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Mathematics for Plumbers and Pipefitters 8th Edition Solution Manual

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    Guide to Accompany Mathematics for Plumbers and Pipefitters Smith • Eighth Edition

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    CONTENTS SECTION 1 REVIEW OF BASIC FUNDAMENTALS Unit 1 Some Basic Rules for Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 2 Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 3 Solving Formulas/Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 4 Square Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 5 Review of Angle Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Unit 6 Conversion of Length Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 SECTION 2 PIPE LENGTH CALCULATIONS Unit 7 Standard Weight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 8 Allowance for Threaded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 9 Copper Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 10 Allowance for Copper Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 11 Plastic Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 12 Allowance for Plastic Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 13 Welding Steel Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unit 14 Allowance for Weld-Type Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Unit 15 Equal Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Unit 16 Angles in Plumbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Unit 17 Offset, Diagonal, Rise, and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Unit 18 Solving for 45° Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Unit 19 45° Diagonal and Pipe Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Unit 20 Three-Pipe Diagrams with a 45° Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Unit 21 Right Angle with a 45° Diagonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Unit 22 45° Offset with Wye Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Unit 23 Wye and Tee-Wye Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Unit 24 The 0.707 Constant in 45° Pipe Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Unit 25 Solving for Other Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Unit 26 Pipe Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Unit 27 Cast Iron Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Unit 28 Cast Iron Assemblies with Various Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Unit 29 1 ⁄ 5 Bend Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Unit 30 Assemblies with Cast Iron Wyes and Tee-Wyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Unit 31 Single Loop Back-Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Unit 32 Grade, Percent Grade, Drop and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Unit 33 Elevation and Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Unit 34 Elevation in Plan View Pipe Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Unit 35 Jumper Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Unit 36 45° Offsets in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Unit 37 Special Case of 45° Offsets in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Unit 38 Rolling Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Unit 39 Combination Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Unit 40 Pipe Length by Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Unit 41 Cast Iron Flanged Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Unit 42 Miter Cuts, Welded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Guide iii

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    SECTION 3 SHEET METAL WORK Unit 43 Shower Pan or Safe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Unit 44 Rectangular Tank Liner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Unit 45 Cylindrical Stretchouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Unit 46 Roof Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 SECTION 4 VOLUMES, PRESSURES, AND CAPACITIES Unit 47 Water Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Unit 48 Rectangular Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Unit 49 Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Unit 50 Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Unit 51 Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Unit 52 Partially Filled Containers of Varying Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Unit 53 Water Pressure, Head, Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Unit 54 Ratio of Pipe Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Unit 55 Pipe Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 SECTION 5 PHYSICS Unit 56 Mechanical Advantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Unit 57 States of Matter and Why it Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Unit 58 Properties of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 SECTION 6 HEATING Unit 59 Heat Loss vs. Radiation Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Unit 60 Radiation Sizing for Total Heat Loss of a Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Unit 61 Estimating Size of Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Unit 62 Sizing Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Unit 63 Heating Problems—Two-Floor House . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 SECTION 7 THE BUILDERʼS LEVEL Unit 64 Word Use in Leveling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Unit 65 Math Aids in Leveling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 SECTION 8 THE BUSINESS OF PLUMBING Unit 66 Starting a Business . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Unit 67 Taking Care of Business . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 iv Guide

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    TO THE INSTRUCTOR ABOUT THE TEXT MATHEMATICS FOR PLUMBERS AND PIPE FITTERS provides instructional material for anyone involved with plumbing and pipe fitting who must develop the ability to interpret pipe diagrams and to correctly measure and com- pute pipe lengths for the installation of required plumbing. After successfully completing the exercises presented in the text, students should understand the mathematics of plumbing and pipe fitting and be able to apply the principles in doing their work. Section 1, Review of Basic Fundamentals, presents a concise review and practice of the essential principles and processes of mathematics needed to work with the text. It is presumed that students have already had instruction in basic fundamentals. Section 2, Pipe Length Calculations, deals with the information concerning pipe diagrams and length-of-pipe cal- culations. The information proceeds logically form simple problems to more complex ones. Each problem is carried through to find the actual lengths to cut the pipe, including fitting allowances. Section 3, Sheet Metal Work, provides a working knowledge of sheet lead material in weight and thickness. The basic stretchouts and some of their uses are included. Section 4, Volumes, Pressures, and Capacities, includes units on volumes and their application to plumbing and pipe fitting. Rectangles, cylinders, spheres and segments are presented, with conversion of the volumes to cubic yards, gallons and weight of water—according to trade needs and interests. Advanced work in changing pressure and head as well as in comparing the capacity of pipes to carry water is also provided. Section 5, Physics, gives practice working with mechanical advantage, states of matter, and properties of gasses. Section 6, Heating, gives basic instruction in calculating heat loss and in estimating amount of radiation and size of pipe required. Both one-floor and two-floor house plans are included. Section 7, The Builder’s Level, introduces the student to the vocabulary and math aids useful to plumbers in their use of the builder’s level. Section 8, The Business of Plumbing, covers the essentials of planning a business and keeping it financially healthy. The Appendix consists of tables and specialized data necessary for the solution of various text problems and tables of general, timesaving information. The data tables, which include pipe fitting allowances and constants as well as the powers and roots and decimal-fractional equivalents of many numbers, will still prove useful after the student has com- pleted the course. They will be useful as permanent handbook-type information at any later time a need arises. ABOUT THE GUIDE The INSTRUCTORS GUIDE shows basic solution methods and fitting allowances for all problems presented in Section 2, Pipe Length Calculations. Answers also are given for most problems in other sections; solutions and diagrams are given in all cases where it is felt that they will be helpful to the instructor. Because plumbing and pipe- fitting work measurements are usually taken to the closest 1 ⁄ 16 inch, answers to problems in the text correct within 1 ⁄ 16 inch are accept- able. An even greater tolerance is allowed for answers given in Section 5, Heating, because when heat loss and radia- tion are figured, the general practice is to round the numbers to allow for a margin of safety. READING A TEXTBOOK In preparation for the use of any text, students should be aware of the particular aids offered. For example, they should be encouraged to answer some of these questions: • What does the Table of Contents show about the areas covered in this book? • When was this book copyrighted? Why is this important? • What is the difference between a section and a unit? • Does this book have spaces for me to write the answers or do I need my own paper and pencil? • Does this book have an index? A glossary? An appendix? If not, why not? If so, what information is available in them? When do I need to use them? • Is an answer key available? Guide v

