Is this Pressure Vessel a Thin or Thick Cylinder?

[edz2012]

Homework Statement

20 m3 of gas at a pressure of 25 bar is to be stored in a cylindrical
pressure vessel 2 m long. Given the following information :

The yield strength of the vessel material is 14,000 psi

If a factor of safety of 5 is to be used, determine:

Whether the vessel should be treated as a thin or thick cylinder.

Homework Equations

iv been given the feed back as follows:
For this question you need to apply the thin cylinder theory to determine the thickness t, then depending on the answer for r/t, determine whether the cylinder should be treated as a thick cylinder. If it is a thick cylinder, then the thick cylinder theory must be applied to determine the thickness of vessel required.

The attempt at a solution

3.1 bar = 100,000 Pa
factor 5 means that maximumstrength
yield strength
=1 /5
1 psi=6894.7N /m2
a) We have PV = RT = PSL (L= 2 m long.)
So the strength of our vessel should be 25⋅105 Pa≈362.6 psi
From the factor of safety we can find the the maximum strength should be
14/5⋅103 psi=2.8⋅103 psi
So, the vessel should be treated as a thick. im told that my attempt is incorrect but i don't know how else to solve it useing the feed back I am given.

 

[CFDFEAGURU]

The length is fixed at 2 m. So, calculate what the diameter needs to be to hold 20 m^3 of gas. From the diameter, calculate what the thickness needs to be and then check the r/t value to determine what set of equations should be used.

Thanks
Matt

 

[SteamKing]

Did you work out the radius of the cylinder required to hold the compressed gas?

The decision on whether to apply thick or thin cylinder theory depends on the ratio r/t, not on what the ratio of the wall stress to yield might be.

 

[edz2012]

can you explain to me how to do this, what equations do i need to use.

 

[CFDFEAGURU]

The equation to figure out the volume is straight forward. Just look it up for a cylinder. A basic thickness equation can easily be derived (or looked up) for the stress in the hoop direction. The longitudinal stress is always 1/2 of the hoop stress. So, the hoop stress governs.

Thanks
Matt