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Chapter 4: Problem 36

Determine the ASTM grain size number if 20 grains per square inch are measured at a magnification of \(50 \times\).

Short Answer

Expert verified
Answer: The ASTM grain size number for the given material is approximately 16.29.

Step by step solution

01

Determine the number of grains per square inch at a 1x magnification

To determine the number of grains per square inch at a 1x magnification, we need to adjust the given value (20 grains) for the magnification. We can calculate n using the following equation: $$n = g \times M^2$$ Where: - g is the number of grains per square inch at the given magnification (20 grains). - M is the magnification (50x). Let's calculate n: $$n = 20 \times (50)^2$$ $$n = 20 \times 2500$$ $$n = 50000$$ There are 50,000 grains per square inch at a 1x magnification.
02

Calculate the ASTM grain size number (G)

Now that we have calculated the number of grains per square inch at a 1x magnification (n), we can use the ASTM grain size equation to determine the ASTM grain size number (G): $$G = n - 1 = 2^{(G-1)}$$ Since we know n, let's rewrite the equation in terms of G: $$G = \log_2 (n) + 1$$ We can now calculate the ASTM grain size number: $$G = \log_2 (50000) + 1$$ $$G ≈ 16.29$$ Therefore, the ASTM grain size number for the given material is approximately 16.29.

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Most popular questions from this chapter

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