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    READING AND WRITING MATHEMATICS Reading a mathematics textbook requires different skills from reading other types of books. Students should be encouraged to develop some special skills. They should be made aware of the specialized vocabulary and its meaning in mathematics problems. The following steps are helpful in the improvement of mathematical reading ability. • Read the whole problem to find out what it is about. • Look for the question or direction that tells what to find or what to do. • Look carefully at the problem to determine the facts that are given: a. Discard irrelevant facts. b. Be sure of the meaning of all words, especially mathematical terms. c. Consider any conversions necessary, such as feet to inches. • Plan the steps necessary in order to arrive at the answer: a. Are any special computing devices or tools needed, such as a calculator, a steel ruler or a micrometer? b. Are any other facts necessary, such as those found in the Appendix? c. Does a drawing help relate the facts to each other? • Prepare the given information: a. Relate the facts in a word statement. b. Write the numbers, formulas, or symbols necessary. c. Estimate the answer. • Use numbers in the mathematical relationship, and compute the necessary information. Round final answers as directed. • Verify the answer: a. Check the problem by checking the arithmetic processes. b. Does the final answer agree with the estimate? c. Does the answer sound reasonable for the situation originally described? d. Is the answer in the proper units or terminology? vi Guide

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    SECTION 1 REVIEW OF BASIC FUNDAMENTALS UNIT 1 SOME BASIC RULES FOR MATHEMATICS Answer these questions. 1) What kind of measure is used to describe the size of a car’s fuel tank? Cubic, volume, three dimensional. 2) What kind of measure is used to order fabric? Square, area, two dimensional. 3) The distance between cities is expressed with what kind of measure? Lineal or linear. 1. 15.7 4. 1700 7.  3 10. 19 13. 0.333 or 1 / 3 2. 9.42 5. 8540 8. 9 11. 0 3. 38.277 or 38.2766 6.  6 9.  2 12. 4 UNIT 2 FORMULAS Do the following problems. 1) 3  3  4  15 5) 3  (5  4) 2  84 9) 3  6  4  3  9 2) (3  3)  4  24 6) (3  5)  4 2  24 10) (3  6  4)  3  3 3) 3  (3  4)  15 7) 3  (5  4 2 )  24 11) 3  (6  4  3)   15 4) 3  3  4 2  51 8) 3  4  3  6  9 12) 3  [(6  4)  3]   27 13) 11  6 2  44 3 2 A. 1. P  50  -0  B. 1. A  210.25 sq. in. C. 1. V  1,728 cu. in. 2. 9  42 m 2. A  1,225 cm 2 2. V  1,000 cm 3 3. P  67  -6  3. A  15.75 sq. ft. 3. V  180 cu. yd. 4. P  19.5 m 4. A  15.75 m 2 4. V  154 m 3 5. C  40.035  5. A  117 sq. ft. 5. V  3,264 cu. ft. 6. C  101.422 cm 6. A  216 sq. in. 6. V  302.76 cm 3 7. P  35.98 ft. 7. A  864 cm 2 7. V  699.435 cu. ft. 8. A  254.34 sq. in. 8. V  11,627.42 cm 3 9. A  2,122.64 cm 2 9. V  5,699.10 cu. in. 10. A  196.25 cm 2 10. A  L  W 11. V  S  S  h UNIT 3 SOLVING FORMULAS/EQUATIONS Practice problems: Formula: A  L  W: this is the formula for the area of a rectangle. Area is equal to length multiplied times width. 1. 60 3. 20 5. 17 2. 9 4. 12 6. 4.5 1. 15 ft. 5. 7.01  9. 4  radius 2. 4 m 6. 17.83 cm 8  diameter 3. 16  -6  7. 4.8  10. 6 cm radius 4. 21 m 8. 4 cm 12 cm diameter UNIT 4 SQUARE ROOT 1. 10  3. 32.02  5. 47.93  2. 17  4. 41.87  6. 16.97  Guide 1

