Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 20, Problem 52P
An experiment is performed to define the relationship between applied stress and the time to fracture for a type of stainless steel. Eight different values of stress are applied, and the resulting data are
| Applied stress x,
|
5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
| Fracture time y, hr | 40 | 30 | 25 | 40 | 18 | 20 | 22 | 15 |
Plot these data and then develop a best-fit equation to predict the fracture time for an applied stress of
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xi = 223.9
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yi = 196
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xi2 = 3056.65
,
xiyi = 2759.6
,
yi2 = 2976
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Values of dose in the sample ranged from 6.0 to 17.6.
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A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of
the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below.
DATA:
Observation
1
2
3
4
5
6
7
8
9
10
11
12
pH above 7 (X)
0.65
0.50
0.93
0.86
1.02
0.94
1.16
1.24
1.30
1.45
1.85
1.89
Units of BCI (Y)
14.5
22.9
15.8
38.3
18.9
20.0
21.4
23.8
23.6
25.2
27.3
29.4
Find the correlation coefficient between pH and BCI (round to the nearest hundredth; place your answer in the box below)
A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States.
They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained
is summarized below.
DATA:
Observation
1
2
3
4
5
6
7
8
9
10
11
12
pH above 7 (X)
0.65
0.75
0.89
0.94
1.12
1.16
1.29
1.35
1.48
1.56
1.73
1.80
Units of BCI (Y)
16.0
18.9
15.6
21.1
23.6
24.9
26.1
29.2
19.3
30.7
33.7
29.4
Find the coefficient of determination between pH and BCI (round to the nearest hundredth; place your answer in the box below)
Chapter 20 Solutions
Numerical Methods for Engineers
Ch. 20 - 20.1 Perform the same computation as in Sec. 20.1,...Ch. 20 - You perform experiments and determine the...Ch. 20 - 20.3 It is known that the tensile strength of a...Ch. 20 - Prob. 4PCh. 20 - 20.5 The specific volume of a superheated steam is...Ch. 20 - Prob. 6PCh. 20 - In Alzheimers disease, the number of neurons in...Ch. 20 - 20.8 The following data were taken from a stirred...Ch. 20 - Prob. 9PCh. 20 - Concentration data were taken at 15 time points...
Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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