How much added mass to raise pressure in vessel?

[Aerohandel]

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.

 

[notnats]

Water will compress about 46 parts per million for each atmosphere increase in pressure.
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

 

[rb1957]

jeff raises some good points. you'll have to combine the (small) compression of the water with the (small) change in volume of the cyclinder.

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

 

[rb1957]

oops,

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

 

[mtnengr]

There are a number of conditions about the fluid and its container that has to be defined. The classical approach is to assume that the pressure varies as a sine function from the top of the fluid to the bottom. The pressure at the exterior wall is governed by the partial derivative dp/dn = - rho d2r/dt2.

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.

 

[RPstress]

I still find this a somewhat scary approach. You're dependent on a structural analysis being actually accurate, as opposed to conservative. Does anyone know if this methodology has ever actually been used?

 

[mtnengr]

RPstress:

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.