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
AI Thread Summary
To fit an iron band over a barrel, it must be heated to a temperature that allows for the necessary expansion, which can be calculated using volume expansion formulas. The assumption that the band’s width remains constant while its thickness expands linearly is confirmed, allowing for the calculation of the desired volume after heating. For thermal stress calculations upon cooling, the cross-sectional area of the band, defined as thickness multiplied by width, is appropriate. All linear dimensions of the band, including radius and gap, expand uniformly when heated, as the material is isotropic. Understanding these principles is crucial for accurately determining the required heating temperature and resulting tension in the band.
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.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »

Similar threads

Equation of state of a rubber band
Replies
13
Views
8K
Rate of Energy Transferred, Aluminum Pot
Replies
5
Views
2K
Heat engines working over time
Replies
7
Views
2K
What is the specific heat of the metal in this specific heat problem?
Replies
3
Views
1K
Heat Transfer: Effect of a Heat Fin
Replies
4
Views
2K
Heat required to increase the temperature
Replies
4
Views
1K
When to convert units of temperature?
Replies
2
Views
2K
Heat needed to expand a circular metal plate
Replies
2
Views
1K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
Replies
8
Views
2K
Experimenting whether the diameter of a pot affects boiling time for water
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top