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    7. 1.414  10. 29.10 cm 13. 12.45  8. 15.05 cm 11. 9  14. 7 cm 9. 18.61 cm 12. 2.24  15. 39.55 cm UNIT 5 REVIEW OF ANGLE MEASURE 1. a. b. Student readings should compare closely with computed measurements. c. Angle C  48° Alternate angles are equal. Angle A  90°  48°  42° Right angle  90° or Angle B  180°  (48°  90°)  42° Sum of 3 angles  180° Angle A  42° Alternate angles are equal. Angle D  Angle C  48° Opposite angles are equal. 2. A  30° D  102° G  48° B  45° E  9° H  67° C  66° F  22° I  78° 3. ∠ A  25° ∠ C  58° ∠ E  160° ∠ B  10° ∠ D  122° ∠ F  31 1 / 2 ° or 31°30  UNIT 6 CONVERSION OF LENGTH MEASURES 11. 85 cm 12. 8.72 m Inches and Fractional Inches and Decimal Feet, Inches and Feet and Decimal Parts of Inch Parts of Inch Fractional Parts of Parts of Foot Inch 1. 19 11 / 16  19.687  1  -7 11 / 16  1.64  2. 42 3 / 8  42.375  3  - 6 3 / 8  3.53  3. 26 3 / 8  26.35  2  -2 3 / 8  2.20  4. 69 15 / 16  69.94  5  -9 15 / 16  5.83  5. 100 1 / 2  100.5  8  - 4 1 / 2  8.38  6. 33 3 / 16  33.19  2  -9 3 / 16  2.77  7. 66 13 / 16  66.84  5  -6 13 / 16  5.57  8. 181 1 / 16  181.08  15  -1 1 / 16  15.09  9. 103 3 / 4  103.75  8  -7 3 / 4  8.65  10. 79 3 / 4  79.75  6  -7 3 / 4  6.65  2 Guide

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    SECTION 2 PIPE LENGTH CALCULATIONS UNIT 7 STANDARD WEIGHT PIPE 1. 1 / 16  2. 1 / 8  , 1 / 8  , 1 / 4  3. A hole drilled, into which a tap is turned to cut internal threads. There must be metal left into which to cut the threads. 4. 1 / 8  5. About 3 / 32  UNIT 8 ALLOWANCE FOR THREADED PIPE 1. e-e  18   [(1 3 / 8   1 3 / 8  )  2( 1 / 2  )]  16 1 / 4  , or 1  - 4 1 / 4  2. e-e  25 1 / 2   [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  24 1 / 4  , or 2  - 1 / 4  3. e-e  40   [(1 1 / 2   1 1 / 8  )  2( 1 / 2  )]  38 3 / 8  , or 3  -2 3 / 8  4. e-e  40   [(1 5 / 16   1 5 / 16  )  2( 1 / 2  )]  38 3 / 8  , or 3  -2 3 / 8  5. e-e  63   [1 3 / 4   1 3 / 4  )  2( 1 / 2  )]  60 1 / 2  , or 5  - 1 / 2  UNIT 9 COPPER TUBING 1. 0.045  2. 0.090  3. K and L 4. The long length would not need joints. It is easier to get in place. 5. Yes. It is a heavier wall than DWV. 6. No. It is not recommended for this service. UNIT 10 ALLOWANCE FOR COPPER FITTINGS 1. e-e  18   ( 1 / 2   1 / 2  )  18  1  17  , or 1  -5  2. e-e  87   (2 7 / 8   2 7 / 8  )  87   5 3 / 4   81 1 / 4  or 6  -9 1 / 4  3. e-e  31 1 / 2   (1 1 / 8   7 / 16  )  31 1 / 2   1 9 / 16   29 15 / 16  or 2  -5 15 / 16  4. e-e  43   (1 7 / 8   5 / 16  )  43   2 3 / 16   40 13 / 16  or 3  4 13 / 14  5. e-e  81   (1 5 / 16   13 / 16  )  81   2 1 / 8   78 7 / 8  or 6  -6 7 / 8  UNIT 11 PLASTIC PIPE 1. C 2. B 3. A 4. A 5. D 6. C 7. C UNIT 12 ALLOWANCE FOR PLASTIC FITTINGS 1. e-e  7 1 / 2   ( 9 / 16   9 / 16 )  6 3 / 8  2. e-e  74   (3 1 / 16   3 1 / 16  )  67 7 / 8  or 5  -7 7 / 8  3. e-e  37   (1 9 / 16   1  )  34 7 / 16  or 2  -10 7 / 16  4. e-e  42 1 / 4   (2 5 / 16   11 / 16  )  39 1 / 4  or 3  -3 1 / 4  5. e-e  92   (1 3 / 4   1  )  89 1 / 4 or 7  -5 1 / 4  UNIT 13 WELDED STEEL PIPING 1. a 3. b 5. d 7. a 9. d 2. c 4. d 6. b 8. c 10. c Guide 3 c-c e-e 1. 18  17  2. 87  81 1 / 4  3. 31 1 / 2  29 15 / 16  4. 43  40 13 / 16  5. 81  78 7 / 8 

