# Crush pressure on an underwater vacuum tube

1. Jul 20, 2008

### Dumb Idea

So... let's say I wanted to drop a pipe on the ocean floor with a 6" inner diameter... which has a pretty strong vacuum in it... what general size/material do you suppose that would require... assume it is miles long.

I guess you could keep the vacuum pipe inside of another pipe that does not have a vacuum.

2. Jul 20, 2008

### mgb_phys

Having a vacuum inside only adds one atmosphere of extra pressure, equal to another 10m of water depth.
Given the depth of water at the ocean flor, the vacuum isn't going to make much difference.

3. Jul 20, 2008

### Dumb Idea

Thanks for that!

So... average ocean floor is 2.5 miles. How big you gotta make a thing, a quasi conventional thing... I mean I couldn't make it out of titanium, to have a 6" ID?

4. Jul 20, 2008

### Q_Goest

Hi Dumb Idea. Welcome to the board.

To determine the adaquecy of a pipe under external pressure, the piping code (ASME B31.3) is generally applicable. That code points you to the ASME Boiler and Pressure Vessel code. If you have a copy of the ASME BPV Div 1, look under para UG-28 for "Thickness of Shells and Tubes under External Pressure". You should have a copy in your library.

5. Jul 21, 2008

### stewartcs

A quick hand calc shows that a 6" diameter carbon steel pipe with a wall thickness of 3/8" and a yield of 80,000 psi (API 5L Grade X-80) will get you to a little over 18,000 feet in the ocean.

I'm assuming there is no load on the pipe. If there is, then that will affect the collapse resistance of the pipe.

CS

6. Jul 21, 2008

### Mech_Engineer

I have no experience designing underwater piping, but a thought that came up to me was buckling.

According to Roark's Table 35, Case 19a "Thin Tube Under Uniform lateral External Pressure; Very Long Tube with Free Ends," the critical external pressure required to buckle the tube would be 1357 psi (Young's Modulus of 29000 ksi, Poisson's Ratio of 0.29). This equates to an approximate depth of about 3000 ft (930 m), far short of the previously stated depth.

7. Jul 21, 2008

### stewartcs

That would be for a vertical pipe under its own self weight. The OP appears to be asking about the collapse pressure rating of a pipe laying on the seabed in 13,500 feet of water depth...so buckling shoudn't be a problem.

If it is vetical, then of course he'll have to consider buckling.

CS

8. Jul 21, 2008

### Mech_Engineer

We are not talking about longitudinal buckling, we are talking about the circular cross-section of the pipe itself buckling. Since the tube would be evacuated (or at least have a very low internal pressure) I think the application is valid.

9. Jul 21, 2008

### Mech_Engineer

Here is the calculation in MathCAD, in pdf form. According to the sheet, he may have to have 0.75 in wall thickness at 13,500 ft, but the sheet is not valid for thick walls so an FEA model may be in order, or another equation if it exists.

#### Attached Files:

• ###### Mathcad - Roark's Formulas for Stress and Strain_ Table 35, Case 19a.pdf
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10. Jul 21, 2008

### stewartcs

The first problem with your calculation is that the radius is not 6.75 inches. The outside diameter is 6.75 inches. Hence, use a radius of 3.375 inches instead. If you do that, your numbers work out to over 24,000 feet!

Secondly, you're not considering the yield strength of different materials. API 5C3 is a good reference for these types of caclulations. They have verified their formulas with emperical tests too.

BTW, as I was typing this I noticed I used 6-in as the OD instead of the ID, so the revised calc would be good for 14,000-ft with the original numbers instead of 18,000-ft.

CS

11. Jul 21, 2008

### Mech_Engineer

Oops! Good catch on the radius/diameter error. Looks like buckling probably won't be a problem at the depths he is talking about. Unfotunately, the equation isn't valid for a .375 wall thickness and 3.375 radius, so the result isn't useful anyway.

Yield strength isn't taken into account in a buckling calculation, only the Modulus of Elasticity and Poisson's ratio.

12. Jul 21, 2008

### stewartcs

No problem, I do it all the time!

I always tend to think of it as the collapse resistance of the pipe instead of buckling. I don't like using the term buckling unless I deal with columns (or vertical pipe in the ocean)!

CS

13. Jul 21, 2008

### stewartcs

That's why I don't think of it in terms of buckling. The yield strength definitely comes into play with collapse resistance of pipe in the ocean! Typically because they are vertical and in order to prevent them from buckling a tension must be applied at the top of the pipe. This results in a degraded or equivalent yield strength of the material which results in less of a collapse resistance.

CS

14. Jul 21, 2008

### Mech_Engineer

Buckling, Elastic Stability, Crush Resistance, it's all the same to me Your explanation definitely makes sense though.