 Comfort
1
1
3
6
7
8
10
11
12
15
16
21
21
21
22
23
23
23
24
25
25
25
25
27
27
27
iii
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iv
Contents
3.3
3.4
3.5
3.6
3.7
3.8
3. 9
3.10
HVAC Cycles
Control Strategies
Architectural, Structural and Electrical Considerations
Conceptual Design
Environmental Criteria for Typical Buildings
Designing for Operation and Maintenance
Codes and Standards
Summary
Chapter 4. Design Procedures: Part 1—Load Calculations
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
28
29
29
30
30
33
34
34
37
Introduction
Use of Computers
Rule of Thumb Calculations
Design Criteria and Documentation Forms
Factors for Load Components
Load Calculations
Dynamic versus Static Load Calculations
Ventilation Loads
Other Loads
Summary
37
38
38
39
45
79
86
86
87
88
Chapter 5. Design Procedures: Part 2—General Concepts
for Equipment Selection
89
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Introduction
Sustainable Systems and Equipment
Maintainability of Systems and Equipment
Criteria for System and Equipment Selection
Options in System and Equipment Selection
The Psychrometric Chart
Effects of Altitude and Temperature
Software-Based Equipment Selection
Summary
Chapter 6. Design Procedures: Part 3—Air Handling Systems
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
Introduction
Fans
Air Duct Design
Registers and Grilles
Louvers
Dampers
Filters
Air Distribution with High Flow Rates
Stratification
Noise Control
Indoor Air Quality
Summary
Chapter 7. Design Procedures: Part 4—Fluid Handling Systems
7.1 Introduction
7.2 Steam
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89
89
90
90
97
100
103
105
105
107
107
107
121
141
143
144
147
148
152
154
155
155
157
157
157
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Contents
7.3
7.4
7.5
7.6
7.7
7.8
7.9
v
Water
High-Temperature Water
Secondary Coolants (Brines and Glycols)
Piping Systems
Pumps
Refrigerant Distribution
Summary
165
167
167
169
196
204
205
Chapter 8. Design Procedures: Part 5—Central Plants
207
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
Introduction
General Plant Design Concepts
Central Steam Plants
Low-Temperature Hot Water Central Plants
High-Temperature Hot Water Central Plants
Fuel Options and Alternate Fuels
Central Chilled Water Plants
Thermal Storage Systems
Central Plant Distribution Arrangements
Cogeneration Plants
Summary
Chapter 9. Design Procedures: Part 6—Automatic Controls
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
207
207
208
210
212
213
214
221
224
225
230
231
Introduction
Control Fundamentals
Control Devices
Instrumentation
Typical Control Systems
Electrical Interfaces
Computer-Based Controls
Control Symbols
Summary
231
232
237
268
269
280
281
284
284
Chapter 10. Equipment: Part 1—Cooling
287
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
Introduction
Refrigeration Cycles
Compressors
Chillers
Condensers
Cooling Towers
Cooling Coils
Radiant Cooling
Evaporative Cooling
Refrigerants
Summary
Chapter 11. Equipment: Part 2—Heating
11.1 Introduction
11.2 General
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287
287
291
295
297
300
304
313
313
316
317
319
319
319
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vi
Contents
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
11.19
11.20
Boilers
Boiler Types
Combustion Processes and Fuels
Fuel-Burning Equipment
Boiler Feedwater and Water Treatment Systems
Boiler Codes and Standards
Boiler Design
Acceptance and Operational Testing
Direct- and Indirect-Fired Heating Equipment
Heat Exchangers—Water Heating
Heat Exchangers—Air Heating
Unit Heaters and Duct Heaters
Terminal Heating Equipment
Heat Pumps
Heat Recovery and Reclaim
Solar Heating
Humidification
Summary
Chapter 12. Equipment: Part 3—Air-Handling Systems
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
Introduction
AHU System Arrangements
Package AHUs
Built-Up (Field-Assembled) AHU
Terminal Units
Individual Room AHUs
Humidity Control
Control of Outside Air Quantity
Effects of Altitude
Exhaust Systems
Smoke Control
Summary
Chapter 13. Electrical Features of HVAC Systems
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
Introduction
Fundamentals of Electric Power
Common Service Voltages
Power Factor
Motors
Variable Speed Drives
Electrical Interface
Uninterruptible Power Supply (UPS)
Standby Power Generation
Electrical Room Ventilation
Lighting Systems
National Electrical Code
Summary
Chapter 14. Design Documentation: Drawings and Specifications
14.1 Introduction
14.2 The Nature of Contracts
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320
321
322
324
328
331
331
332
332
332
333
337
340
342
346
354
354
358
361
361
363
375
378
379
380
383
384
386
387
387
387
389
389
389
390
391
391
393
394
396
397
397
398
398
398
401
401
402
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Contents
14.3 Drawings
14.4 Specifications
14.5 Summary
Chapter 15. After Design: Through Construction to Operation
15.1
15.2
15.3
15.4
vii
403
404
415
417
Introduction
Participation During Construction
Commissioning
Summary
417
417
421
422
Chapter 16. Technical Report Writing
425
16.1
16.2
16.3
16.4
16.5
16.6
16.7
Introduction
Organization of a Report
Writing with Clarity
Use of Tables and Figures
Printing and Binding
Letter Reports
Summary
Chapter 17. Engineering Fundamentals: Part 1—Fluid Mechanics
17.1
17.2
17.3
17.4
17.5
17.6
425
425
427
427
428
428
428
431
Introduction
Terminology in Fluid Mechanics
Law of Conservation of Mass
The Bernoulli Equation (Law of Conservation of Energy)
Flow Volume Measurement
Summary
431
431
432
432
434
435
Chapter 18. Engineering Fundamentals: Part 2—Thermodynamics
437
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
Introduction
Thermodynamics Terms
First Law of Thermodynamics
Second Law of Thermodynamics
Efficiency
Coefficient of Performance
Specific Heat Cp
Summary
Chapter 19. Engineering Fundamentals: Part 3—Heat Transfer
19.1
19.2
19.3
19.4
19.5
19.6
19.7
Introduction
Heat Transfer Modes
Thermal Conduction
Thermal Convection
Thermal Radiation
Latent Heat and Moisture
Summary
Chapter 20. Engineering Fundamentals: Part 4—Psychrometrics
20.1 Introduction
20.2 Thermodynamic Properties of Moist Air
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437
437
438
439
440
440
441
441
443
443
443
443
446
448
449
451
453
453
453
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viii
Contents
20.3
20.4
20.5
20.6
20.7
20.8
Tables of Properties
Psychrometric Charts
HVAC Processes on the Psychrometric Chart
The Protractor on the ASHRAE Psychrometric Chart
Effects of Altitude
Summary
Chapter 21. Engineering Fundamentals: Part 5—Sound and Vibration
21.1
21.2
21.3
21.4
21.5
21.6
21.7
Introduction
Definitions
Methods of Specifying and Measuring Sound
Sound and Vibration Transmission
Ambient Sound Level Design Goals
Reducing Sound and Vibration Transmission
Summary
Chapter 22. Indoor Air Quality (IAQ)
