Pressure vessel wall dimensions

Question

I am trying to design a small cooling setup which has two parts: the compressed air vessel and the turbines. My understanding is that the compressed air, upon being released, passes through the turbine and loses its energy to a useful process (the turbine could run another compressor for instance) and thus becomes cold. This cold air is then released where needed (a room, a fridge etc.)
Visualized:

Vessel material: stainless-steel 316-grade
Design temperature is 150°C (Assume a value upto 200°C for easier calculations, if you want)
How thick should the walls at points A, B and C be to be safe with these three design pressures?
Design pressure ? =5516 kPa
Design pressure ? =4482 kPa
Design pressure ? =2758 kPa
I don't need exact answers, but a largest (for safety) approximate would be fine too. If you could give me the relevant formulae and laws (capsule shaped vessels) so I could calculate it myself, I would really appreciate it! Note that I am a newbie, so correct mistakes in the design itself.
Thank you!

blacksmith37 · Answer

That is certainly the hard way to do it. You could go to a local welding supplier and buy or lease a standard steel pressure bottle / tank ; good for probably 3 X your maximum pressure (designed and built in conformance to ASME Sec. 8 , Div.1 ). Stainless steel is certainly not needed for air or most gasses. You don't need a turbine to get the cooling effect of expanding gas. By leasing a bottle with normal full pressure ( roughly 15000 kpa ) and using a standard pressure regulator , you could get several minutes of cooling.

Answered by blacksmith37 on April 7, 2021

r13 · Answer

First thing first, you need to get hand on the ASME Boiler and Pressure Vessel Code (BPVC Code). Starting division 8, section 1, for safety and quality of your pressure vessel.
After checking on all relevant provisions/standards, you can use the equations to derive the required wall thickness for your application.

Notation
σ_H = hoop stress, psi or MPa
D = outer diameter, in or mm
E = modulus of elasticity, psi or MPa
P = pressure under consideration, psi or MPa
P_i = internal pressure, psi or MPa
P_o = external pressure, psi or MPa
r = radius to point of of interest, in or mm
r_i = internal radius, in or mm
r_o = external radius, in or mm
t = wall thickness, in or mm
∆_P = change in pressure, psi or MPa
Note, the above formulas may be used with both imperial and metric units, just keep the units consistent.

Pressure vessel wall dimensions

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