Re: Very small nuclear submarines?

"Keith W" <keithnospam@xxxxxxxxxxxxxxxxxxxxx> wrote in message
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"Arved Sandstrom" <asandstrom@xxxxxxxxxxxxx> wrote in message
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"Keith W" <keithnospam@xxxxxxxxxxxxxxxxxxxxx> wrote in message
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"Mark Borgerson" <mborgerson.at.comcast.net> wrote in message
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That's not length of the boat. It's published diving depth.

Aha. I was mislead by the fact that the ratio of the two numbers
was close to the ratio of the lengths of the boat. That does make
me think that there may be an engineering reason that smaller boats
dive deeper.

If nothing else a larger cylinder will fail at a lower pressure than
a smaller cylinder made of material of the same thickness and
strength.

True dat. Considering the opposite case (pressure vessels holding stuff
in),
the stress S in the wall of a thin-skin pressure vessel of radius R,
wall
thickness t, and internal pressure P is

S = PR/2t

(thin-skin means t < 0.1R). With t held the same, as R increases, so
does
the stress. For compression the general argument is similar.


Indeed but much more complex as the mechanism of failure
is buckling rather than tensile failure, which is why I didnt post
the equation, I couldnt see how to do it in ASCII anyway :)

Come on, man, you show your tender age! What ever happened to using ASCII
art? :-)

Seriously, why not (_ for subscript, ^ for superscript)

P_e = 2 * M_e * t^2 / sqrt((3 - 3 * R_p^2) * r^2)

where P_e = classical elastic buckling pressure for an ideal sphere, M_e =
modulus of elasticity for the material, t = wall thickness, R_p = Poisson's
ratio for the material, and r = radius to mid-shell.

A simplified (empirical to a degree) equation is

P_e = 1.22 * M_e * (t/r)^2

The inelastic buckling equation for an ideal sphere is

S_max = 3pb^3 / 2(b^3 - a^3)

where p = external pressure, and a and b are the inner and outer diameters.
S_max is set to the yield strength.

In the first case (the classical and semi-empirical elastic buckling
pressure), if t = constant while r increases, P_E decreases. Similarly, in
the second case, if (b-a) increases with b-a = constant, we see that the
stress must also increase.

Q.E.D.

AHS


.

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