How much added mass to raise pressure in vessel?
How much added mass to raise pressure in vessel?
(OP)
Hello,
If I have a cylindrical pressure vessel, and am testing for failure, I would like to load it several thousands of cycles between 0 psi and a pressure, p. How much water do I have to pump into the vessel (with known volume), in order to raise the pressure to p?
Thanks.
If I have a cylindrical pressure vessel, and am testing for failure, I would like to load it several thousands of cycles between 0 psi and a pressure, p. How much water do I have to pump into the vessel (with known volume), in order to raise the pressure to p?
Thanks.





RE: How much added mass to raise pressure in vessel?
ie
Delta Vwater = 46*10^-6*P when P in bar
The pressure vessel will expand as the shell stretches, so you will need to know the stress in the shell and the modulus of elasticity of the material.
Assuming the shell is uniformly stressed, the increase in volume will be
Delta Vvessel=(stress/modulus of elasticity)^3
Be careful with the units.
It might be easier to do a test with a bucket pump and see how much water comes our when the pressure is relieved
Jeff
RE: How much added mass to raise pressure in vessel?
for 1psi pressure, it looks like the water will compress 0.000046/14.7*V (so this much water will need to be added).
for 1 psi pressure, the cyclinder volume will increase by (assuming only radial strain) V*(R/tE), so this volume would need to be added. if the cyclinder is unstiffened you can include the longitudinal strain.
so for 1psi pressure the volume of water to be added is something like V*((0.000046/14.7)+(R/tE)) ...
but like jeff says, this is just a guide; have a pressure sensor tell you the pressure achieved.
possibly someone out there remembers water tank testing and can help out some more.
good luck
RE: How much added mass to raise pressure in vessel?
the volume increase is ...
hoop stress = pR/t
hoop strain = hoop stress/E
loaded circumference = 2piR(1+pR/tE)
loaded radius = R(1+pR/tE)
[interesting, the radial strain is equal to the hoop strain]
loaded volume = pi*R^2*(1+pR/tE)^2*L
so the increase in volume (under 1 psi pressure) is ...
pi*R^2*2(R/tE)*L
so the combined effects are ...
increase in volume = V*((0.000046/14.7)+(2R/tE))
for 1 psi pressure
RE: How much added mass to raise pressure in vessel?
A fluid mass can be used in these cases, but you have to be aware of the boundary conditions and internals. Might I suggest that you go to:
http://www.volcano.net/~d.citerley refs. 10, 12, 13 and 15 under the publications link.
RE: How much added mass to raise pressure in vessel?
RE: How much added mass to raise pressure in vessel?
The references used in my previous discussion provides the necessary experimental verifications. Nothing scary about the fact that an analytical approach can provide accurate predictions if you provide verification. Some of the expreiments were LOCA for nuclear power plant suppression pools.
The verifications were for symmetric and nonsymmetric loads.