22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8
Introduction
Basics of IAQ Design
Methods of Providing Acceptable IAQ
Design Considerations for Acceptable IAQ
Additional Design Considerations for Acceptable IAQ
Protection of Outside Air Intakes
IAQ and Energy Conservation
Summary
Chapter 23. Sustainable HVAC Systems
23.1
23.2
23.3
23.4
23.5
23.6
23.7
Introduction
Energy-Efficient “Green” Buildings
HVAC Sustainable Design Approaches
Energy Efficiency Compliance
Indoor Air Quality Compliance
Bridging the Gap Between Energy Efficiencies and IAQ Requirements
Summary
Chapter 24. Smoke Management
24.1 Introduction
24.2 Basics Statements, Codes, Definitions and
Design Guides for Smoke Management Systems
24.3 Atrium and Mall Smoke Management Design Requirements
24.4 Zoned Smoke Management System
24.5 Design Procedure for Zoned Smoke Control
24.6 Zoned Smoke Management Calculation Example
24.7 Implementation and Performance Testing
24.8 Testing of Zoned Smoke Control Systems
24.9 Note of Caution on Smoke Machine or Smoke Bomb Testing
24.10 Summary
Index
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455
455
461
465
467
468
469
469
469
470
473
475
477
484
485
485
486
487
490
497
499
504
506
507
507
508
508
509
509
510
521
523
523
524
526
541
544
545
548
549
550
552
553
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Preface
I had already written what seemed like a pretty good preface, but after
working a while on the text I realized that there was a major change since
the fourth edition and that the change was the computer. The computer has
made a sea change in the attitude of the HVAC designer. But, understanding computer usage cannot substitute for an understanding of the subject
the computer is being used on. So, while this fifth edition recognizes the
changes that are taking place and talks a great deal about energy conservation, as well as computer usage for design and control, we are still emphasizing the fundamentals of HVAC.
When I started as an apprentice in my father’s heating and sheet metal
business in 1938, HVAC was not in the vocabulary. Most residential heating systems were coal-fired furnaces with air distribution by natural gravity. Larger homes and offices probably had steam or hot water radiation.
Control was manual as was the need to shovel in some coal from time to
time. Air cooling systems were limited to movie theaters and a few public
buildings and many of these used ice banks as a cooling source. The first
residential forced-air HVAC systems came out in the early 1940s and we
had to do a lot of learning.
I have been an HVAC designer/engineer since 1953, which is almost
pre-computer. My introduction to computer usage was the opportunity to
design the HVAC system for the “Stretch” computer, built for the Los Alamos Lab in the late1950s—custom-built, three million dollars, 30 feet long,
and fully dependent on a climate- controlled room. Today’s desktop is much
faster and has more memory and doesn’t need air conditioning, but that is a
matter of evolution over many years.
In the early 1960s a group of mechanical engineers formed APEC (Automated Procedures for Engineering Consultants) to combine forces to
write programs for HVAC calculations. It was moderately successful, using punch card input and the best computers available at the time. By the
late 1960s the HVAC control manufacturers were racing to be first in the
growing field of computer-based controls and controllers. By 1970 this
ix
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x
Preface
had developed to the extent of getting considerable notice and discussion
in my book on control systems for HVAC.
By trial and error and a great deal of ingenuity the computer control
business has grown to include even small systems, and now we have wireless technology to make it even easier. And, of course, we now use computers for calculations, drafting, specifications and everything else in the
design office.
What Michael Myers and I are trying to do in this book is to talk about
the basics of HVAC design, whether manual or computerized, so that the
reader can understand why and how the design fills the need. If we lose
sight of the fundamentals—what things mean and how they work—we are
in for trouble. We hope you can avoid that.
Roger W. Haines
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Acknowledgments
It is impossible to remember or acknowledge all the people who have contributed to my education over these ninety-odd years. My father taught me
the sheet metal trade. The faculty at Iowa State University gave me good
theoretical training. All the people I’ve dealt with in my work experience
have helped—other engineers, contractors, manufacturer’s representatives,
clients. I still remember the owner who took pity on a poor apprentice
and taught me how to properly file a screwdriver tip. My many friends at
ASHRAE taught me much through formal and informal discussion.
A few names must be mentioned: Ted Neubauer was my first model of
a truly professional engineer. John Blossom introduced me to the problem
solving process in Chapter 2. Ralph Thompson and Doug Hittle taught me
electronics and many other things. Frank Govan wrote the section on boilers in Chapter 11. Don Bahnfleth taught me how to write reports. Frank
Bridgers and Don Paxton gave me my first job as an engineer, along with
basic training in design and professional attitudes. My editors at McGrawHill, Larry Hager and Joy Bramble Oehlkers, helped me organize for publication. My new co-author, Michael Myers, has helped greatly in bringing
us up-to-date in a changing environment.
Finally and always, I could accomplish nothing without the support,
encouragement and patience of Wilma, my wife of sixty-nine years.
Roger W. Haines
xi
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ABOUT THE AUTHORS
Roger W. Haines, P.E., a distinguished 50-year member of
ASHRAE, is widely recognized as one of the foremost authorities in the field of HVAC engineering. He is the author of Roger
Haines on HVAC Controls and is a frequent contributor to HPAC
Engineering magazine.
Michael E. Myers, P.E., LEED AP, has been an HVAC,
plumbing, and fire protection consulting engineer for 30 years.
A member of ASHRAE, an ASHRAE Region XII Chair, and
an ASHRAE Distinguished Lecturer for Smoke Management
Systems Design, he is currently a Senior Mechanical Engineer
with JALRW Engineering Group, Inc., in Ft. Myers, Florida.
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Introduction
I.1
Definition and Purpose of HVAC Systems
Heating, ventilating and air conditioning (HVAC) is defined as the simultaneous control of temperature, humidity, radiant energy, air motion and
air quality within a space for the purpose of satisfying the requirements of
comfort or a process. Not included in the definition, but often required, is
the control of pressure in the conditioned space relative to adjacent areas.
