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• # Thermal expansion of a tube

Discussion in 'Calculations' started by LandroverDom, Sep 6, 2010.

1. ### LandroverDomMember

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Hi

I would like some help please on calculating the increased size of a tube due to increased temperature.

This tube forms part of an assembly inside a pressure vessel and I need to ensure the necessary clearances are in place so this tube can be free to expand as temperature increases.

The technical details of the problem are as follows:-

Tube Material - PTFE
Coefficient of linear thermal expansion 1 degC 10-5

Initial Temperature - 20 deg C
Elevated Temperature - 200 deg C
Change in Temperature - 180 deg C

Tube Outside Diameter - 399mm
Tube Inside Diameter - 356mm
Tube Length - 190mm

Any help in calculating what the tube sizes will be when at 200 deg C would be greatly appreciated.

Thanks

Dominic

2.
3. ### LandroverDomMember

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I stated the units for Coefficient of liner thermal expansion which was 1/degC 10-5 but forgot to state the actual value which is 13.

Thanks

Dominic

4. ### ConnectUTSActive Member

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Dominic:

Let me confirm the CFE as being 13*10^(-5).

With a temperature change of 180C the expansion is 23.4 mm / meter

When calculating the radial expansion of a tube you use the mean diameter and the wall thickness. The mean diameter is 377.5mm when cold. The mean diameter when hot is 377.5*1.0234 or 386.34mm - an increases of 8.335mm.

The wall thickness goes through a similar change or 22.00. The final OD of the part tube will be approximately 408.34mm.

5. ### LandroverDomMember

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Hi Niel

Thanks for the response, Am I correct that the the length would theoretically increase to 102.34mm?

Kind Regards

Dominic

6. ### alanhoActive Member

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Given that your original tube length is 190mm, wouldn't the final length be 194.45mm?

7. ### juice01Member

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Could someone explain the thermal expansion coefficient? I am studying it at the moment but I am a little confused on how it it used.
Mick

8. ### alanhoActive Member

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The coefficient of thermal expansion or CTE describes how the dimensions (linear, area, volume) of an object changes with the increase/decrease in temperature. Note that the temperature concerned is with the object and not with the surroundings. It measures the fractional change in size per degree change in temperature.

Hope this helps.

9. ### juice01Member

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Yea that helps a bit alanho.

Have you got a formula for this? If this bar is 190mm. How did you work out that it will expand 4.45mm?

Mick

10. ### alanhoActive Member

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I made a mistake in my earlier post. The linear expansion should be .445mm instead.

As Dominic stated in his earlier posts, the CTE is 13 (micron/meter-Deg C). This means for every degree C change, the length will differ by 13microns for every meter.

The temperature change is 180 C, which means a change of 2.34mm for every meter for this temperature difference.
The original length at initial temperature is 190mm. And since every meter (1000mm) will give you 2.34mm expansion, for 190mm length: 190/1000 X 2.34 = .445mm.

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