The formula you mentioned, d1 = d0 [dt α + 1], represents the thermal expansion of a pipe. However, it seems there might be a misunderstanding or a typographical error in the formula you provided.
The correct formula for calculating the thermal expansion of a pipe is given by:
ΔL = L0 α ΔT
Where: ΔL is the change in length of the pipe L0 is the initial length of the pipe α is the coefficient of linear expansion of the material ΔT is the change in temperature
This formula calculates the change in length of a pipe due to thermal expansion. It does not involve diameter (d1 and d0) as mentioned in your formula.
To find a reference for the thermal expansion formula, you can refer to various engineering and physics textbooks or online resources that discuss the topic of thermal expansion. Some common references for such information include:
- "Fundamentals of Heat and Mass Transfer" by Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt.
- "Thermal Physics" by Charles Kittel and Herbert Kroemer.
- "Introduction to Solid State Physics" by Charles Kittel.
- "Materials Science and Engineering: An Introduction" by William D. Callister Jr. and David G. Rethwisch.
These textbooks should provide detailed explanations of the thermal expansion phenomenon and the formula for calculating the change in length due to temperature variations.