EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 17, Problem 7P
Fit the following data with
(a) A saturation-growth-rate model,
(b) A power equation, and
(c) A parabola. In each case, plot the data and the equation.
| x | 0.75 | 2 | 3 | 4 | 6 | 8 | 8.5 |
| y | 1.2 | 1.95 | 2 | 2.4 | 2.4 | 2.7 | 2.6 |
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100
80
60
40
20
0.002
0.004
0.006
0.008
0.01
0.012
Strain, in/in.
FIGURE P1.17
1.18 Use Problem 1.17 to graphically determine the following:
a. Modulus of resilience
b. Toughness
Hint: The toughness (u) can be determined by calculating the area under
the stress-strain curve
u =
de
where & is the strain at fracture. The preceding integral can be approxi-
mated numerically by using a trapezoidal integration technique:
u, = Eu, = o, + o e, - 6)
%3D
c. If the specimen is loaded to 40 ksi only and the lateral strain was found to
be -0.00057 in./in., what is Poisson's ratio of this metal?
d. If the specimen is loaded to 70 ksi only and then unloaded, what is the
permanent strain?
Stress, ksi
Stress, a (MPa)
Strain, e (x10* m/m)
Yong Modulus, E (GPa)
3.963
40.0
99.1
7.926
75.0
106
11.89
105.0
113.2
1.85
122.0
130.0
19.81
144,0
137.6
Table 2 Stress and Strain
3|Page
Dissections
1. Draw the graph of stress against strain
2. Discusses the obtained results
3. From the graph find. stress ? Yong Modulus, E?
4. Why Compression test is important in industry ?
The following table lists temperatures and specific volumes of water vapor at
two pressures:
p = 1.5 MPa
v(m³/kg)
p = 1.0 MPa
T ("C)
v(m³/kg)
T ("C)
200
0.2060
200
0.1325
240
280
0.2275
0.2480
240
280
0.1483
0.1627
Data encountered in solving problems often do not fall exactly on the grid of
values provided by property tables, and linear interpolation between adjacent
table entries becomes necessary. Using the data provided here, estimate
i. the specific volume at T= 240 °Č, p = 1.25 MPa, in m/kg
ii. the temperature at p = 1.5 MPa, v = 0.1555 m/kg, in °C
ii. the specific volume at T = 220 °C, p = 1.4 MPa, in m'/kg
Chapter 17 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 17 - Given these data 8.8 9.5 9.8 9.4 10.0 9.4 10.1 9.2...Ch. 17 - Given these data 29.65 28.55 28.65 30.15 29.35...Ch. 17 - 17.3 Use least-squares regression to fit a...Ch. 17 - 17.4 Use least-squares regression to fit a...Ch. 17 - 17.5 Using the same approach as was employed to...Ch. 17 - Use least-squares regression to fit a straight...Ch. 17 - Fit the following data with (a) A...Ch. 17 - Fit the following data with the power model...Ch. 17 - 17.9 Fit an exponential model...Ch. 17 - 17.10 Rather than using the base-e exponential...
Ch. 17 - 17.11 Beyond the examples in Fig. 17.10, there are...Ch. 17 - 17.12 An investigator has reported the data...Ch. 17 - An investigator has reported the data tabulated...Ch. 17 - 17.14 It is known that the data tabulated below...Ch. 17 - 17.15 The following data are...Ch. 17 - Given these data x 5 10 15 20 25 30 35 40 45 50 y...Ch. 17 - 17.17 Fit a cubic equation to the following...Ch. 17 - Use multiple linear regression to fit x1 0 1 1 2 2...Ch. 17 - Use multiple linear regression to fit x1 0 0 1 2 0...Ch. 17 - Use nonlinear regression to fit a parabola to the...Ch. 17 - 17.21 Use nonlinear regression to fit a...Ch. 17 - 17.22 Recompute the regression fits from Probs....Ch. 17 - Develop, debug, and test a program in either a...Ch. 17 - A material is tested for cyclic fatigue failure...Ch. 17 - The following data show the relationship between...Ch. 17 - 17.26 The data below represents the bacterial...Ch. 17 - The concentration of E. coli bacteria in a...Ch. 17 - 17.28 An object is suspended in a wind tunnel and...Ch. 17 - 17.29 Fit a power model to the data from Prob....Ch. 17 - Derive the least-squares fit of the following...Ch. 17 - 17.31 In Prob. 17.11 we used transformations to...
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