Engineering Fundamentals and Problem Solving, 6e
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Transcript Engineering Fundamentals and Problem Solving, 6e
Engineering
Fundamentals and Problem Solving, 6e
Chapter 5
Representation of Technical Information
Chapter Objectives
1. Recognize the importance of collecting, recording,
plotting, and interpreting technical data for engineering
analysis and design
2. Put into practice methods for graphical presentation of
scientific data and graphical analysis of plotted data
3. Develop the ability to graph data using uniform and
nonuniform scales
4. Apply methods of selected points and least squares for
determining the equation that gives the best-fit line to the
given data
5. Determine the most appropriate family of curves (linear,
power, or exponential) that gives the best fit to the given
data
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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General Graphing Procedures
1. Select the type of graph paper
• rectangular [aka rectilinear]
• semilog
• log-log)
and appropriate grid spacing for
the given data.
2. Choose the location of the
horizontal and vertical axes.
3. Determine the scale units
(range) for each axis
4. Graduate and calibrate the axes
using the 1, 2, 5 rule.
5. Identify each axis completely.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
3
General Graphing Procedures-cont’d
6. Plot points and use permissible
symbols.
7. Double check any point that
deviates from the line.
8. Draw the curve or curves.
9. Identify each curve, add title,
and include other necessary
notes.
10. Darken lines for good
reproduction.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Log–log and Semilog graph paper
Log-log: Power curves: y=bxm
Semilog: Exponential curves: y=bemx
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
5
Axis designations
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
6
Axis breaks
Axes should begin at zero
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Graduations and Calibrations
Scale marks (ticks) are Graduations.
Numerical values assigned to significant graduations
are Calibrations
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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1, 2, 5 Rule
The smallest division of the axis should be a positive
or negative integer power of 10 times 1, 2, or 5.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
9
Axis Labeling
The axis label should contain the name of the
variable, its symbol, and its units.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
10
Calibrating log scales
Preferred method of calibrating log scales uses
powers of 10 on major graduations
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Plotting data points
Observed:
Empirical:
Theoretical:
• Data points connected • Interpretation of what
• Graph of an
by straight irregular
occurs between data
equation.
line segments.
points.
• Smooth and without
• Line does not
• Smooth line fitted to the
symbols.
penetrate circles
data points.
• Every point is a data
• Data may or may not
point.
fall on curve.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Graph key
• Defines symbols and
line types.
• On a portion of the
grid.
• Enclosed in a border.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Method of selected points for linear
equations
1.
Plot the data on rectangular
paper, draw in best straight
line to fit plotted points
2.
Select 2 points on the line (not
necessarily data points) and
record their values
3.
Substitute points into the
linear equation y=mx+b
4.
Solve for m and b
5.
Chose a third point on the line
to verify the equation
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
14
Method of selected points for power
curves
1.
Plot the data on log-log paper,
draw in best straight line to fit
plotted points
2.
Select 2 points on the line (not
necessarily data points) and
record their values
3.
Substitute points into the
power equation
log y = m log x + log b,
4.
Solve for m and b
5.
Chose a third point on the line
to verify the equation
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
15
Method of selected points for
exponential curves
1. Plot the data on semilog paper,
draw in best straight line to fit
plotted points
2. Select 2 points on the line (not
necessarily data points) and
record their values
3. Substitute points into the
exponential equation
log y = mx log e + log b,
4. Solve for m and b
5. Chose a third point on the line
to verify the equation
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 1
The velocity of an experimental automobile is
measured at specified time intervals. Determine
the equation of a straight line constructed through
the points recorded in the following table.
Time, t, s
0
5
Velocity, V,
m/s
24 33
10
15
20
25
30
35
40
62
77
105
123
151
170
188
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 1 – cont’d
Procedure:
• Plot data on rectangular
graph paper.
• Select two points on the
line, A(t1, V1) and B(t2, V2),
and record the values of
these points.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 1 – cont’d
Procedure:
• Plot data on rectangular
graph paper.
• Select two points on the
line, A(t1, V1) and B(t2, V2),
and record the values of
these points.
A(10, 60)
B(35, 165)
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 1 – cont’d
• Substitute the points A and B into V = mt + b.
60 = m(10) + b
165 = m(35) + b
• Solve the equations for m and b giving:
V = 4.2t + 18
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 2
A solid object is dropped from a tall building, and
the values, time versus distance are as recorded in
the table below.
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 2 - cont’d
Procedure:
• Plot the data on log-log
paper.
• Select two points on the
line.
A(1.5,11)
B(6,175)
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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Example Problem 2 - cont’d
• Substitute these values into the general equation
log s = m log t + log b.
log 175 = m log 6 + log b
log 11 =m log 1.5 + log b
• Solve for m and b resulting in:
s = 4.9t2.0
Engineering: Fundamentals and Problem Solving, 6e
Eide Jenison Northup Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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