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    UNIT 14 ALLOWANCE FOR WELD-TYPE FITTINGS Size -fitting -fitting Inch C to C one Allowance two Allowance E to E 2 A 19 7 / 16 flange 1 / 4 tee 2 1 / 8 17 1 / 16 B 9 1 / 2 tee 2 1 / 8 flange 1 / 4 7 1 / 8 C 33 flange 1 / 4 LR Ell 3 1 / 8 25 5 / 8 D 22 LR Ell 3 1 / 8 SR Ell 2 1 / 8 16 3 / 4 E 10 SR Ell 2 1 / 8 45° Ell 1 3 / 8 6 1 / 2 3 A 19 7 / 16 flange 5 / 16 tee 3 1 / 8 16 B 9 1 / 2 tee 3 1 / 8 flange 5 / 16 6 1 / 16 C 33 flange 5 / 16 LR Ell 4 5 / 8 28 1 / 16 D 22 LR Ell 4 5 / 8 SR Ell 3 1 / 8 14 3 / 8 E 10 SR Ell 3 1 / 8 45° Ell 2 4 7 / 8 4 A 19 7 / 16 flange 5 / 16 tee 4 1 / 8 15 B 9 1 / 2 tee 4 1 / 8 flange 5 / 16 5 1 / 16 C 33 flange 5 / 15 LR Ell 6 1 / 8 26 9 / 16 D 22 LR Ell 6 1 / 8 SR Ell 4 1 / 8 11 3 / 4 E 10 SR Ell 4 1 / 8 45° Ell 2 5 / 8 3 1 / 4 5 A 19 7 / 16 flange 5 / 16 tee 5 1 / 8 14 B 9 1 / 2 tee 5 1 / 8 flange 5 / 16 4 1 / 15 C 33 flange 5 / 16 LR Ell 7 5 / 8 25 1 / 16 D 22 LR Ell 7 5 / 8 SR Ell 5 1 / 8 9 1 / 4 E 10 SR Ell 5 1 / 8 45° Ell 3 1 / 4 1 1 / 4 UNIT 15 EQUAL SPACING 1. 17 1 / 2   17.5  ; 17.5   2  8.75  or 8 3 / 4  J: c-c  8 3 / 4  e-e  8 3 / 4   [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  7 1 / 2  (threaded) e-e  8 3 / 4   ( 3 / 8   3 / 8  )  8  (copper) e-e  8 3 / 4   ( 1 / 2   1 / 2  )  7 3 / 4  (PVC) K: c-c  8 3 / 4  e-e  8 3 / 4   [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  7 1 / 2  (threaded) e-e  8 3 / 4   ( 3 / 8   3 / 8  )  8  (copper) e-e  8 3 / 4   ( 1 / 2   1 / 2  )  7 3 / 4  (PVC) 2. 41   3  13.666 or 13 11 / 16  L: c-c  13 11 / 16  e-e  13 11 / 16   [(1 1 / 2   1 1 / 2  )  2( 1 / 2  )]  11 11 / 16  (threaded) e-e  13 11 / 16   ( 3 / 4   3 / 4  )  12 3 / 16  (copper) e-e  13 11 / 16   ( 11 / 16   11 / 16  )  12 5 / 16  (PVC) M: c-c  13 11 / 16 e-e  13 11 / 16   [(1 1 / 2   1 1 / 2  )  2( 1 / 2  )]  11 11 / 16  (threaded) e-e  13 11 / 16   ( 3 / 4   3 / 4  )  12 3 / 16  (copper) e-e  13 11 / 16   ( 11 / 16   11 / 16  )  12 5 / 16  (PVC) N: c-c  13 11 / 16  e-e  13 11 / 16   [(1 1 / 2   1 1 / 2  )  2( 1 / 2  )]  11 11 / 16  (threaded) e-e  13 11 / 16   ( 3 / 4   3 / 4  )  12 3 / 16  (copper) e-e  13 11 / 16   ( 11 / 16   11 / 16  )  12 5 / 16  (PVC) 3. 67 1 / 2   67.5  ; 67.5  4  16.875  or 16 7 / 8  P: c-c  16 7 / 8  e-e  16 7 / 8   [(1   1 3 / 8  )  2( 1 / 2  )]  15 1 / 2  , or 1  -3 1 / 2  (threaded) e-e  16 7 / 8   ( 1 / 4   1 / 2  )  16 1 / 8  or 1  -4 1 / 8  (copper) e-e  16 7 / 8   ( 5 / 16   9 / 16  ) or 1  -4  (PVC) 4 Guide

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    Q: c-c  16 7 / 8  e-e  16 7 / 8   [(1 3 / 8   1 3 / 8  )  2( 1 / 2  )]  15 1 / 8  , or 1  -3 1 / 8  (threaded) e-e  16 7 / 8   ( 1 / 2   1 / 2  )  15 7 / 8  or 1  -3 7 / 8  (copper) e-e  16 7 / 8   ( 9 / 16   9 / 16  )  15 3 / 4  or 1  -3 3 / 4  (PVC) R: c-c  16 7 / 8  e-e  16 7 / 8   [(1 3 / 8   1 3 / 8  )  2( 1 / 2  )]  15 1 / 8  , or 1  -3 1 / 8  (threaded) e-e  16 7 / 8   ( 1 / 2   1 / 2  )  15 7 / 8  or 1  -3 7 / 8  (copper) e-e  16 7 / 8   ( 9 / 16   9 / 16  )  15 3 / 4  or 1  -3 3 / 4  (PVC) 4. 32 5 / 8   32.625  ; 32.625   2  16.312 5   16 5 / 16  T: c-c  16 5 / 16  e-e  16 5 / 16   [( 3 / 4   1  )  2( 3 / 8  )]  15 5 / 16  or 1  -3 5 / 16  (threaded) e-e  16 5 / 16   ( 3 / 16  5 / 16 )  15 13 / 16  or 1  -3 13 / 16  (copper) e-e  16 5 / 16   ( 1 / 4   3 / 8  )  15 11 / 16  or 1  -3 11 / 16 (PVC) U: c-c  16 5 / 16  e-e  16 5 / 16   [(1   3 / 4  )  2( 3 / 8  )]  15 5 / 16  or 1  -3 5 / 16  (threaded) e-e  16 5 / 16   ( 5 / 16  3 / 16 )  15 13 / 16  or 1  -3 13 / 16  (copper) e-e  16 5 / 16   ( 3 / 8   1 / 4  )  15 11 / 16  or 1  -3 11 / 16 (PVC) UNIT 16 ANGLES IN PLUMBING 1. Complementary Fitting Angle Angle Bend 90° 0° 1 / 4 72° 18° 1 / 5 60° 30° 1 / 6 45° 45° 1 / 8 22 1 / 2 ° 67 1 / 2 ° 1 / 16 11 1 / 4 ° 78 3 / 4 ° 1 / 32 2. 50 / 360  5 / 36 bend 3. 1 / 9  360  40°, fitting angle 90°  40°  50°, complementary angle 4. A—fitting angle B—right angle C—complementary angle D—fitting angle E—complementary angle F—right angle UNIT 17 OFFSET, DIAGONAL, AND RISE OR RUN 1. 45° fitting angle Guide 5

