Final answer:
To find the ASTM grain size number for 30 grains per square inch at 250x magnification, convert the grain count to the equivalent at 100x magnification, and then use the ASTM E112 formula to calculate the grain size number.
Step-by-step explanation:
To determine the ASTM grain size number when 30 grains per square inch are measured at a magnification of 250, we use the formula given by ASTM E112:
N = 2(G-1)
where N is the number of grains per square inch at 100x magnification, and G is the ASTM grain size number. However, since the measurement given is at 250x magnification, we need to convert it to the equivalent at 100x magnification.
Since the number of grains per unit area changes with the square of the magnification (inversely), we can use the following relationship:
N100x = N250x \(\frac{100}{250}\)^2 = 30 \(\frac{100}{250}\)^2 = 30 \(\frac{2}{5}\)^2 = 30 \(\frac{4}{25}\) = 30 \* \frac{4}{25}
After calculating N100x, we then insert it into the first formula to solve for G, the ASTM grain size number.
We assume the number of grains per square inch at 100x will be fewer since it’s a lower magnification, and the area will appear larger. The larger area would contain fewer grains within a square inch when viewed under a lower magnification.