Re: gas container

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

Very elegant (see below) !  How come I did not think about this
simple approach myself?

For the electrostatic pressure of 235300 atm (due to 1 mC of charge
uniformly distributed over a dielectric shell of R=1 cm) the shell
thickness must exceed 23 cm. This was found by assuming that
the tensile strength of the dielectric is 5200 MN/m^2 (same as for
steel, which is not realistic) and without a safety factor. For a
strong plastic the necessary shell thickness would probably be
close to one meter or more. A very thick shell to confine the
space charge of one millicoulomb. Does Jack's recipe remain
valid when t>>R?
                                    Ludwik Kowalski
P.S.
By the way, the same charge on the outer surface of a metallic
sphere (R= 1 cm) would result in E=9*10^8 V/m. At such strong
field charges would already be escaping  into a vacuum by
autoemission, a QM process of tunneling.

But a charge of 0.1 mC would not leak significantly by autoemission.
The electric pressure of 2353 atm due to such charge,  would call for
a plastic shell whose thickness is 1 cm or more. Still a very thick
layer for only 100 microcoulombs of a net Q.  Mister Pauli must be
very strong to hold 0.1 mC on the surface of a metallic sphere
whose R=1 cm.

JACK L. URETSKY wrote:

> Hi all-
>         From a former aero engineer:
>         Answers to questions like this can be found in engineering handbooks,
> such as the Mechanical Engineering Handbook.
>         My physicist analysis, in the meantime, is that the spherical shell is
> under tension.  Draw any circumference (great circle) to divide the shell in
> half.  The total force on a half-shell, perpendicular to the plane of the circle,
> is just the pressure times the projected area: F= p*pi*r^2, r being the radius.
> The force per unit length of shell is F divided by 2pi*r, so if t is the shell
> thickness, then the stress is  s =pr/2t.  The stress should be less than the
> yield stress of the metal, and handbooks tell you how big a safety factor to
> apply to your calculation.
>                                 Regards,
>                                         Jack
>
> > > > Suppose that a spherical shell of thickness d is used to contain a
> > > > gas whose pressure is given, for example, 100 or 100,000 atm.
> > > > What is the necessary value of d for steel?...
> > Any mechanical engineer (or a physicist, chemist, etc.) to help us?