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The oxygen equivalence number of a weld is a number that
Chapter 2, Problem 14E(choose chapter or problem)
The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds” (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s–136s) presents several equations for computing the oxygen equivalence number of a weld. One equation, designed to predict the hardness of a weld, is \(X=O+2N+(2/3)C\), where X is the oxygen equivalence, and O, N, and C are the amounts of oxygen, nitrogen, and carbon, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, \(\mu_O=0.1668\), \(\mu_N=0.0255\), \(\mu_C=0.0247\), \(\sigma_O=0.0340\), \(\sigma_N=0.0194\), and \(\sigma_C=0.0131\).
a. Find \(\mu_X\).
b. Suppose the weight percents of O, N, and C are independent. Find \(\sigma_X\).
Equation Transcription:
Text Transcription:
X=O+2N+(2/3)C
mu_0=0.1668
mu_N=0.0255
mu_C=0.0247
sigma_O=0.0340
sigma_N=0.0194
sigma_C=0.0131
mu_X
sigma_X
Questions & Answers
QUESTION:
The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds” (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s–136s) presents several equations for computing the oxygen equivalence number of a weld. One equation, designed to predict the hardness of a weld, is \(X=O+2N+(2/3)C\), where X is the oxygen equivalence, and O, N, and C are the amounts of oxygen, nitrogen, and carbon, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, \(\mu_O=0.1668\), \(\mu_N=0.0255\), \(\mu_C=0.0247\), \(\sigma_O=0.0340\), \(\sigma_N=0.0194\), and \(\sigma_C=0.0131\).
a. Find \(\mu_X\).
b. Suppose the weight percents of O, N, and C are independent. Find \(\sigma_X\).
Equation Transcription:
Text Transcription:
X=O+2N+(2/3)C
mu_0=0.1668
mu_N=0.0255
mu_C=0.0247
sigma_O=0.0340
sigma_N=0.0194
sigma_C=0.0131
mu_X
sigma_X
ANSWER:
Solution:
Step 1
The equation which used to predict the hardness of a weld is X= 0+ 2N+ (2/3) C , where X is the oxygen equivalence , O, N, C are the amounts of oxygen, nitrogen and carbon.
We have to find
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if the weight percentage of O, N, and C are independent.