How to ascertain bursting pressure of a sphere ? Any formula relating shell thickness and pressure?

Question

A sphere has been designed with boiler quality steel plate of suitable thickness for certain application in which the pressure inside is about 6 Kg/cm2 . Due to corrosion / erosion , the shell thickness comes down and in some locations holes are formed. The weak / damaged areas of shell are being patched cutting open the desired shell portion and welding new plates of original thickness. How to ensure , that , the sphere is healthy enough to operate under the designed working conditions? In case the shell is likely to explode , how to predict and take corrective steps? How to calculate energy inside the sphere with the said operating pressure ? In case of explosion for the said operating pressure , what is the likely impact?

Answer 1

You say "boiler quality" but you do not say what the working fluid is or the size of the shell. if it is a large shell or contains steam, I would be very wary of any repairs done by someone who needs to ask here. The impact of an explosion _could_ be very severe, resulting in considerable loss of life and property, but it depends a lot on the size of the container. If you are using a sphere instead of a cylinder with hemispherical ends, I'd guess the shell is of limited size, but still, you don't say how large it is.

I believe most areas of most industrialized countries will have boiler/ pressure vessel inspectors, try asking the the local government or your insurance carrier.

By the way, 6kg [force] /cm^2 seems rather odd units,  I would think about 60N/cm^2 or 600kPa or 6bar would be more usual, sure Pounds (force) per square inch is commonly used in the US, but if one is going to use SI units one might as well use them consistently.

Answer 2

From BS 5500 (pressure vessel code)

The minimum thickness with purely internal pressure (no vacuum) can be given by:

e = pD/4f-1.2p

e = wall thickness mm

p = pressure in N/mm^2

D = inside diameter mm

f = the allowable stress (find your yield stress for your material and take 75% of it as the allowable stress or 50% of the tensile stress whichever is lower)

Again with pressure vessels your repairs should be welded by a coded welder, stress relieved and then non destructively tested by xray or ultrasonic testing to check for cracks in the weld. Be very careful!