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Re: [PSUBS-MAILIST] TANK / PSI QUESTION
These are very dissimilar cases. In the case of internal pressure, the
pressure actually acts to deform the vessel in a manner which increases
roundness. Imagine looking at a cross section of the cylinder in
question (i.e. a circle, with a wall thickness). Now mentally divide
that circle in half. The tensile stress in the cylinder wall will need
to be the value that holds those halves together in the presence of the
internal pressure - i.e. the pressure multiplied by the projected area.
In this case, that internal pressure divided by the inner diameter times
the length of the cylinder (giving an area) gives you the force, which
is countered by the tensile stress in the area of the cylinder walls -
i.e. (OD-ID) multiplied by that same length - the length cancels, which
is why we can examine this as a 2-D problem. Now imagine perturbing the
geometry of the circle - i.e. making a dent in the cylinder wall, either
to the inside or the outside - the direction doesn't really matter. You
will notice that the tensile force in the cylinder wall acts to
straighten out the dent. As with a pressurized can or pop bottle, when
you squeeze it, provided you don't do it so hard as to cause plastic
(non-recoverable) deformation, the internal pressure will return it to
its former shape.
This is not the case with an externally pressurized vessel. A vessel
subjected to external pressure acts similarly in that the compressive
stress in the cylinder wall will ideally be equal to the external
pressure multiplied by the projected area (which is now the OD, not the
ID of the cylinder), giving the compressive force, and we divide this by
the area of the cylinder walls to get the compressive stress in the
cylinder wall. The difference in this case is that, if you then dent
the cylinder wall in either direction, putting it out of round, it is
not self-correcting, and in fact will cause a stress concentration which
tends to cause the cylinder to buckle and crush. Any deviation from the
perfectly round case needs to be accounted for by calculating based on
the largest perfectly round circle (largest OD, smallest ID) than can be
inscribed within the circle that actually exists (subject to
manufacturing and measurement accuracy). This is complicated even
further when extrapolated to the 3-D case, since our largest circle
becomes a largest cylinder, which must exist in an actual cylinder that
needs not only be round, but also of concentric cross-section as you
travel along its length. Anything outside of that is extranneous
material, as far as the calculations are concerned. A good
demonstration of this is standing on an empty pop can. A 200 lb person
can, if careful, balance themselves on an intact aluminum soda can.
Now, if someone bumps it, even slightly, the resulting deformation is
unrecoverable and the can crushes. Since it is not possible to
fabricate perfectly round cylinders which do not deform, we must do the
next best thing - a combination of thicker than theoretically required
wall thickness, in conjunction with bracing (i.e. ring stiffeners) to
prevent any deformation from excessively reducing the theoretically
perfect cylinder that exists within the fabricated one.
Clear as mud?
-Sean
Norm Parmley wrote:
Here's a question to the more mechanical types. If I have a normal
rounded metal tank rated for an internal pressure of 200 psi then, I
could assume it would be capable of 200 psi external pressure?
Norm P.
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