Another factor that becomes important in many applications is the noise
level associated with the air conditioning equipment. For engineering purposes the definition should also be extended to include the lowest lifecycle cost of conditioning the air by right-sizing of equipment to meet the
particular application with the lowest operating and maintenance costs.
Since a major use of our energy on this planet goes toward conditioning
the air that we breathe in the built environment we must place an emphasis
on more sustainable, i.e., “green,” HVAC systems, that use less energy
and include environmentally friendly methods and components to reduce
the system’s impact on the world’s fuel supplies while providing healthy
indoor environments.
Most people associate air conditioning with cooling but, as the definition states, air conditioning is a great deal more than that. Comfort must
also be defined—a difficult task because the sensation of comfort varies
with the individual and the level of activity. Cleanliness relates to the broad
subject of indoor air quality, which includes not only dust and dirt but also
gaseous contaminants, viruses, and bacteria.
It quickly becomes evident that to accomplish true air conditioning is not
all that simple and, in some industrial or institutional applications, it may be
very difficult. Not unlike medicine, HVAC is part science and part art.
This book discusses various air conditioning design procedures and systems and to give the reader the tools necessary to understand and solve
many air conditioning problems. Intertwined in the pages of this book is the
xiii
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xiv
Introduction
emphasis on designing systems that are more energy efficient than in the
past and promote a healthy indoor environment for the building occupants.
HVAC engineers and designers are increasingly required to know and implement the latest methods for improving indoor air quality, providing comfort, lowering energy usage and using environmentally friendly refrigerants.
For simplicity the acronym HVAC (Heating, Ventilating and Air Conditioning) is used unless only one of these factors is being discussed. Throughout
the book frequent reference is made to the American Society of Heating,
Refrigerating and Air Conditioning Engineers (ASHRAE) Handbooks1, the
primary and authoritative reference books for the HVAC and refrigeration
industries. The reference book entitled Industrial Ventilation: A Manual of
Recommended Practice2 is also definitive in many applications.
I.2
Engineering as a Business
One of the fallacies of engineering education in an earlier day, perhaps
even at present, is the failure to recognize and teach that engineers are
business people first and engineers second.
A simplified version of the fundamentals of business identifies the divisions of marketing, management and production. Most engineers become
proficient in production, i.e., in the mastery and use of technical knowledge, but only some engineers are effective managers and few engineers
are successful marketers. The reader is, therefore, asked to remember the
importance of satisfying the customer, be it client or boss, and of conducting the work in a technically correct but also profitable manner, encouraging a repeat performance.
In the context of this book, being an engineer in a businesslike way
implies designing HVAC systems which achieve the desired level of performance with a satisfactory combination of first costs and subsequent
operating and maintenance costs, all in a timely and efficient design process. The businesslike engineer is also communicative and easy to work
with. The modern HVAC engineer must be open minded and willing to
explore new methods with the client in order to meet the client’s needs
and expectations. The successful business minded HVAC engineer must
be part of the design team with input to and from the owner, architect and
contractor. The business minded engineer should also embrace the latest
methods of producing and issuing his or her design through the use of
B.I.M. (Building Information Management) design-drafting CADD software or equivalent.
I.3
HVAC System Design
“HVAC system design is an intellectual process, commonly involving
teamwork and iteration, which leads to a device, system and/or process
which satisfies a need.”3
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Introduction
xv
The design of HVAC systems is based on scientific principles of mathematics, physics and chemistry as developed in discussions of thermodynamics, fluid mechanics, heat transfer and psychrometrics. Discussions of
these topics are provided in later chapters. Beyond the basic science are a
great many empirical and experience factors which modify the calculated
data. These make the HVAC process an art as well as a science. This book
offers procedures and encourages the reader to develop insights which will
lead to intuitive understanding of many engineering problems.
I.4
Computers in HVAC Design and Operation
Short of the ability to reason or to exhibit a sense of right or wrong, the
computer, processing gigabytes of information in nanoseconds, challenges
and often, though not always, surpasses the human mind in information
management.
Beginning with the APEC programming effort in the 1960s and early
attempts to use computers for system design and control in the 1970s, we
realize that today computers are ubiquitous in the HVAC industry. Later
chapters In this book will discuss computer usage in detail. For now, note
that, while we must and should deal extensively with computers, it is necessary to remember that computers (so far) lack the judgment of the experienced professional.
The computer can handle more data than we might ever pursue were we
limited to manual calculations. Therefore, our solutions may seem more
precise. But remember the GIGO (Garbage In, Garbage out) rule. We must
not tout output to ten significant places when the input had only three. Nor
should we be excited about volumes of information when all we want to do
is differentiate between a small or medium or large piece of equipment.
Computers are managed by software programs which manipulate and
present information. The programs are created by and are only as good as
the programmer. Programs may reflect the biases of a sponsor. Program
cost is no indication of value.
The strength of the computer in quickly manipulating input information
to a useful output form is also a weakness if the input is erroneous. There is
no substitute for the knowledgeable provider of input and the experienced
interpreter of output. For the tyro, this means extra care in both input and
interpretation, together with the willingness to ask advice of the experienced co-worker.
This book begins with a discussion of the “old fashioned” manual calculation procedures so that the reader may provide a manual “check” of
computer results. Systems can be designed without resort to computers.
I.5
Need for Orderly Procedures
Abraham Lincoln’s alleged composition and editing of the Gettysburg
Address on the back of an envelope was an oratorical success but a bad
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xvi
Introduction
example for the technical professions. In today’s highly technical, regulated and litigious society there is no substitute for organized analysis and
documented design effort. Detailed, orderly design records, with the underlying assumptions clearly stated and with explanations of how and why
decisions were made, are worth their weight in lawyers when inevitable
questions arise. Good design notes and calculations make for easy checking. They also help when there is a change in assignment and someone else
takes over or supplements the work. Experience has shown that the details
of a design procedure cannot be recalled accurately after a lapse of six
to twelve months. Yet, it is typically at or beyond that time that questions
arise in the operation, review or alteration of the system.
For purposes of consistency and effective use of time, many design procedures are standardized with the use of forms or formats, computer programs, spreadsheets, and the like. Such standardization serves the design
process by compacting the repetitive and mundane, thus allowing more
time for creativity. This book describes some useful procedures but leaves
great latitude for individual designers to develop their own design methods
and procedures.
