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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 measurement1

Metric Measurement

Dry Volume


Metric measurement2

Metric Measurement

Liquid Measures


Metric measurement3

Metric Measurement

Temperature


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


End of chapter 4

End of Chapter 4


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