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    2. 22 1 / 2 ° fitting angle 3. 11 1 / 4 ° fitting angle 4. 72° fitting angle UNIT 18 SOLVING FOR 45° ANGLES 1. Run  9  ; 9 2  9 2  162 Diagonal  162  12.727  Diagonal  12.728  9  1.414  offset Offset  9  12.727  0.707  diagonal 2. Offset Run Diagonal a. 10  10  14.14  14 1 / 8  b. 1  -4  1  -4  22.624  22 5 / 8  c. 21.21  21 3 / 16  21.21  21 3 / 16  2  -6  d. 3  -5  3  -5  57.974  58  e. 28.987  29  28.987  29  3  -5  f. 1  -2  1  -2  19.796  19 13 / 16  g. 20 cm 20 cm 28.28 cm h. 106.05 cm 106.05 cm 150 cm 6 Guide

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    UNIT 19 45° DIAGONAL AND PIPE LENGTH Note: Diagonal K = offset  constant. 1. K: c-c  8 1 / 4   1.414  11.665 5   11 11 / 16  e-e  11 11 / 16   [(1   1  )  2( 1 / 2  )]  10 11 / 16  (threaded) e-e  11 11 / 16   ( 1 / 4   1 / 4  )  11 3 / 16  (copper) e-e  11 11 / 16   ( 5 / 16   5 / 16  )  11 1 / 16  (PVC) 2. K: c-c  9   1.414  12.726   12 3 / 4  or 1  - 3 / 4  e-e  12 3 / 4   [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  11 1 / 2  (threaded) e-e  12 3 / 4   ( 5 / 16   5 / 16  )  12 1 / 8  or 1  - 1 / 8  (copper) e-e  12 3 / 4   ( 5 / 16   5 / 16  )  12 1 / 8  or 1  - 1 / 8  (PVC) 3. K: c-c  11 1 / 2   1.414  16.261   16 1 / 4  or 1  -4 1 / 4  e-e  16 1 / 4   [( 3 / 4   3 / 4  )  2( 1 / 2  )]  15 3 / 4  or 1  -3 3 / 4  (threaded) e-e  16 1 / 4   ( 3 / 16   3 / 16  )  15 7 / 8  or 1  -3 7 / 8  (copper) e-e  16 1 / 4   ( 1 / 4   1 / 4  )  15 3 / 4  or 1  -3 3 / 4  (PVC) 4. K: c-c  18   1.414  25.452   25 7 / 16  or 2  -1 7 / 16  e-e  25 7 / 16   [(1 5 / 16   1 5 / 16  )  2( 1 / 2  )]  23 13 / 16  or 1  -11 13 / 16 (threaded) e-e  25 7 / 16   ( 7 / 16   7 / 16  )  24 9 / 16  or 2  - 9 / 16  (copper) e-e  25 7 / 16   (1  1  )  23 7 / 16  or 1  -11 7 / 16  (PVC) 5. K: c-c  22 3 / 4   1.414  32.168 5   32 3 / 16  or 2  -8 3 / 16  e-e  32 3 / 16   [(1 5 / 16   1 5 / 16  )  2( 1 / 2  )]  30 9 / 16  or 2  -6 9 / 16  (threaded) e-e  32 3 / 16   ( 7 / 16   7 / 16  )  31 5 / 16  or 2  -7 5 / 16  (copper) e-e  32 3 / 16   (1   1  )  30 3 / 16  or 2  -6 3 / 16  (PVC) 6. c-c  24   1.414  33.936   33 15 / 16  or 2  -9 15 / 16  e-e  33 15 / 16   [(1 7 / 16   1 7 / 16  )  2( 1 / 2  )]  32 1 / 16  or 2  -8 1 / 16  (threaded) e-e  33 15 / 16   ( 9 / 16   9 / 16  )  32 13 / 16  or 2  -8 13 / 16  (copper) e-e  33 15 / 16   (1 1 / 8   1 1 / 8  )  31 11 / 16  or 2  -7 11 / 16  (PVC) 7. c-c  27 1 / 2   1.414  38.885   38 7 / 8  or 3  -2 7 / 8  e-e  38 7 / 8  [(1 7 / 16   1 7 / 16  )  2( 1 / 2  )]  37  or 3  -1  (threaded) e-e  38 7 / 8  ( 9 / 16   9 / 16  )  37 3 / 4  or 3  -1 3 / 4  (copper) e-e  38 7 / 8  (1 1 / 8   1 1 / 8  )  36 5 / 8  or 3  - 5 / 8  (PVC) 8. c-c  45   1.414  63.63   63 5 / 8  or 5  -3 5 / 8  e-e  63 5 / 8  [(1 11 / 16   1 11 / 16  )  2( 1 / 2  )]  61 1 / 4  or 5  -1 1 / 4  (threaded) e-e  63 5 / 8  ( 3 / 4   3 / 4  )  62 1 / 8  or 5  -2 1 / 8  (copper) e-e  63 5 / 8  (1 1 / 2   1 1 / 2  )  60 5 / 8  or 5  - 5 / 8  (PVC) 9. c-c  66 1 / 2  1.414  94.031   94  or 7  -10  e-e  94   [(1 11 / 16   1 11 / 16  )  2( 1 / 2  )]  91 5 / 8  or 7  -7 5 / 8  (threaded) e-e  94   ( 3 / 4   3 / 4  )  92 1 / 2  or 7  -8 1 / 2  (copper) e-e  94   (1 1 / 2   1 1 / 2  )  91  or 7  -7  (PVC) UNIT 20 THREE-PIPE DIAGRAMS WITH A 45° OFFSET 1. J: c-c  9  e-e  9   [(1 1 / 2   1 1 / 8  )  2( 1 / 2  )]  7 3 / 8  K: c-c  11   1.414  15.554   15 9 / 16 or 1  -3 9 / 16  e-e  15 9 / 16  [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  14 5 / 16  or 1  -2 5 / 16  L: c-c  30   (9   11  )  30   20   10  e-e  10   [(1 1 / 8   1 1 / 2  )  2( 1 / 2  )]  8 3 / 8  2. J: c-c  12  or 1  e-e  12   ( 3 / 8   3 / 16  )  11 7 / 16  K: c-c  13 1 / 2   1.414  19.089   19 1 / 16  or 1  -7 1 / 16  e-e  19 1 / 16   ( 3 / 16  3 / 16 )  18 11 / 16  or 1  -6 11 / 16  L: c-c  42 1 / 2   (12   13 1 / 2  )  17  or 1  -5  e-e  17   ( 3 / 16   3 / 8  )  16 7 / 16  or 1  -4 7 / 16  Guide 7

