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Contents. Section 1 —Introduction to Plumbing Section 2—Plumbing Systems Section 3—Plumbing System Design and Installation Section 4—Plumbing Services Section 5—Career Development and Plumbing History. Section 1. Introduction to Plumbing. Chapter 4. Mathematics for Plumbers.

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contents
Contents
  • Section 1—Introduction to Plumbing
  • Section 2—Plumbing Systems
  • Section 3—Plumbing System Design and Installation
  • Section 4—Plumbing Services
  • Section 5—Career Development and Plumbing History
section 1
Section 1

Introduction to Plumbing

chapter 4
Chapter 4

Mathematics for Plumbers

objectives
Objectives
  • Read a rule accurately to nearest 1/16.
  • Add and subtract fractions and whole numbers.
  • Compute pipe offsets using the Pythagorean theorem and trigonometric functions.
  • Apply the formulas for finding area and volume.
  • Explain and apply SI metric measure in finding length, area, volume, and temperature.
  • Convert customary measure to metric measure.
measurement
Measurement

(Goodheart-Willcox Publisher)

measurement1
Measurement

Reading Fractions of an Inch

  • Read from nearest 1/4 divisions to get precise reading.

(Goodheart-Willcox Publisher)

measurement2
Measurement

Adding Lengths

(Goodheart-Willcox Publisher)

measurement3
Measurement

Subtracting Lengths

(Goodheart-Willcox Publisher)

measurement4
Measurement

Subtracting Unequal Denominators

(Goodheart-Willcox Publisher)

measurement5
Measurement

Borrowing from the Whole Number

(Goodheart-Willcox Publisher)

changing inches to feet
Changing Inches to Feet

(Goodheart-Willcox Publisher)

changing feet to inches
Changing Feet to Inches

Multiply the dimension given in feet by 12 to get the number of inches.

(Goodheart-Willcox Publisher)

review
Review

Identify each measurement indicated.

  • 5 1/2
  • A.
  • B.
  • C.
  • D.
  • E.
  • 4 9/16
  • 3 13/16
  • 3 1/16
  • 1 11/16

(Goodheart-Willcox Publisher)

review1
Review

Add the following dimensions:

A. 6 5/8 + 1 3/4 =

B. 3 3/16 + 4 3/4 =

C. 2 8 3/8 + 4 6 15/16 =

D. 5 4 13/16 + 9 5/8  =

  • 8 3/8

7 15/16

7 3 5/16

6 2 7/16

review2
Review

Subtract the following dimensions:

A. 9 3/4 – 3 3/8 =

B. 1 2 1/4 – 8 1/8 =

C. 12 6 3/4 – 7 4 7/8 =

D. 6 9 11/16 – 3 10 13/16 =

6 3/8

6 1/8

5 1 7/8

2 10 7/8

computing pipe offsets
Computing Pipe Offsets

(Goodheart-Willcox Publisher)

computing pipe offsets1
Computing Pipe Offsets

Pythagorean Theorem

(Goodheart-Willcox Publisher)

computing pipe offsets2
Computing Pipe Offsets

Pythagorean Theorem (continued)

  • Pythagorean theorem applies to all right triangles.

(Goodheart-Willcox Publisher)

computing pipe offsets3
Computing Pipe Offsets

Trigonometric Functions

(Goodheart-Willcox Publisher)

computing pipe offsets4
Computing Pipe Offsets

Trigonometric Functions (continued)

  • Theoretical Length vs. Actual Length

Actual length of pipe = Theoretical length –Laying lengthof fittings

(Goodheart-Willcox Publisher)

computing pipe offsets5
Computing Pipe Offsets

Simple Methods

(Goodheart-Willcox Publisher)

computing pipe offsets6
Computing Pipe Offsets

Plumber’s Rule

(Goodheart-Willcox Publisher)

review3
Review
  • Find the travel of the pipe required to join two pipes at a 45 angle that are offset at each of the following distances:
    • A. 30 =
    • B. 18 =
    • C. 1 3 =
    • D. 2 9 =

42.42 or 4 7/16

25.45 or 25 7/16

22.21 or 22 1/4

46.66 or 46 11/16

computing area and volume
Computing Area and Volume

Square or Rectangular Surface

(Goodheart-Willcox Publisher)

computing area and volume1
Computing Area and Volume

Area of Circles

(Goodheart-Willcox Publisher)

computing area and volume2
Computing Area and Volume

Volume of a Rectangular Tank

(Goodheart-Willcox Publisher)

computing area and volume3
Computing Area and Volume

Volume of a Cylindrical Tank

(Goodheart-Willcox Publisher)

review4
Review
  • Compute the area of the following:
    • A. 6 6 square =
    • B. 4 9 12 3 rectangle =
    • C. 8 6 diameter circle =
    • D. 4 9 radius circle =

42.25 sq. ft.

58.19 sq. ft.

2,289 sq. in.

10,202 sq. in.

review5
Review

Compute the volume of these tanks:

A.B.

615.44 cu. ft.

63 cu. ft.

computing slope of pipe
Computing Slope of Pipe

(Goodheart-Willcox Publisher)

metric measurement
Metric Measurement

Length

(Goodheart-Willcox Publisher)

metric measurement2
Metric Measurement

Liquid Measures

review6
Review
  • Identify the metric units of measurement used when measuring:
    • A. Distance:
    • B. Liquid volume:
    • C. Dry volume:
    • D. Temperature:

meter, centimeter, millimeter

liter or cubic centimeter

cubic meter

Celsius or Kelvin

review7
Review
  • Convert each of the following customary measurements to the equivalent metric measurement.
    • A. Distance: 1 3 
    • B. Liquid measure: 22 cu. ft. 
    • C. Dry volume: 135 cu. ft. 
    • D. Temperature: 85 F 

68.44 cm.

623.04 L

3.77 cu. meters

29.7 Celsius

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