Instructorʼs Guide iii
Mathematics for Plumbers and Pipefitters 8th Edition
Solution Manual
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
iv Instructorʼs Guide
Unit 41 Cast Iron Flanged Fittings ………………………………………………………………………………………………………………………….30
Unit 42 Miter Cuts, Welded Pipe …………………………………………………………………………………………………………………………….30
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
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?