I.6
Equations
A new and unusual feature of this edition is the first chapter on “equations.” This contains most or all of the equations used in HVAC, with the
“most used” placed first. This is in the front of the book as an easy reference for the experienced designer. The derivation of some of these equations is discussed in later chapters and will make them more understandable. We recommend skipping this chapter until the reader has acquired a
better sense of how these equations apply.
References
1. ASHRAE Handbooks, four volumes, one volume republished each year. Available from
American Society of Heating, Refrigerating and Air Conditioning Engineers, 1791 Tullie Circle, NE, Atlanta, GA 30329. All material from the Handbooks is copyright by
ASHRAE. (The Handbooks are now available on CDs.)
2. Industrial Ventilation, A Manual of Recommended Practice, American Conference of
Governmental Industrial Hygienists, Inc. (ACGIH)
3. F.W. Incropera, Purdue University, Annual Newsletter, 1992.
HVAC_book.indb xvi
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Chapter
1
HVAC Equations for Everyday Use
1.1
Introduction
The purpose of this chapter is to place the frequently (and not so frequently) used equations for everyday HVAC calculations in one location. Have
you ever needed to know how to calculate the brake horsepower of a pump
quickly but don’t remember the equation for it? Or have you ever needed
to calculate the EDR of a steam system in order to size a steam condensate return pump and receiver? It can be a tedious and time-consuming
process to find this information. Therefore, this chapter will give some of
the most important as well as some of the least known HVAC equations
for your use in one convenient location.
The following equations are stated without derivation or example applications. Some of the equations will be used in examples in later chapters of
this book. This chapter is divided into two parts. The first covers frequently
used equations. The second part contains equations that will not be frequently used but are needed for comprehensiveness. It is the responsibility
of the user to understand and apply the equations in the proper and correct
manner. We suggest that this chapter be used after basic HVAC knowledge
has been attained by the reader.
1
HVAC_book.indb 1
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2
Chapter One
PART 1—FREQUENTLY USED HVAC EQUATIONS
1.2
Air Side Equations
1.2.1
Abbreviations and Definitions for Air Side Equations
1. CFM cubic ft per min
2. V velocity, ft/min
3. TMIXED mixed air temperature, °F
4. TOA outside air temperature, °F
5. TRA return air temperature, °F
6. TSAROOM supply air temperature to room, °F
7. TSROOM desired sensible room temperature, °F
8. TSACOIL supply sensible air temperature leaving coil, °F
9. TSADUCT duct supply air temperature, °F
10. EAT entering air temperature, °F
11. LAT leaving air temperature, °F
12. SP static pressure, in of H2O
13. VP velocity pressure, in of H2O
14. TP total pressure, in of H2O
15. ACH air changes per hour
16. BTU British Thermal Unit
(1 BTU = energy to raise 1 pound of water 1°F)
17. BTUH British Thermal Units per hour
18. BTUHSROOM sensible load of the room/space
19. MBH 1000 BTUH
20. MAT mixed air temperature, °F
21. BHP brake horsepower
22. h enthalpy, BTU/lbm
23. lbm pound mass
24. density of air, lbm/ft3
25. L duct length, ft
26. Dh hydraulic diameter, in
27. pf total static pressure differential, in of water
28. P perimeter of duct, in
29. A area of duct, in2
30. a major axis, in
31. b minor axis, in
HVAC_book.indb 2
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HVAC Equations for Everyday Use
3
32. De equivalent duct diameter, in
33. SH specific heat at design temperature and pressure, Btu/lb · °F
34. dr density ratio for air compared to sea level
35. te temperature air entering duct section
36. tl temperature air leaving duct section
37. ta temperature air surrounding duct section
38. D diameter of duct, in
39. L length of duct, ft
40. U overall heat transfer coefficient of duct wall, BTU/h · ft2 · °F
41. d density of insulation, lb/ft2
42. KA Dimensional constant for altitude
1.2.2
Air Side Equations
Supply CFM to room: CFM =
BTUHSROOM
(TSROOM − TSAROOM ) × 1.08
(1.2.1)
Basic outside air requirement for the space breathing zone:
Vbz = Rpz × Pz + Raz × Az1
Where
Vbz uncorrected outside air to the breathing zone, CFM
Rpz CFM/person (See Table 22.2)
Pz zone/room population
Raz CFM/ft2 of the zone/room (see Table 22.2)
Az floor area of the zone/room, ft2
⎛
⎞
⎟
( CFM ) × ⎜⎜ 60 minutes
⎟
hour
⎝
⎠
ACH
=
Air changes per hour:
volume room (ft 3 )
Duct velocity (FPM):
(1.2.1a)
(1.2.2)
CFM
or
area ft 2
(1.2.3a)
V = 4005 × VP
(1.2.3b)
TP = SP + VP
(1.2.4)
V=
Total pressure (in of H2O):
VP(standard air):
HVAC_book.indb 3
⎛ V ⎞
VP = ⎜
⎝ 4005 ⎟⎠
2
(1.2.5a)
9/1/09 1:45:57 PM
4
Chapter One
V(based on pressure):
V = 1096.7
VP
(1.2.5b)
V(standard air):
V = 4005 VP
(1.2.5c)
V(at given pressure):
V = K A VP
(1.2.5d)
Where 4005 = dimensional constant at sea level KA
KA =
Dimensional constant:
4005
(1.2.5e)
dr
See Table 4.3 for values of dr.
CFM in duct:
(
)
CFM = area ( ft 2 ) × ( V
Mixed air temperature:
)
(1.2.6)
⎛ CFM SA − CFM RA ⎞
⎛ CFM SA − CFM OA ⎞
× TOA + ⎜
MAT = ⎜
⎟
⎟ × TRA (1.2.7)
CFM SA
CFM SA
⎠
⎠
⎝
⎝
Fan heat (motor in air stream):
⎛
watts ⎞ ⎛
BTUH ⎞
× ⎜ 3.413
Q fan = BHP × ⎜ 745.7
⎟
hp ⎠ ⎝
watt ⎟⎠
⎝
(
)
(1.2.8)
Fan heat air temperature rise:
Δ t of =
(
Q fan
) (
CFM fan × 1.08
(1.2.9)
)
Where CFMfan is adjusted for altitude. See Table 4.3.
Total cooling coil Load:
(
)
BTUH total = CFM × h( EAT ) − h( LAT ) × 4.5 × 0density
.075 lbs
(1.2.10)
ft3
density
Where 0.075 lbs is the air density ratio adjustment based on altitude
ft3
or temperature. See Table 4.3 for elevation adjustment.
