callister7e_sm_ch04_34

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4-44 
 4.34 (a) This part of problem asks that we compute the number of grains per square inch for an ASTM 
grain size of 6 at a magnification of 100x. All we need do is solve for the parameter N in Equation 4.16, inasmuch 
as n = 6. Thus 
 
 N = 2n−1 
 
= 26−1 = 32 grains/in.2
 
 (b) Now it is necessary to compute the value of N for no magnification. In order to solve this problem it is 
necessary to use Equation 4.17: 
 
 
N M
M
100
⎛ 
⎝ ⎜ 
⎞ 
⎠ ⎟ 
2
= 2n−1 
 
where NM = the number of grains per square inch at magnification M, and n is the ASTM grain size number. 
Without any magnification, M in the above equation is 1, and therefore, 
 
 
N1
1
100
⎛ 
⎝ ⎜ 
⎞ 
⎠ ⎟ 
2
= 26−1 = 32 
 
And, solving for N1, N1 = 320,000 grains/in.
2. 
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