Pressure vessel made with a metal tube and a clear polycarbonate lid

[carveranderson]

TL;DR

I'm building a DIY pressure tube to run some experiments in at 100-200 psi max and not sure how to calculate thickness of a poly or acrylic lid that will be safe to look in at those pressures :)

The tube I'm using is 6" long, 6" diameter and .5" wall thickness and made of 6061 aluminum. The bottom is a 6" diameter, 3/8" thick MIC6 Cast Aluminum Disc. The top I TRIED is a 6" diameter, 1/2" thick clear polycarbonate disc. Both top and bottom are bolted on with a 1/16" buna-n o-ring and 6 evenly distributed 1/4-20 stainless bolts on each end. At about 80-90 psi (and a safe distance away) I can see the lid start to flex and begins to leak around the o-ring, but only on the poly top. The aluminum bottom seems fine. I think all the aluminum sides are plenty of overkill, but the poly lid doesn't seem adequate. What calculations would I need to use to determine what thickness poly I'd need at that 6" diameter to avoid flexing and breaking the seal at up to 200 psi? Any help with what calculations and formulas I'd use here would be appreciated in case I need to make this smaller in size, etc. Thanks!

 

[jrmichler]

Assuming the O-ring is in a 6.5" diameter groove, the total force on the ends is the area times the pressure. The area is 33 square inches, the pressure 200 PSI, so the total force is 6,640 lbs and the force on each bolt is 1100 lbs. While a 1/4" bolt should (barely) hold that, the safety factor is way too small. Use 12 bolts on each end.

For the end, acrylic is bad and polycarbonate is good. Acrylic can shatter into high speed razor sharp pieces, while polycarbonate will stretch out of shape if if fails.

Basic relations:
Stress is inversely proportional to thickness cubed and directly proportional to pressure.
Deflection is inversely proportional to thickness squared and directly proportional to pressure.

If you double the polycarbonate thickness to 1" and increase the pressure from 80 to 200 PSI, the stress will be 30% and the deflection will be 60% of that with the 0.5" end at 80 PSI. Using 12 bolts instead of 6 will further reduce deflection and stress between the bolts.

And pressure tests from a safe distance are always a good idea. A better idea is to pressure test to twice your working pressure, and to do the pressure test using a liquid such as water instead of air.

 

[AZFIREBALL]

You need to provide a metal reinforcing ring around the plastic end. It should be just wide enough to accommodate the bolts on top and should run down the sides about 1/2 inch or more (outside the 6 inch dia.). Make the lip on top at least 3/8 inch thick (where the bolts go through.) and the vertical leg at least 3/8 inch thick.
The cross section of, one side, is a upside down 'L' shape like this 'Γ '.
Pressure testing the device remotely is advised!

 

[OmCheeto]

...
up to 200 psi? Any help with what calculations and formulas I'd use here would be appreciated in case I need to make this smaller in size, etc. Thanks!

Hmmm... Thanks for asking. After doing some calculations, I've decided I would never try such an experiment.
At 200 psi, a 6 inch diameter, 1 lb lid, upon failure of the retaining mechanism would accelerate at 55,500 m/s^2.
Maintained for 1/10 of a second, that translates to a speed 20 times that of 45 caliber bullet. Roughly 12,400 mph.

I generally do the maths prior to investing time and money into odd projects.

I also searched for something that you could buy that fits your description. I had zero luck. But I did find one DIY fellow who built something similar to what you're attempting to make.

Like some have already mentioned, he set up a remote viewing station while initially testing his device.

@≈6:20 in the video, he describes how far he got away from his potential bomb.

 

[carveranderson]

@OmCheeto , thanks! In the video, he mentions using engineering formulas to figure out what thicknesses needed and he was expecting much higher pressures, implying this was overkill. I can't seem to figure out what formulas are needed to determine what thickness you'd need of polycarbonate (or aluminum) at a given diameter and pressure. It's sounding like I may need to reduce the size of this chamber a good bit, but what formulas would I need to use to do the math ahead of time? I found Barlow's Formula, which if I understand it correctly says my 6" dia, .5" wall aluminum tube has a bursting pressure of around 7,500 psi, so I figure I'm pretty good there. Just can't figure out what formula is needed to calculate the end caps.

@jrmichler , I'm using an 049 o-ring with OD of 5.192" that barely fits the 5" ID of the tube. So not sure that helps your calculations much, but there is only 5" diameter of the poly spanning the ID of the tube. The 1/4-20 bolts are centered in the .5" thickness wall.

 

[carveranderson]

@OmCheeto , @jrmichler , if the MIC6 3/8" thick plate I'm using on the bottom is sufficient (again not sure what formula for that), could I maybe use that on the top as well instead of poly, and get a small sight glass insert? I've got a small camera with it's own light source I could mount looking in the sight glass that should let me see good enough inside. Thanks!

 

[jrmichler]

If you want the equations for stress and deflection in disks with pressure and perimeter support, get a copy of Roark's Formulas for Stress and Strain: https://www.amazon.com/dp/0071742476/?tag=pfamazon01-20. You don't need a recent edition, the older editions will have the formulas.

At 200 psi, a 6 inch diameter, 1 lb lid, upon failure of the retaining mechanism would accelerate at 55,500 m/s^2.
Maintained for 1/10 of a second, that translates to a speed 20 times that of 45 caliber bullet. Roughly 12,400 mph.

An object accelerating at 55,500 m/s^2 for 0.1 seconds would move 277 meters in that time. The pressure behind the lid starts to drop as soon as a gap opens. If we assume that that acceleration lasts for 0.005 meters, the time would be 0.0004 seconds, and velocity 23 m/sec. The final velocity would be a lot higher, but still subsonic.

 

[Baluncore]

And pressure tests from a safe distance are always a good idea. A better idea is to pressure test to twice your working pressure, and to do the pressure test using a liquid such as water instead of air.

That is good advice. Any air or gas present will store significant energy. That is a significant hazard.
The initial pressure test should be done with cold water only.

 

[OmCheeto]

...
An object accelerating at 55,500 m/s^2 for 0.1 seconds would move 277 meters in that time. The pressure behind the lid starts to drop as soon as a gap opens. If we assume that that acceleration lasts for 0.005 meters, the time would be 0.0004 seconds, and velocity 23 m/sec. The final velocity would be a lot higher, but still subsonic.

Well, that'll teach me to check all the kinematics equations next time. I looked at only "vf = vi + at".
I wonder what variable(s) makes exploding tires so deadly? The first one in the following video was supposedly at 90 psi, just half of what the OP is planning on working with.

 

[Baluncore]

I wonder what variable(s) makes exploding tires so deadly?

Blunt force, traumatic amputation, followed by massive blood loss.
The mind is willing, but the tensile strength of flesh is weak.

 

[jrmichler]

Once upon a time, somebody gave me an old single cylinder reciprocating refrigeration compressor. I added a motor, then tested it by soldering a piece of copper tubing to a pair of tin cans soldered together. I was at least smart enough to put the cans into a barrel, then some planks weighted with a piece of railroad track on top. When it blew, it bounced the planks and made a boom that shook the house. The cans were turned into several pieces of sheet metal. My mother was on the second floor and ran down to the basement expecting to see a dead son. When she saw I was alive and undamaged, she turned around without saying a word. Tough woman.
This is PF. Maybe somebody could calculate the stored energy in the OP's pressure vessel and compare to the energy released by high explosive, which is about 2000 BTU per pound.

 

[berkeman]

I'll do the calculation. Give me a google-minute...