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Chapter 4: Problem 35

Determine the ASTM grain size number if 30 grains per square inch are measured at a magnification of 250

Short Answer

Expert verified
Question: Determine the ASTM grain size number when 30 grains per square inch are observed at a magnification of 250X. Answer: The ASTM grain size number is approximately 8.55.

Step by step solution

01

1. Convert the number of grains at 250X magnification to 100X magnification

First, let's find the relationship between the numbers of grains at 100X and 250X magnification: N (100X) / N (250X) = (250 / 100)^2. Now, we can calculate the number of grains per square inch at 100X magnification by using the given value, 30 grains per square inch at 250X magnification: N (100X) = 30 * (250 / 100)^2.
02

2. Calculate the number of grains per square inch at 100X magnification

Now, let's calculate the value of N (100X) using the formula derived in the previous step: N (100X) = 30 * (2.5)^2 N (100X) = 30 * 6.25 N (100X) = 187.5
03

3. Determine the ASTM grain size number

We have the number of grains per square inch at 100X magnification. Now we can use the ASTM grain size number formula to determine the grain size number, G: N = 2^(G-1). Here, N = 187.5. To solve for G, we can take the logarithm base 2 of both sides of the equation: log_2(N) = G - 1. Now, we can plug in the value of N and solve for G: log_2(187.5) = G - 1. G = log_2(187.5) + 1.
04

4. Calculate the ASTM grain size number

Finally, let's calculate the value of G using the formula derived in the previous step: G = log_2(187.5) + 1 G ≈ 7.55 + 1 G ≈ 8.55 The ASTM grain size number is approximately 8.55.

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