How do I determine the hoop stress in the pressure hull of a submerged cylindrical pressure vessel?

Question

With this how do I take into account the external pressure of the water on the tank? Hoop stress=Pr/t only accounts for the internal pressure? I have the yield stress of the material.

Answer 1

This could turn out to be a complicated problem depending on what the internal pressure in the tank is and what the external pressure due to the depth of the water is.

The internal pressure puts the shell in tension and you would want the absolute maximum tension stress to be limited to the yield stress, with no safety factor.

However the stress due to the pressure of the water on the shell is a compressive stress, and if the compressive stress is too much higher than the tensile stress the shell will fail by buckling, way before the shell material ever reaches the yield stress because the shell will fail by buckling instead of by tearing and that will happen at a point way below the yield stress.



The equation for compressive hoop stress is the same as for tensile hoop stress, but the equations for failure by buckling are more complicated.

Answer 2

The pressure (P) is actually the differential pressure across the hull in psi. For a pressure vessel above ground the expanding pressure (P) will be the measured gage pressure which is that differential pressure. Thet hoop stress will be in tension. For a submarine vessel the crushing pressure (P) would be the pressure equivalent to the depth of submergence less the pressure inside the vessel. The pressure inside the hull is probably atmospheric. That stress will be in compression.

To simplify the situation, assume that the depth is such that the underwater orientation of the vessel is insignificant to the working of the problem.

Answer 3

Easiest would be to take internal pressure and subtract the external pressure at the top of the vessel to get an effective pressure to use in the equation.