Coil sensible load:
BTUH sensible = CFM × (1.08 × ΔT) × 0density
.075 lbs
(1.2.11)
AF = (air density) SH 60 min/hr
(1.2.12)
ft3
Air factor:
HVAC_book.indb 4
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HVAC Equations for Everyday Use
5
VAV terminal unit coil heating capacity:
) ( )
) (
(
BTUH total = TSROOM − TSADUCT × Heating CFM space × 1.08 + BTUH SROOM
Where 1.08 1.08
(1.2.13)
BTU/hr
at sea level
ft 3
× °F
min
See Table 4.3 for values at different elevations.
Rectangular to round duct equivalent2:
Where
⎛
⎞
1.3 × ( wh)0.625
⎟
De = ⎜
⎜⎝ w + h 0.250 ⎟⎠
)
(
(1.2.14)
w duct width
h duct height
De equivalent round duct diameter, in
See Chapter 6.
Round to flat oval duct equivalent2
De =
1.55 A0.625
⎛ b2 ⎞
A=⎜
⎟ +b a−b
⎝ 4 ⎠
)
(1.2.16)
P b 2(a b)
(1.2.17)
(
See Chapter 6.
(1.2.15)
P0.25
Duct insulation heat gain/loss2:
⎡ UPL ⎛ t + t
⎞⎤
Q=⎢
× ⎜ e l − ta ⎟ ⎥
⎠ ⎥⎦
⎢⎣ 12 ⎝ 2
(1.2.18a)
Duct leaving air temperature2:
(
)
t y − 1 + 2ta
tl = e
y +1
y=
2.4 A × Vd
rectangular ducts
U × P× L
0.6 D × Vd
round ducts
U×L
See Chapter 6, Equation 6.11.
y=
HVAC_book.indb 5
(1.2.18b)
(1.2.18c)
(1.2.18d)
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6
Chapter One
1.3
Fan Laws
1.3.1
Fan Law Abbreviations
1. CFM cubic ft per min
2. D fan diameter, in
3. SP static pressure (in of H2O)
4. TP total pressure (in of H2O)
5. RPM revolutions per min
6. HP horsepower
7. d density of air, lbs/ft3
8. CFMMAX maximum CFM of fan based at critical speed
9. CFM1 original CFM of fan
10. RPMMAX critical speed
11. HPName Plate motor name plate horsepower
12. Subscript1 original condition; subscript2 new condition;
subscripttested actual field-tested values
13. SE static efficiency
1.3.2
Fan Law Equations1
3
⎛ D ⎞ ⎛ RPM 2 ⎞
CFM 2 = CFM1 × ⎜ 2 ⎟ × ⎜
⎟
⎝ D1 ⎠ ⎝ RPM1 ⎠
2
2
⎛ D ⎞ ⎛ RPM 2 ⎞ ⎛ d2 ⎞
SP2 = SP1 × ⎜ 2 ⎟ × ⎜
⎟ ×⎜ ⎟
⎝ D1 ⎠ ⎝ RPM1 ⎠ ⎝ d1 ⎠
2
⎛D ⎞
CFM 2 = CFM1 × ⎜ 2 ⎟ ×
⎝ D1 ⎠
RPM 2
d1
×
RPM1
d2
⎛D ⎞
SP2
d1
×
RPM 2 = RPM1 × ⎜ 1 ⎟ ×
SP1
d2
⎝ D2 ⎠
2
(1.3.2)
3
5
⎛ D ⎞ ⎛ RPM 2 ⎞ ⎛ d2 ⎞
HP2 = HP1 × ⎜ 2 ⎟ × ⎜
⎟ ×⎜ ⎟
⎝ D1 ⎠ ⎝ RPM1 ⎠ ⎝ d1 ⎠
(1.3.3)
(1.3.4)
(1.3.5)
3
⎛ D ⎞ ⎛ SP ⎞ 2
d1
HP2 = HP1 × ⎜ 2 ⎟ × ⎜ 2 ⎟ ×
d2
⎝ D1 ⎠ ⎝ SP1 ⎠
HVAC_book.indb 6
(1.3.1)
(1.3.6)
9/1/09 1:46:02 PM
HVAC Equations for Everyday Use
7
3
⎛ D ⎞ ⎛ CFM 2 ⎞
RPM 2 = RPM1 × ⎜ 1 ⎟ × ⎜
⎟
⎝ D2 ⎠ ⎝ CFM1 ⎠
(1.3.7)
3
4
⎛d ⎞
⎛ CFM 2 ⎞
⎛D ⎞
× ⎜ 2⎟
SP2 = SP1 × ⎜ 1 ⎟ × ⎜
⎟
⎝ d1 ⎠
⎝ CFM1 ⎠
⎝ D2 ⎠
(1.3.8)
3
4
⎛ CFM 2 ⎞ ⎛ d2 ⎞
⎛D ⎞
HP2 = HP1 × ⎜ 1 ⎟ × ⎜
⎟ ×⎜ ⎟
⎝ CFM1 ⎠ ⎝ d1 ⎠
⎝ D2 ⎠
(1.3.9)
CFM based on critical speed of fan:
⎛ RPM MAX ⎞
CFM MAX = CFM1 × ⎜
⎟
⎝ RPM1 ⎠
(1.3.10)
New brake horsepower at critical speed:
⎛ RPM MAX ⎞
BHPmax rpm = HP1 × ⎜
⎟
⎝ RPM1 ⎠
3
(1.3.11)
Maximum RPM of fan with original motor:
RPM max horsepower = RPM tested × 3
HPnameplate
BHPtested
(1.3.12)
Maximum RPM of fan based on fan pressure class:
RPM at max sp = RPM tested ×
SPmax fanclass
SPtested
(1.3.13)
Fan actual BHP based on total pressure and static efficiency:
BHP =
CFM × TP
6356 × SE
1.4
Heat Transfer Equations2
1.4.1
Abbreviations and Definitions for Heat Transfer Equations
(1.3.14)
1. Q heat, BTU/hr
2. U U-value of material (conductance), BTU/h · ft2 · °F
3. A area, ft2
4. SHGC solar heat gain coefficient, dimensionless
HVAC_book.indb 7
9/1/09 1:46:03 PM
8
Chapter One
5. CLTD cooling load temperature difference, °F
6. Tin interior air temperature, °F
7. Tout exterior air temperature, °F
8. L thickness, in
9. Apf total area of glass, ft2
10. Et incident total irradiance, BTU/hr · ft2
11. SC glass shading coefficient dimensionless
12. MSHGF maximum solar heat gain factor for fenestration exposure
13. CLF cooling load factor
1.4.2
Basic HVAC Heat Transfer Equations2
1. Basic conduction: Q U A (T1 T2)
2. Basic glass heat gain:
Q U Apf (tout tin) (SHGC)Apf Et or
Q U Apf (tout tin) A SC MSHGF CLF
SHGC
0.87
4. Q U A CLTD
3.