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    3. J: c-c  15  or 1  -3  e-e  15   [(1 3 / 8   1  )  2( 1 / 2  )]  13 5 / 8 or 1  -1 5 / 8  K: c-c  16   1.414  22.624   22 5 / 8  or 1  -10 5 / 8  e-e  22 5 / 8   [(1   1  )  2( 1 / 2  )]  21 5 / 8  or 1  -9 5 / 8  L: c-c  53 3 / 4   (15   16  )  22 3 / 4  or 1  -10 3 / 4  e-e  22 3 / 4   [(1   1 3 / 8  )  2( 1 / 2  )]  21 3 / 8  or 1  -9 3 / 8  4. J: c-c  14  e-e  14   (1 9 / 16   1  )  11 7 / 16  K: c-c  32   1.414  45.248   45 1 / 4  or 3  -9 1 / 4  e-e  45 1 / 4   (1   1  )  43 1 / 4  or 3  -7 1 / 4  L: c-c  60   (14   32  )  14  or 1  -2  e-e  14   (1   1 9 / 16  )  11 7 / 16  5. J: c-c  70   34   36  ; 36   2  18  or 1  -6  e-e  18   (1 3 / 4   1 1 / 8  )  15 1 / 8  or 1  -3 1 / 8  K: c-c  34   1.414  48.076   48 1 / 16  or 4  - 1 / 16  e-e  48 1 / 16   (1 1 / 8   1 1 / 8  )  45 13 / 16  or 3  -9 13 / 16  L: c-c  18  or 1  -6  e-e  18   (1 1 / 8   1 3 / 4  )  15 1 / 8  or 1  -3 1 / 8  6. J: c-c  72   16 3 / 4   55.25  ; 55.25  2  27.625   27 5 / 8  or 2  -3 5 / 8  e-e  27 5 / 8   [(1 15 / 16   1 7 / 16  )  2( 1 / 2  )]  25 1 / 4  or 2  -1 1 / 4  K: c-c  16 3 / 4   1.414  23.684 5   23 11 / 16  or 1  -11 11 / 16  e-e  23 11 / 16   [(1 7 / 16   1 7 / 16  )  2( 1 / 2  )]  21 13 / 16  or 1  -9 13 / 16  L: c-c  27 5 / 8  e-e  27 5 / 8   [(1 7 / 16   1 15 / 16  )  2( 1 / 2  )]  25 1 / 4  or 2  -1 1 / 4  7. M: c-c  5  e-e  5   [(1   3 / 4  )  2( 3 / 8  )]  4  N: c-c  5 1 / 2   1.414  7.777   7 3 / 4  e-e  7 3 / 4   [( 3 / 4   3 / 4  )  2( 3 / 8  )]  7  O: c-c  17   (5   5 1 / 2  )  6 1 / 2  e-e  6 1 / 2   [( 3 / 4   1  )  2( 3 / 8  )]  5 1 / 2  8. M: c-c  7 3 / 4  e-e  7 3 / 4   ( 1 / 2   1 / 4  )  7  N: c-c  8   1.414  11.312   11 5 / 16  e-e  11 5 / 16   ( 1 / 4   1 / 4  )  10 13 / 16  O: c-c  33   (7 3 / 4   8  )  17 1 / 4  or 1  -5 1 / 4  e-e  17 1 / 4   ( 1 / 4   1 / 2  )  16 1 / 2  or 1  -4 1 / 2  9. M: c-c  9 1 / 2  e-e  9 1 / 2   [(1 3 / 8   1  )  2( 1 / 2  )]  8 1 / 8  N: c-c  9 1 / 2   1.414  13.433   13 7 / 16  or 1  -1 7 / 16  e-e  13 7 / 16   [(1   1  )  2( 1 / 2  )]  12 7 / 16  O: c-c  39   (9 1 / 2   9 1 / 2  )  20  or 1  -8  e-e  20   [(1   1 3 / 8  )  2( 1 / 2  )  18 5 / 8  or 1  -6 5 / 8  10. M: c-c  12 1 / 2  e-e  12 1 / 2   [(1 1 / 2   1 1 / 8  )  2( 1 / 2  )]  10 7 / 8  N: c-c  15 1 / 2   1.414  21.917   21 15 / 16  or 1  -9 15 / 16  e-e  21 15 / 16   [(1 1 / 8   1 1 / 8  )  2( 1 / 2  )]  20 11 / 16  or 1  -8 11 / 16  O: c-c  45 3 / 4   (12 1 / 2   15 1 / 2  )  17 3 / 4  or 1  -5 3 / 4  e-e  17 3 / 4   [(1 1 / 8   1 1 / 2  )  2( 1 / 2  )]  16 1 / 8 or 1  -4 1 / 8  11. M: c-c  48   12   36  ; 36   2  18  or 1  -6  e-e  18   ( 3 / 4   5 / 16  )  16 15 / 16  or 1  -4 15 / 16  N: c-c  12   1.414  16.698   16 15 / 16  or 1  -4 15 / 16  e-e  16 15 / 16   ( 5 / 16   5 / 16  )  16 5 / 16  or 1  -4 5 / 16  O: c-c  18  or 1  -6  e-e  18   ( 5 / 16   3 / 4  )  16 15 / 16  or 1  -4 15 / 16  12. M: c-c  55   21   34  ; 34   2  17  or 1  -5  e-e  17   [(1 3 / 4   1 5 / 16  )  2( 1 / 2  )]  14 15 / 16  or 1  -2 15 / 16  N: c-c  21   1.414  29.694   29 11 / 16  or 2  -5 11 / 16  8 Guide

