Solution Manual For Mathematics for Plumbers and Pipefitters, 8th Edition

Instructor’s Guide to Accompany Mathematics for Plumbers and Pipefitters Smith • Eighth Edition Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Instructorʼs Guide iii CONTENTS SECTION 1 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 REVIEW OF BASIC FUNDAMENTALS Some Basic Rules for Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving Formulas/Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Square Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of Angle Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion of Length Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SECTION 2 1 1 1 1 2 2 PIPE LENGTH CALCULATIONS Unit 7 Standard Weight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 8 Allowance for Threaded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 9 Copper Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 10 Allowance for Copper Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 11 Plastic Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 12 Allowance for Plastic Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 13 Welding Steel Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 14 Allowance for Weld-Type Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 15 Equal Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 16 Angles in Plumbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 17 Offset, Diagonal, Rise, and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 18 Solving for 45° Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 19 45° Diagonal and Pipe Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 20 Three-Pipe Diagrams with a 45° Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 21 Right Angle with a 45° Diagonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 22 45° Offset with Wye Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 23 Wye and Tee-Wye Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 24 The 0.707 Constant in 45° Pipe Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 25 Solving for Other Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 26 Pipe Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 27 Cast Iron Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 28 Cast Iron Assemblies with Various Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 29 1⁄ 5 Bend Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 30 Assemblies with Cast Iron Wyes and Tee-Wyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 31 Single Loop Back-Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 32 Grade, Percent Grade, Drop and Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 33 Elevation and Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 34 Elevation in Plan View Pipe Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 35 Jumper Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 36 45° Offsets in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 37 Special Case of 45° Offsets in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 38 Rolling Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 39 Combination Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 40 Pipe Length by Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 41 Cast Iron Flanged Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit 42 Miter Cuts, Welded Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 3 3 3 3 4 4 5 5 6 7 7 9 9 10 12 13 14 14 15 16 17 17 18 18 19 19 21 22 23 24 25 30 30 iv Instructorʼs Guide SECTION 3 Unit 43 Unit 44 Unit 45 Unit 46 Shower Pan or Safe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangular Tank Liner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylindrical Stretchouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roof Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SECTION 4 Unit 47 Unit 48 Unit 49 Unit 50 Unit 51 Unit 52 Unit 53 Unit 54 Unit 55 SHEET METAL WORK VOLUMES, PRESSURES, AND CAPACITIES Water Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangular Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partially Filled Containers of Varying Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Pressure, Head, Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of Pipe Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pipe Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SECTION 5 31 32 34 36 37 37 37 37 38 38 38 38 39 PHYSICS Unit 56 Mechanical Advantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Unit 57 States of Matter and Why it Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Unit 58 Properties of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 SECTION 6 Unit 59 Unit 60 Unit 61 Unit 62 Unit 63 HEATING Heat Loss vs. Radiation Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Sizing for Total Heat Loss of a Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimating Size of Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sizing Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heating Problems—Two-Floor House . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SECTION 7 40 41 42 42 42 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 Instructorʼs Guide v 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 compute 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 calculations. 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 completed 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 acceptable. An even greater tolerance is allowed for answers given in Section 5, Heating, because when heat loss and radiation 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? vi Instructorʼs Guide 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? Instructorʼs Guide 1 SECTION 1 UNIT 1 REVIEW OF BASIC FUNDAMENTALS 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 2. 9.42 3. 38.277 or 38.2766 UNIT 2 10. 19 11. 0 12. 4 13. 0.333 or 1/3 FORMULAS Do the following problems. 1) 3 3 4 15 2) (3 3) 4 24 3) 3 (3 4) 15 4) 3 3 42 51 A. 1. P 50-0 2. 9 42 m 3. P 67-6 4. P 19.5 m 5. C 40.035 6. C 101.422 cm 7. P 35.98 ft. UNIT 3 7. 3 8. 9 9. 2 4. 1700 5. 8540 6. 6 5) 3 (5 4)2 84 6) (3 5) 42 24 7) 3 (5 42) 24 8) 3 4 3 6 9 9) 3 6 4 3 9 10) (3 6 4) 3 3 11) 3 (6 4 3) 15 12) 3 [(6 4) 3] 27 13) 11 62 44 32 B. 1. A 210.25 sq. in. 2. A 1,225 cm2 3. A 15.75 sq. ft. 4. A 15.75 m2 5. A 117 sq. ft. 6. A 216 sq. in. 7. A 864 cm2 8. A 254.34 sq. in. 9. A 2,122.64 cm2 10. A 196.25 cm2 C. 1. V 1,728 cu. in. 2. V 1,000 cm3 3. V 180 cu. yd. 4. V 154 m3 5. V 3,264 cu. ft. 6. V 302.76 cm3 7. V 699.435 cu. ft. 8. V 11,627.42 cm3 9. V 5,699.10 cu. in. 10. A L W 11. V S S h 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 2. 9 3. 20 4. 12 5. 17 6. 4.5 1. 15 ft. 2. 4 m 3. 16 -6 4. 21 m 5. 7.01 6. 17.83 cm 7. 4.8 8. 4 cm 9. 4 radius 8 diameter 10. 6 cm radius 12 cm diameter 3. 32.02 4. 41.87 5. 47.93 6. 16.97 UNIT 4 1. 10 2. 17 SQUARE ROOT 2 Instructorʼs Guide 7. 1.414 8. 15.05 cm 9. 18.61 cm UNIT 5 10. 29.10 cm 11. 9 12. 2.24 13. 12.45 14. 7 cm 15. 39.55 cm 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° B 45° E 9° C 66° F 22° 3. ∠A 25° ∠C 58° ∠B 10° ∠D 122° UNIT 6 CONVERSION OF LENGTH MEASURES G 48° H 67° I 78° ∠E 160° ∠F 311/2° or 31°30 11. 85 cm 12. 8.72 m Inches and Fractional Parts of Inch 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 19 11/16 42 3/8 26 3/8 69 15/16 100 1/2 33 3/16 66 13/16 181 1/16 103 3/4 79 3/4 Inches and Decimal Parts of Inch 19.687 42.375 26.35 69.94 100.5 33.19 66.84 181.08 103.75 79.75 Feet, Inches and Fractional Parts of Inch 1-7 11/16 3- 6 3/8 2-2 3/8 5-9 15/16 8- 4 1/2 2-9 3/16 5-6 13/16 15-1 1/16 8-7 3/4 6-7 3/4 Feet and Decimal Parts of Foot 1.64 3.53 2.20 5.83 8.38 2.77 5.57 15.09 8.65 6.65