# Thermal expansion of diameter of pipe filled with water

1. Jun 17, 2004

### thermalquestion

I would like to calculate the new diameter and thickness of a steel pipe filled with water.

At 20oC the pipe ID is 0.1016m and thickness is 0.0127m.
Coef vol th exp water 21e-5/oC
coef lin th exp steel 1.2e-6
The pipe can be assumed 1m in length.

I calculated that the water would expand by 1.89e-5m^3 and if there was a solid steel cylinder replacing the water it would expand by 3.25e-6m^3.
So, assuming water is incompressible I think I can not ignore the expansion of the water.
In this case do I take the expansion of the water only to calculate the new ID?
How then do I calculate the new thickness of the pipe?
I'm confised.
Any help appreciated.
P

2. Jun 17, 2004

### Gokul43201

Staff Emeritus
Is this a problem out of a book, or are you trying to solve a real problem ?

Is the change in temperature 20C ?

Are the ends of the pipe closed off, creating a cylindrical vessel completely filled with water ?

3. Jun 18, 2004

### thermalquestion

This is not a problem out of a book. I genuinely have a pipe filled with water.The pipe is actually part of a flow loop but lets assume there is zero flow. The water is encased by the pipe and cann ot spill over. The change in temperature is 5oC. Changing from 20-25oC. 20oC is the datum.
P

4. Jun 18, 2004

### HallsofIvy

Staff Emeritus
In that case the best way to answer the question is experimentation- actually set this up, fill it with water of the appropriate temperature and measure!

5. Jun 19, 2004

### thermalquestion

Are you saying there is no calculation which can be used to estimate this? The uncertainty in the measurement may be bigger than the effect.
P

6. Jun 19, 2004

### Gokul43201

Staff Emeritus
Your problem is not stated clearly enough. If the water is in an open line, there is no effect from the water. Even if not, there are probably enough bubbles/air gaps to accomodate the expansion of the water.

The expansion of diameter(s) and length of the pipe will depend on how it is constrained - ie : the boundary conditions. Are you suggesting you want to treat this section of pipe as being so far removed from the constraints that it can be assumed to behave like a free body ?

7. Jun 19, 2004

### Gokul43201

Staff Emeritus
So, neglecting the effect of water and assuming the length and diameter are both unconstrained (no clamps need to be considered), the new diameter is given by

$$d' = d(1 + \alpha \delta T)$$ and the new length is

$$L' = L(1 + \alpha \delta T)$$ , where $$\delta T$$ is the temperature change.

ie : the interior volume expands as if it were a cylinder of steel.

The new volume of the pipe material is

$$V' = V(1 + 3\alpha \delta T)$$

From the V' and d', you can calculate the new thickness, t' = D' - d'.

$$V' = \frac {\pi L'} {4}(D'^2 - d'^2)$$

Last edited: Jun 19, 2004
8. Jul 16, 2004

### thermalquestion

OK, I wasn't sure if this linear calculation was sufficient and was probably just making it unnessisarily complicated. Yes, the water is in an open system so the expansion of the water can be ignored, you are right. Thanks.

9. Jul 16, 2004

### thermalquestion

Since the pipe is not a cylinder there are two boundaries to be considered. The outer and inner diameter. How do calculate both the inner and outer diameter? I understand the outer diameter if the pipe is a solid cylinder but how to treat the internal diameter in the case of a hollow cylinder?