SC =
1.5
Fluid Handling
1.5.1
Abbreviations and Definitions for Fluid Handling1
(1.4.1)
(1.4.2a)
(1.4.2b)
(1.4.3)
(1.4.4)
1. GPM gallons per min
2. lbm /minute pound mass per min
3. EWT entering water temperature
4. LWT leaving water temperature
5. ft hd head in ft of water
6. T temperature difference, °F
7. P pressure, lbs/in2
8. Z height above datum, ft
9. Pabs absolute pressure, lbs/in2
10. Pgage gauge pressure, lbs/in2
11. Patm atmospheric pressure, lbs/in2, 14.7 psia @ sea level
12. SG or specific gravity, mass of liquid/mass of water at 39° F
water 1, dimensionless
13. Cp = specific heat, BTU/lb · °F
HVAC_book.indb 8
9/1/09 1:46:04 PM
HVAC Equations for Everyday Use
9
14. SW specific weight at given temperature, lbs/ft3
15. Q Btu/hr
16. BHP brake horsepower
ft • lbs
17. 1BHP = 33, 000 minute
18. eff pump efficiency, dimensionless fraction ⱕ 1
19. RPM speed, revolutions per min
20. Subscript1 original condition; subscript2 new condition
21. H feet of head, ft. hd.
22. hg system pressure, ft. hd.
V2
23. hv velocity head,
, ft. hd.
2g
1.5.2
Fluid Handling Equations
T EWT LWT
(1.5.1)
Pabs Pgage Patm
(1.5.2)
1 PSI 2.31 ft hd for clear water, SG 1
(1.5.3)
Calculating required GPM for all fluids:
) (
)
⎛
⎞
Q × 7.48 gallons
(
ft 3
⎟
GPM = ⎜
⎜ C p × ( EWT − LWT × SG × SW × 60 min
⎟
hr ⎠
⎝
)
(1.5.4)
Simplified required GPM required using clean water:
GPM =
Q
500 × EWT − LWT
(
)
(1.5.5)
Head loss for open system:
H Z hg hv
Pump brake horsepower:
BHP =
(GPM ) × ( ft hd )
(3960) × ( eff )
(1.5.6)
(1.5.7)
Pump laws (based on constant impeller size, SG, piping system
and variable pump speed):
Change of flow:
HVAC_book.indb 9
⎛ GPM1 ⎞
= ⎜
⎟
Hf2
⎝ GPM 2 ⎠
H f1
2
(1.5.8)
9/1/09 1:46:05 PM
10
Chapter One
Find new flow based on pump speed:
⎛ RPM 2 ⎞
GPM 2 = GPM1 × ⎜
⎟
⎝ RPM1 ⎠
(1.5.9)
New brake horsepower BHP:
3
⎛ RPM 2 ⎞
BHP2 = BHP1 × ⎜
(1.5.10)
⎟
⎝ RPM1 ⎠
Pump laws (based on variable impeller size, constant pump speed,
SG and piping system):
⎛ Diameter2 ⎞
GPM 2 = GPM1 × ⎜
(1.5.11)
⎟
⎝ RPM1 ⎠
⎛ Diameter2 ⎞
H 2 = H1 × ⎜
⎟
⎝ RPM1 ⎠
2
⎛ Diameter2 ⎞
BHP2 = BHP1 × ⎜
⎟
⎝ RPM1 ⎠
(1.5.12)
3
1.6
Power and Energy
1.6.1
Abbreviations and Definitions for Power and Energy
(1.5.13)
1. Eff efficiency, dimensionless ratio
2. Kw kilowatts
3. VA volt · amps
4. Amps amperes
5. PF power factor, dimensionless real power
watts
P
= =
apparent power
S volt • amps
6. HP horsepower
7. hpout output horsepower
8. Wattsin input watts
9. V volts
10. 3 three-phase
1.6.2
Power Equations3
Efficiency:
Eff =
HVAC_book.indb 10
(746) × ( hp )
out
Wattsin
(1.6.1)
9/1/09 1:46:06 PM
HVAC Equations for Everyday Use
11
Three-phase power:
Kw3 =
V × Amps × PF × 3
1000
VA3 = V × Amps × 3
746 × HP
Amps3 =
Eff3 =
3 × V × Eff × PF
746 × HP
V × Amps × PF × 3
Single-phase power:
Kw =
1.7
1.7.1
(1.6.3)
(1.6.4)
(1.6.5)
V × Amps × PF
1000
(1.6.6)
746 × HP
V × Eff × PF
(1.6.7)
746 × HP
V × Amps × PF
(1.6.8)
Amps =
Eff =
(1.6.2)
Steam Equations
Steam Abbreviations and Definitions
1. hfg enthalpy of steam at given pressure (latent heat of vaporization)
2. Q heating load in BTU/hr
3. v specific volume
4. t temperature, °F
5. m mass flow rate, lbs/hr
6. hf 1 enthalpy of condensate before steam trap, BTU/lb
7. hf 2 enthalpy of condensate at flashed condensate pressure, BTU/lb
8. hf g 2 latent heat of vaporization at flashed condensate pressure,
BTU/lb
9. P % of flashed steam
1.7.2
Steam Equations
Heating coil required steam flow rate:
m=
HVAC_book.indb 11
Q
h fg
(1.7.1)
9/1/09 1:46:07 PM
12
Chapter One
Where hfg = Latent heat of vaporization at specific operating pressure.
See any steam tables for value of hfg.
Steam condensate trap sizing:
Steam trap capacity minimum 2 lb/hr requirement of
steam heating coil capacity, heat exchanger or main piping
drip locations.
(1.7.2)
Steam flash tank sizing:
Percent of condensate flashed to steam:
hf 1 − hf 2
P=
× 100
h fg 2
(1.7.3)
PART 2—INFREQUENTLY USED HVAC EQUATIONS
1.8
Air Side Equations
1.8.1
Air Side Abbreviations and Definitions
1. duct roughness factor, ft
2. v kinematic viscosity, ft2/s
3. V duct velocity, ft/min
4. pf duct friction loss, in of water
5. f, f Colebrook equation duct friction factor, dimensionless
6. Dh Hydraulic diameter, in
7. Re Reynolds number, dimensionless
8. TR temperature, °R Rankine T(°F) 459.67
9. PSIA absolute pressure, lb per sq in
10. Ra gas constant for dry air (53.352 ft · lbf/lbm · °R)
11. Rw gas constant for water vapor (85.778 ft · lbf/lbm · °R)
12. WS humidity ratio at saturation, lba/ lbda
13. W humidity ratio, lba/ lbda
14. relative humidity, %
15. degree of saturation
16. pws saturation pressure, psia
17. pws(t*) saturation pressure for t*, psia
18. t* thermodynamic wet bulb temperature, °F
19. t dry bulb temperature of moist air, °F
20. W *s humidity ratio at given t*
21. Mw mass of water vapor in air sample, lbm
HVAC_book.indb 12
9/1/09 1:46:08 PM
HVAC Equations for Everyday Use
13
22. Ma mass of dry air in sample, lbm
23. q specific humidity, dimensionless
24. va specific volume of dry air, ft3/lb
25. R universal gas constant, 1545.32 ft · lbf/lb mol · °R
26. density of air, lbm/ft3
27. P perimeter of duct cross-section, in
1.8.2
Duct Friction Loss2
Darcey equation for duct friction loss:
⎛ 12 fL ⎞ ⎛ V ⎞
p f = ⎜
⎟ ⎜
⎟
⎝ Dh ⎠ ⎝ 1097 ⎠
2
(1.8.1)
Hydraulic radius for noncircular ducts:
Dh 4A/P
(1.8.2)
Colebrook equation for duct friction loss:
⎛ 12
2.51 ⎞
= −2 log ⎜
+
⎟
f
⎝ 3.7 Dh Re f ⎠
1
(1.8.3)
Altshul/Tsal equation for duct friction loss:
⎛ 12
68 ⎞
f = 0.11 ⎜
+
⎟
⎝ Dh Re ⎠
0.25
'
(1.8.4)
If f ⱖ 0.018: f f
If f 0.018: f 0.85f 0.0028
Reynolds number for all air conditions:
Re =
DhV
720v
(1.8.5a)
Reynolds number for standard air
Re 8.56DhV
1.8.3
Psychrometrics2
PSIA gauge pressure atmospheric pressure
M
humidity ratio W = W
Ma
See Section 20.2.
HVAC_book.indb 13
(1.8.5b)
(1.8.6)
9/1/09 1:46:09 PM
14
Chapter One
specific humidity q =
relative humidity =
W
(1 + W )
(1.8.7)
(1.8.8)
)( f p /p )
(
1− 1−
s
ws
Saturation pressure from 148°F to 32°F ln( pws ) =
−1.021416462 + 04
+ ( −4.89350301 +
TR
)
( −5.37657944 − 03)T + (1.92023769 − 07)T
( 3.55758316 − 10)T + ( −9.03446883 − 14 )T +
( 4.1635019) ln (T )
2
R
R
3
(1.8.9)
4
R
R
R
Saturation pressure from 32°F to 392°F ln( pws ) =
−1.044039708 + 04
+ ( −0.112946496 +
TR
)
( −2.7022355 − 02 )T + (1.2890360 − 05)T +
( −2.478068 − 09)T + (6.5459673) ln T
2
R
R
(1.8.10)
3
R
R
Humidity ratio at saturation temperature t*:
( ) ⎞⎟
⎜⎝ p − p ( t ) ⎟⎠
⎛
Ws* = 0.62198 ⎜
pws t *
(1.8.11)
*
ws
Humidity ratio:
(1093 − 0.556t )W − 0.240 (t − t )
W=
*
*
s
*
1093 + 0.444t − t *
(1.8.12)
Humidity ratio at saturation:
Degree of saturation:
()
()
⎛ pws t ⎞
Ws = 0.62198 ⎜
⎟
⎝ p − pws t ⎠
=
W
|
Ws t , p
(1.8.13)
(1.8.14)
Volume of moist air mixture v
HVAC_book.indb 14
9/1/09 1:46:10 PM
HVAC Equations for Everyday Use
⎛RT ⎞
v = ⎜ a R ⎟ 1 + 1.6078W
⎝ p ⎠
(
)
15
(1.8.15)
Enthalpy of the moist air (BTU/lb):
h 0.240t W(1061 0.444t)
(1.8.16)
Moist air sample water vapor partial pressure, psia:
pw =
( pW )
0.62198 + W
(1.8.17)
Dew-point temperature for 32°F to 200°F:
td 100.45 33.193ln(pw) 2.319ln(pw)2 0.17074ln(pw)3 1.2063(pw)0.1984
(1.8.18)
Dew-point temperature for less than 32°F:
td 90.12 26.142ln(pw) 0.8927ln (pw)2
(1.8.19)
Adiabatic mixing of two air streams:
h2 − h3 W2 − W3 ma1
=
=
h3 − h1 W3 − W1 ma 2
(1.8.20)
Where ma mass flow rate of air, lb dry air/min.