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    e-e  29 11 / 16   [(1 5 / 16   1 5 / 16  )  2( 1 / 2  )]  28 1 / 16  or 2  -4 1 / 16  O: c-c  17  or 1  -5  e-e  17   [(1 5 / 16   1 3 / 4  )  2( 1 / 2  )]  14 15 / 16  or 1  -2 15 / 16  UNIT 21 RIGHT ANGLE WITH A 45° DIAGONAL 1. J: c-c  16  e-e  16   ( 3 / 8   1 / 4  )  15 3 / 8  or 1  -3 3 / 8  K: c-c  30   16   14  ; 14   1.414  19.796   19 13 / 16  or 1  -7 13 / 16  e-e  19 13 / 16   ( 1 / 4   1 / 4  )  19 5 / 16  or 1  -7 5 / 16  L: c-c  36   14   22  or 1  -10  e-e  22   ( 1 / 4   3 / 8  )  21 3 / 8  or 1  9 3 / 8  2. J: c-c  21  or 1  -9  e-e  21   [(2 11 / 16   2 1 / 16  )  2( 3 / 4  )]  17 1 / 4  or 1  -5 1 / 4  K: c-c  43   21   22  ; 22   1.414  31.108   31 1 / 8  or 2  -7 1 / 8  e-e  31 1 / 8   [(2 1 / 16   2 1 / 16  )  2( 3 / 4  )]  28 1 / 2  or 2  -4 1 / 2  L: c-c  38   22   16  or 1  -4  e-e  16   [(2 1 / 16   2 11 / 16  )  2( 3 / 4  )]  12 3 / 4  or 1  - 3 / 4  3. J: c-c  19 1 / 2  or 1  -7 1 / 2  e-e  19 1 / 2   [(2 1 / 4   1 11 / 16  )  2( 1 / 2  )]  16 9 / 16  or 1  -4 9 / 16  K: c-c  48   19 1 / 2   28 1 / 2  ; 28.5  1.414  40.299   40 5 / 16  or 3  -4 5 / 16  e-e  40 5 / 16   [(1 11 / 16   1 11 / 16  )  2( 1 / 2  )]  37 15 / 16  or 3  -1 15 / 16  L: c-c  60   28 1 / 2   31 1 / 2  or 2  -7 1 / 2  e-e  31 1 / 2   [(1 11 / 16   2 1 / 4  )  2( 1 / 2  )]  28 9 / 16  or 2  -4 9 / 16  4. J: c-c  26 1 / 2  or 2  -2 1 / 2  e-e  26 1 / 2   (1 1 / 8   7 / 16  )  24 15 / 16  or 2  - 15 / 16  K: c-c  63   26 1 / 2   36 1 / 2  ; 36.5  1.414  51.611   51 5 / 8  or 4  -3 5 / 8  e-e  51 5 / 8   ( 7 / 16   7 / 16  )  50 3 / 4  or 4  -2 3 / 4  L: c-c  58   36 1 / 2   21 1 / 2  or 1  -9 1 / 2  e-e  21 1 / 2   ( 7 / 16   1 1 / 8  )  19 15 / 16  or 1  -7 15 / 16  5. J: c-c  76   40 1 / 4   35 3 / 4  or 2  -11 3 / 4  e-e  35 3 / 4   ( 1 / 2   1 / 4  )  35  or 2  -11  K: c-c  40 1 / 4   1.414  56.9135  or 56 15 / 16  or 4  -8 15 / 16  e-e  56 15 / 16   ( 1 / 4   1 / 4  )  56 7 / 16  or 4  -8 7 / 16  L: c-c  71   40 1 / 4   30 3 / 4  or 2  -6 3 / 4  e-e  30 3 / 4   ( 1 / 4   1 / 2  )  30  or 2  -6  UNIT 22 45° OFFSET WITH WYE FITTING 1. J: c-c  8  e-e  8   [(1 15 / 16   1 15 / 16  )  2( 1 / 2  )]  5 1 / 8  K: c-c  45 1 / 2   8  37 1 / 2  or 3  -1 1 / 2  e-e  37 1 / 2   [(3 9 / 16   1 15 / 16  )  2( 1 / 2  )]  33  or 2  -9  L: c-c  23   1.414  32.522   32 1 / 2  or 2  -8 1 / 2  e-e  32 1 / 2   [(3 9 / 16   1 7 / 16  )  2( 1 / 2  )]  28 1 / 2  or 2  -4 1 / 2  M: c-c  45 1 / 2   (8   23  )  14 1 / 2  or 1  -2 1 / 2  e-e  14 1 / 2   [(1 7 / 16   1 15 / 16 )  2( 1 / 2  )]  12 1 / 8  or 1  - 1 / 8  2. J: c-c  15  or 1  -3  e-e  15   (1 3 / 4   1 1 / 8  )  12 1 / 8  or 1  - 1 / 8  K: c-c  67   15   52  or 4  -4  e-e  52   (2 7 / 8   1 3 / 4  )  47 3 / 8  or 3  -11 3 / 8  L: c-c  30   1.414  42.42  42 7 / 16  or 3  -2 7 / 16  e-e  42 7 / 16   (2 7 / 8   1 1 / 8  )  38 7 / 16  or 3  -2 7 / 16  M: c-c  67   (15   30  )  22  or 1  -10  e-e  22   (1 1 / 8   1 3 / 4  )  19 1 / 8  or 1  -7 1 / 8  Guide 9

