# Calculating the Thickness of a Glass Tube which contains a Vacuum

I am looking for borosilicate glass tubes which can be used to contain a vacuum, so the top is sealed and then there is a vacuum pump at the bottom where the edges are also sealed, effectively making a vacuum in a glass tube.

The only thing to mention is that the walls need to be somewhat thicker than normal to protect against implosion due to the fact that there will be a vacuum inside, so I need an idea of how thick the glass needs to be bearing in mind that the inner diameter is 20 cm.

The pressure outside the cylinder is atmospheric and the pressure inside is very low and can be taken to be 0. Is there a formula or computation which would give me a good approximation for how thick the tube needs to be? I also appreciate that there could be some shear stress due to the tube needing to be so thick.

Let's call the diameter of your glass pipe, D, and assume the top and bottom of the tube are domes in a gentle transition from cylinder so we can ignor the local stress concentration.

The pressure, P, being radial around the pipe causes only compression and no moment or shear in the glass.

If we cut the glass longitudinally we have two half cylinders such that the thickness, t, of the glass has to counter total pressure per unit length. Let's call the required stress of the glass, S.

t× S= P×D

t= P×D/S= 1atm× D/S

The compression strength of normal glass is in the range of 1000psi, but it can vary depending on many factors so you check it, then you plug it in the above formula and use the required safety factor in your industry to get the thickness, t.

• I currently have a 9cm inner diameter glass tube with thickness 3mm and estimated that if I want to increase the inner diameter to 20cm then the thickness needs to be 7mm. However, I have now switched to perspex and I can only get 20cm inner diameter with 3mm wall thickness. Based on the strength of perspex in comparison to lab glass, do you think this would be sufficient thickness to contain a vacuum, as I feel like perspex is a great deal stronger than glass. Apologies if this is a stupid question as I don't know anything about materials and structures unfortunately.
– Tom
Dec 10, 2019 at 18:00
• @tom.most likely it will. But Iwe can do a more accurate estimate if you have the data sheet on the perspex. Dec 10, 2019 at 18:08
• I don't think the manufacturer has data sheets but will ask, in the meantime I found a data sheet at another manufacturer for what looks to be the same ie. acrylic tube directplastics.co.uk/pub/pdf/datasheets/…
– Tom
Dec 10, 2019 at 18:32
• @Tom, assuming the compression strength is similar to tensile strength, 75MPa. which is roughly 700kg/cm2 it should be more than adequate. because you have 20cm*1atm=20kg/cm length pressure. while you have available 0.3*700=210kg/cm. Dec 10, 2019 at 20:12