I am trying to determine the final diameter of a heated shaft with initial tempe

Question

I am trying to determine the final diameter of a heated shaft with initial temperature 70 deg F and final temperature 375 deg F. I have used two different methods which produce different answers. initial diameter is 8.499 in, thermal expansion coefficient is 16.3(10^-6) m/m-K

1. Area thermal expansion

2. Diameter only Thermal expansion

I am able to solve for final diameter d =8.5225 in

Which of these analyses provides the more accurate answer?

I am trying to determine the final diameter of a heated shaft with initial temperature 70 deg F and final temperature 375 deg F. I have used two different methods which produce different answers. initial diameter is 8.499 in, thermal expansion coefficient is 16.3(10^-6) m/m-K 1. Area thermal expansion frac{Delta D}{D_{i}}=beta Delta T I am able to solve for final diameter d =8.5225 in Which of these analyses provides the more accurate answer? A=frac{pi }{4}d^{^{2}} I am able to solve for the final diameter d = 8.5108 2. Diameter only Thermal expansion frac{Delta A}{A_{i}}=beta Delta T using

Explanation / Answer

The second method provides you the accurate answer because by using Area thermal expansion the term d^2 constitutes for more error rather than d which is used in the second method so go for the second method

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