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    3. J: c-c  12  or 1  e-e  12   (2 5 / 16   1 3 / 8  )  8 5 / 16  K: c-c  53   12   41  or 3  -5  e-e  41   (3 5 / 8   2 5 / 16  )  35 1 / 16  or 2  -11 1 / 16  L: c-c  24   1.414  33.936   33 15 / 16  or 2  -9 15 / 16  e-e  33 15 / 16   (3 5 / 8   1 1 / 2  )  28 13 / 16  or 2  -4 13 / 16  M: c-c  53   (12   24  )  17  or 1  -5  e-e  17   ( 1 1 / 2   2 5 / 16 )  13 3 / 16  or 1  -1 3 / 16  4. J: c-c  22  or 1  -10  e-e  22   [(2 1 / 4   2 1 / 8  )  2( 1 / 2  )  18 5 / 8  or 1  -6 5 / 8  K: c-c  56   22  34  or 2  -10  e-e  34   [(4 3 / 8   2 1 / 4  )  2( 1 / 2  )]  28 3 / 8  or 2  -4 3 / 8  L: c-c  9 3 / 4   1.414  13.7865   13 13 / 16  or 1  -1 13 / 16  e-e  13 13 / 16   [(4 3 / 8   1 11 / 16  )  2( 1 / 2  )]  8 3 / 4  M: c-c  56   (22   9 3 / 4  )  24 1 / 4  or 2  - 1 / 4  e-e  24 1 / 4   [(1 11 / 16  2 1 / 4  )  2( 1 / 2  )]  21 5 / 16  or 1  -9 5 / 16  5. J: c-c  11 3 / 4  e-e  11 3 / 4   (1 7 / 8   1 / 2  )  9 3 / 8  K: e-e  26   11 3 / 4   14 1 / 4  or 1  -2 1 / 4  c-c  14 1 / 4   (2 7 / 8   1 7 / 8  )  9 1 / 2  L: c-c  8 1 / 2   1.414  12.019   12  or 1  -0  e-e  12   (2 7 / 8   3 / 4  )  8 3 / 8  M: c-c  26   (11 3 / 4   8 1 / 2  )  5 3 / 4  e-e  5 3 / 4   ( 3 / 4   1 7 / 8  )  3 1 / 8  6. J: c-c  19  or 1  -7  e-e  19   [(2 1 / 4   1 13 / 16  )  2( 1 / 2  )]  15 15 / 16  or 1  -3 15 / 16  K: c-c  70   19   51  or 4  -3  e-e  51   [(4 1 / 16   2 1 / 4  )  2( 1 / 2  )]  45 11 / 16  or 3  -9 11 / 16  L: c-c  29   1.414  41.006   41  or 3  -5  e-e  41   [(4 1 / 8   1 7 / 16  )  2( 1 / 2  )]  36 7 / 16  or 3  - 7 / 16  M: c-c  70   (19   29  )  22  or 1  -10  e-e  22   [(1 7 / 16   1 15 / 16  )  2( 1 / 2  )]  19 5 / 8  or 1  -7 5 / 8  UNIT 23 WYE AND TEE-WYE ASSEMBLIES 1. c-c e-e J. 14  11 1 / 2  K. 48  42 7 / 8  L. 38 3 / 16  34 1 / 2  M. 21  17 3 / 16  2. c-c e-e J. 19 1 / 2  17 5 / 8  K. 50 1 / 2  46 13 / 16  L. 43 13 / 16  40 15 / 16  M. 19 1 / 2  17 9 / 16  3. c-c e-e J. 21 3 / 4  17 3 / 16  K. 55 3 / 4  50 1 / 2  L. 47 3 / 8  42 5 / 8  M. 22 1 / 4  18 3 / 16  10 Guide

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