1.9
Fluid Handling1,2,3
1.9.1
Abbreviations and Definitions
1. Cp specific heat, BTU/lb · °F
2. Hf head friction loss, ft of H2O
3. f Colebrook equation friction factor, dimensionless
4. K sum of resistance coefficients for fittings and valves in piping
section, dimensionless
5. L length of piping, ft
6. D inside pipe diameter, ft
7. d inside pipe diameter, in
8. g gravitational constant 32.2 ft/sec2
9. V velocity, ft/sec
10. Re Reynolds number
11. e absolute roughness of pipe, ft
HVAC_book.indb 15
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16
Chapter One
12. w density of fluid, lb/ft3
13. dynamic viscosity lb/ft · sec
14. SG or specific gravity mass of liquid/mass of water at 39°F,
water 1, dimensionless
1.9.2
Fluid Handing Equations
Piping friction loss (Darcy-Weisbach equation):
Hf = f
L V2
V2
+K
2g
D 2g
(1.9.1)
Colebrook equation for piping friction factor:
⎛ e
2.51 ⎞
= −2 log10 ⎜
+
⎟
f
Re f ⎠
⎝ 3.7 D
1
(1.9.2)
Reynolds number for piping:
Re =
1.9.3
VDw
all fluids, Re = 7742
Vd
for water
(1.9.3)
Steam Equation
EDR steam load BTUH
240
(1.9.4)
Where: EDR equivalent direct radiation
1.10
Smoke Management Equations4
Steady state fire mass consumption:
m=
Where
Q Δt
Hc
(1.10.1)
m total fuel mass consumed (lb) or (kg)
Q heat release rate (BTU⁄sec) or (kW)
t duration of fire (sec)
Hc heat of combustion of fuel (BTU⁄lb) or (kJ⁄kg)
t-squared fire mass consumption:
m=
HVAC_book.indb 16
333Δt 3
H c t g2
(1.10.2)
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HVAC Equations for Everyday Use
17
Where
m total fuel mass consumed (lb) or (kg)
tg growth time of fire (sec)
t duration of fire (sec)
Hc heat of combustion of fuel (BTU⁄lb) or (kJ⁄kg)
1.10.1
Smoke Layer Calculations
Steady state fires (uniform cross section for height, A/H2 0.9 to 1.4,
z/H 0.2, prior to smoke exhausting)
⎛ 13 ⎞
tQ
⎜ 4 ⎟
⎜
3 ⎟
z
= 0.67 − 0.28 ln ⎜ H ⎟
(1.10.3a)
A
H
⎟
⎜
⎜ H2 ⎟
⎠
⎝
Where
z distance from the base of the fire to the bottom of the
smoke layer (ft)
H ceiling height above the fire surface (ft)
t time (sec)
Q heat release rate for steady state fire (BTU⁄sec)
A cross-sectional area of the space being filled with
smoke (ft2)
⎛ 13 ⎞
tQ
⎜ 4 ⎟
⎜
3 ⎟
z
= 1.11 − 0.28 ln ⎜ H ⎟
H
⎜ A ⎟
⎜ H2 ⎟
⎠
⎝
(1.10.3b)
Where
z distance from the base of the fire to the bottom of the
smoke layer (m)
H ceiling height above the fire surface (m)
t time (sec)
Q heat release rate for steady state fire (kW)
A cross-sectional area of the space being filled with
smoke (m2)
Unsteady fires (t-squared fires) (uniform cross section for height, A/H2
= 0.9 to 2.3, z/H > 0.2, prior to smoke exhausting)
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18
Chapter One
⎛
⎞
z
t
= 0.23
3
⎜
5 ⎟
H
⎜ t 25 H 45 ⎛ A ⎞ ⎟
⎜⎝ H 2 ⎟⎠ ⎟
⎜⎝ g
⎠
−1.445
(1.10.4a)
Where
z distance from the base of the fire to the bottom of the
smoke layer (ft)
H ceiling height above the fire surface (ft)
t time (sec)
tg growth time (sec)
A cross-sectional area of the space being filled with
smoke (ft)
⎛
⎞
z
t
= 0.91
3
⎜
5 ⎟
H
⎜ t 25 H 45 ⎛ A ⎞ ⎟
⎜⎝ H 2 ⎟⎠ ⎟
⎜⎝ g
⎠
−1.445
(1.10.4b)
Where
z distance from the base of the fire to the bottom of the
smoke layer (m)
H ceiling height above the fire surface (m)
t time (sec)
tg growth time (sec)
A cross-sectional area of the space being filled with
smoke (m)
The following are the empirical equations from NFPA 92B for atrium
fires that are not under balconies:
2
(1.10.5a)
zl 0.533Qc ⁄5
1
5
when z zl, m (0.022Qc ⁄3 z ⁄3) 0.0042Qc
(1.10.5b)
3
when z ⱕ zl, m 0.0208Qc ⁄5 z
(1.10.5c)
Where
zl limiting elevation (flame height) (ft)
Qc convective portion of heat release rate (BTU⁄sec)
z distance above the base of the fire to the smoke interface
layer (ft)
m mass flow rate in plume at height z (lb⁄sec)
m 0.071Qc ⁄3 z ⁄3 0.0018Qc
1
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5
(1.10.5d)
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HVAC Equations for Everyday Use
19
when z zl, m (0.022Qc ⁄3 z ⁄3) 0.0042Qc
(1.10.5e)
when z ⱕ zl, m 0.0208Qc ⁄5 z
(1.10.5f)
1
5
3
Where
zl limiting elevation (m)
Qc convective portion of heat release rate (kW)
z distance above the base of the fire to the smoke interface
layer (m)
m mass flow rate in plume at height z (kg⁄sec)
The smoke layer temperature can be calculated from the following:4
Ts = To +
Qc (1 − )
mC p
(1.10.6)
Where
Ts smoke layer temperature, °F(°C)
To ambient temperature, °F(°C)
Qc convective portion of HHR, BTU⁄sec (kW)
m mass flow rate of exhaust air, lb⁄sec (kg⁄sec)
Cp specific heat of plume gases, BTU⁄lb (kg⁄kJ)
wall heat transfer fraction (dimensionless)
The convective portion of the HHR is determined by:4
Where
Qc XcQ
(1.10.7)
Qc convective portion of heat release rate, BTU⁄sec (kW)
Q heat release rate, BTU⁄sec (kW)
Xc convective heat fraction (0.7 default)
Density of the plume gases can be calculated from the following
equation:4
T
s = r r
(1.10.8)
Ts
Where
s density of exhaust gases, lbm⁄ft (kg⁄m )
Ts temperature of exhaust gases, absolute, °R (°K)
Tr reference temperature absolute, °R (°K)
r density at reference temperature, absolute, lbm⁄ft (kg⁄m )
2
3
2
3
The following are the empirical equations from NFPA 92B for atrium
balcony spill plume:
1
(1.10.9a)
m 0.12 (QW 2) ⁄3 (zb 0.25H)
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20
Chapter One
Where
m mass flow rate in plume, (lb⁄sec)
Q heat release rate (HHR) of fire (BTU⁄sec)
W width of the plume under the balcony (ft)
zb height above the underside of the balcony
to the smoke layer interface (ft)
H height of the balcony above the base of the fire (ft)
1
m 0.36 (QW 2) ⁄3 (zb 0.25H)
(1.10.9b)
Where
m mass flow rate in plume (kg⁄sec)
Q heat release rate (HHR) of fire (kW)
W width of the plume under the balcony (m)
zb height above the underside of the balcony
to the smoke layer interface (m)
H height of the balcony above the base of the fire (m)
References
1. ASHRAE Pocket Guide for Air Conditioning, Heating, Ventilation and Refrigeration
(Inch-Pound Edition), 1993.
2. ASHRAE Handbook, Fundamentals, 2005.
3. Engineering Cookbook, 1999, Loren Cook Company, Inc.
4. NFPA 92B Standard for Smoke Management in Malls, Atria, and Large Spaces, 2009.
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