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Chapter 4: Problem 47

For an ASTM grain size of 6, approximately how many grains would there be per square inch under each of the following conditions? (a) At a magnification of \(100 \times\) (b) Without any magnification

Short Answer

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Question: For a material with an ASTM grain size of 6, calculate the number of grains per square inch (a) at a magnification of 100x, and (b) without any magnification. Answer: (a) At a magnification of 100x, there would be approximately 1024 grains per square inch. (b) Without any magnification, there would be approximately 0.1024 grains per square inch.

Step by step solution

01

Use the formula to find the number of grains per square inch at 100x magnification

Given an ASTM grain size of 6 (n = 6), we will use the formula to find the number of grains per square inch at 100x magnification: Number of grains per square inch = \((2^{6-1})^2 = (2^5)^2 = 32^2 = 1024\) At a magnification of 100x, there are 1024 grains per square inch. Now let's find the number of grains per square inch without any magnification.
02

Adjust the formula to find the number of grains per square inch without any magnification

Since the given formula calculates the number of grains per square inch at 100x magnification, we need to adjust it for no magnification. To do that, we divide the number of grains per square inch at 100x magnification (1024) by the area magnification factor (100x100). Number of grains per square inch without magnification = \(\frac{1024}{100 \times 100}\)
03

Calculate the number of grains per square inch without any magnification

Now we can calculate the number of grains per square inch without any magnification: Number of grains per square inch without magnification = \(\frac{1024}{100 \times 100} = \frac{1024}{10000} = 0.1024\) Without any magnification, there are approximately 0.1024 grains per square inch. In conclusion, for an ASTM grain size of 6: (a) At a magnification of 100x, there would be approximately 1024 grains per square inch. (b) Without any magnification, there would be approximately 0.1024 grains per square inch.

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