# Q about Thermal expansion of steel tube

• posted
Dear All,
I'm a student of physics and I have two Q.
First, When the temperature of steel tube is changed, How can I
calculate the change of outer diameter and inner diameter of tube?
the oute diameter is 40mm, the inner diameter is 30 mm, the length of
tube is 100mm
Next, When the temperature of steel tube is changed, How can I
calculate the change of length of tube?
the oute diameter is 40mm, the inner diameter is 30 mm, the length of
tube is 300mm
Best Regards,
Aref,
snipped-for-privacy@yahoo.com
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You need to have the coefficient of linear expansion for the material. and the appropriate "length"
delta_L = alpha * delta_T * L
alpha = coeff. linear expansion delta_T = change in temp L = length
all in a consistent set of units, of course. Determining alpha is a typical high school or college introductory physics experiment. -- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)
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Change in circumference due to heating = pi*d*a*delta_T a=as above (alpha) d=original diameter delta_T=as above
You can see that it is tha same formula just for axial expansion (contraction).
• posted
Both the previous replies assume a large diameter and very thin wall and are an approximation. In your case the wall thickness is over 16% of the hole diameter, so these approaches would have a considerable error. Fortuantely the correct answer is also fairly simple.
Actually, the OD of the tube will expand volumetrically the same as if it were a solid cylinder with no hole. The hole will expand in volume the same as if it were a solid cylinder of the same material.
There are two types of expansion to be consdered: volumetric expansion and linear expansion. The change in volume is simply
deltaV = B * V0 * deltaT
where B is the coefficient of volumetric expansion (.000036/C for steel), V0 is the inital volume and deltaT is the change in temperature in C. This will tell you how much the volumes of your cylinders change.
There will also be a change in length of the cylinders
deltaL = A * L0 * deltaT
Where A is the coefficient of "linear" expansion (.000012/C for steel)* and L0 is the initial length. From this you can find out how much the cylinder will elongate.
If you know the new length and you know the new volumes, it is simple to figure out what the new diameters will be.
Now, go do you homework and stop screwing around on the Internet!
Don Kansas City
*
note that A is always exactly one-third of B for a material.
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Don,
Won't the inside diameter shrink? The material expands with heat, thus causing the inside diameter to get smaller.
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Nope. This is freshman physics.
Don Kansas City
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No, just as any hole gets larger. This is why when you have a fitted joint you can't get apart heating it can help. -- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)
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"Don A. Gilmore" wrote in news:_Glkf.3429\$Dk.2016 @tornado.rdc-kc.rr.com:
True, but the fundamental reason is that the 3d matrix of atoms are all getting pushed further apart in all directions. If you think about it that way, this mysterious behaviour is much simplified.
Cheers
Greg
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A good explanation for 1-d, 2-d and 3-d thermal expansion is found here: