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Introduction to Engineering Linear & Logarithmic ScalesPowerPoint Presentation

Introduction to Engineering Linear & Logarithmic Scales

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### Introduction to EngineeringLinear & Logarithmic Scales

Agenda

Linear & Logarithmic Scales

Linear vs. Linear Plot

Log-Log Plot

Semi-log (log v. linear) plot

Working With Data

- Engineers often collect large amounts of data
- Two common ways to analyze the data are:
- Write an equation to fit the data.
- Graph the data.

Working with Equations Describing Engineering Phenomena and Data

- Plotting data with appropriate scales can be very helpful in display of data and interpretation
- Choosing the right scale can make the appear on a straight line
- Choosing the right scale allows you to plot data ranging over several orders of magnitude on a single page.

-20 Data

-15

-10

-5

0

5

10

15

20

0.1

1

10

100

Linear and Logarithmic ScalingLinear axis:

Logarithmic axis:

Three Examples Data

- Temperature Expansion
- Linear Y = mX + B

- Wind Force
- Power Equation Y = bXm

- Population Growth
- Y = bemX

Length, L Data

a

L

1

Lo

dT

Linear Relationship Example Temperature Expansion of PipeL = a (T – To) + Lo

L = a (dT) + Lo

(Form : Y = mX + b)

Power Relationship Example DataWind Force on Road Sign

- Wind Force on a Sign F = P A
- P = 0.0036 V2
- F = 0.0036 V2 A

- Where
- P = pressure in lb/ft2
- V = velocity in ft/sec

- (Form Y = bXm)

Y = bX Datam

Y = bX Datam Linear Form: log Y = log b + m log X Y* = m X* + b

Y = bXm Data Linear Form: log Y = log b + m log X Y* = m X* + b

Exponential Relationship Example DataPopulationGrowth

Y = bemX Linear Form: ln Y = ln b + m XY* = m X + b

Assignment Data

- Assignment #8
- Log and Semi-Log Review sheet
- Bring a floppy disk to class tomorrow

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