Contents

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# Contents - PowerPoint PPT Presentation

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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Presentation Transcript
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

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

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Measurement

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Measurement

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Measurement

Subtracting Lengths

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Measurement

Subtracting Unequal Denominators

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Measurement

Borrowing from the Whole Number

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Changing Inches to Feet

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Changing Feet to Inches

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

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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

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Review

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

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

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Computing Pipe Offsets

Pythagorean Theorem

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Computing Pipe Offsets

Pythagorean Theorem (continued)

• Pythagorean theorem applies to all right triangles.

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Computing Pipe Offsets

Trigonometric Functions

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Computing Pipe Offsets

Trigonometric Functions (continued)

• Theoretical Length vs. Actual Length

Actual length of pipe = Theoretical length –Laying lengthof fittings

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Computing Pipe Offsets

Simple Methods

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Computing Pipe Offsets

Plumber’s Rule

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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

Square or Rectangular Surface

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Computing Area and Volume

Area of Circles

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Computing Area and Volume

Volume of a Rectangular Tank

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Computing Area and Volume

Volume of a Cylindrical Tank

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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.

Review

Compute the volume of these tanks:

A.B.

615.44 cu. ft.

63 cu. ft.

Computing Slope of Pipe

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Metric Measurement

Length

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Metric Measurement

Liquid Measures

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

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