What Temperature Must an Iron Band Be Heated to Fit a Barrel?

  • Thread starter Thread starter e(ho0n3
  • Start date Start date
  • Tags Tags
    Band Fit Heating
Click For Summary

Homework Help Overview

The problem involves determining the temperature required to heat an iron band so that it can fit over a barrel, as well as calculating the tension in the band once it cools back to room temperature. The context includes concepts of thermal expansion and thermal stress.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss whether the width of the band remains constant while its thickness expands linearly. There is also consideration of whether to use volume expansion or linear dimensions for calculations. Questions arise about the behavior of the radius of the band and the implications of it being a thin ring.

Discussion Status

Participants are exploring different assumptions regarding the expansion of the band and its dimensions. Some guidance has been offered regarding the linear expansion of dimensions, but there is still uncertainty about the implications of the band being a thin ring and how that affects the radius and gap when heated.

Contextual Notes

There is a discussion about the isotropic nature of the material and how that affects the expansion of the band. Participants are also considering the implications of the band being a closed versus an open ring.

e(ho0n3
Messages
1,349
Reaction score
0

Homework Statement


A barrel of diameter D at 20 degrees Celsius is to be enclosed by an iron band. The circular band has an inside diameter of d at 20 degrees Celsius. It is w wide and t thick. (a) To what temperature must the band be heated so that it will fit over the barrel? (b) What will be the tension in the band when it cools to 20 degrees Celsius?


Homework Equations


For (a) I will need the equations to calculate the volume of the band and the change in volume of the band when heated. For (b), I will need the equation for determining thermal stress.


The Attempt at a Solution


For (a), is it safe to assume that the wideness of the band remains the same while the thickness of the band expands linearly? If so, then I can calculate the the desired volume after heating and use the volume expansion formula to determine the change in temp.

For (b), the equation for thermal stress has area as one of its variables. The area is some cross-section of the material. In the case of the band, will the cross-section used be t x w?
 
Physics news on Phys.org
e(ho0n3 said:
For (a), is it safe to assume that the wideness of the band remains the same while the thickness of the band expands linearly? If so, then I can calculate the the desired volume after heating and use the volume expansion formula to determine the change in temp.
All linear dimensions expand by the same factor. No need to consider volume.

For (b), the equation for thermal stress has area as one of its variables. The area is some cross-section of the material. In the case of the band, will the cross-section used be t x w?
That seems reasonable.
 
Doc Al said:
All linear dimensions expand by the same factor. No need to consider volume.

Does that mean that the radius of the band expands linearly? I'm playing it safe by dealing with the volume because I don't know the answer to this question.
 
e(ho0n3 said:
Does that mean that the radius of the band expands linearly?
Yes it does.
 
Why is that? Suppose the band is a thin ring that is not closed. Does the radius still expand or does the gap in the ring just get smaller when the ring is heated? I would suspect the latter.
 
All linear dimensions expand the same way (assuming the material is isotropic). The radius will expand, as will the gap.
 

Similar threads

Heat Transfer: Effect of a Heat Fin
  • · Replies 4 ·
Replies
4
Views
3K
Rate of Energy Transferred, Aluminum Pot
  • · Replies 5 ·
Replies
5
Views
2K
What is the specific heat of the metal in this specific heat problem?
  • · Replies 3 ·
Replies
3
Views
1K
Heat engines working over time
  • · Replies 7 ·
Replies
7
Views
2K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
What is the Maximum Temperature for a Copper Block at 1000 atm Pressure?
  • · Replies 3 ·
Replies
3
Views
4K
Heat required to increase the temperature
  • · Replies 4 ·
Replies
4
Views
2K
Heat needed to expand a circular metal plate
  • · Replies 2 ·
Replies
2
Views
2K
When to convert units of temperature?
  • · Replies 2 ·
Replies
2
Views
2K
Experimenting whether the diameter of a pot affects boiling time for water
  • · Replies 15 ·
Replies
15
Views
3K