Re: shock wave as pressure builds in a vacuum?

[Stefan Jeglinski <jeglin@4PI.COM>]

From various commentators:
> So one can suppose that a rapid air flow impinges on the
> delicate? membrane and perhaps especially if it flutters,
> it may breach.

The fluttering is one of the theories I mentioned (briefly). dx/dt of
the membrane surface exceeds some mechanical parameter.

>  I suppose there is some reason for keeping
> the membrane thin? Perhaps a strain-gage is attached to it?

FWIW, the membrane is an ultrathin polymer window that allows x-rays
in the 100eV range to pass. Behind the window is a silicon x-ray
detector under high vacuum. On the outside of the window is the
chamber of an electron microscope, which normally operates under a
medium to high vacuum, but which is also exposed to lower vacuums for
sample change and atmosphere for maintenance. (The
technique/instrument is EDS, Energy Dispersive Spectroscopy).

Normally, venting to atmosphere is done slowly, but there are
instances of window breakage during catastrophic venting. The physics
question is whether it is plausible that catastrophic venting alone
can break the window, which is designed to withstand a 1 atm
differential under steady state conditions (so it can be shipped and
handled etc). As mentioned in my original post, the window is backed
by a sparse grid for extra mechanical support.

> You may want to look into the design and operation of the Baratron pressure
> sensor:

Lot of reading there. Clearly the baffle is designed to prevent
something of the sort of thing that is being discussed here.

> And what about a "fuse" to protect the essential
> membrane? A large high vacuum cavity with a
> membrane weaker that the one to be protected.

The issue is not so much how to prevent it. The description above of
the actual device is enough to eliminate many "solutions." I'm just
wanting to understand the breakage from a physics standpoint.

>         I am not sure why you do not like the
> water-rushing-in analogy.  The inrushing air has a
> linear momentum that must be "absorbed" by the
> membrane.  To the zeroth approximation it is
> similar to water hammer.

Let's do back of the envelope, zeroth approximation. Force due to a
fluid cylinder of cross-sectional area A moving at velocity v,
density rho, that impinges on a flat surface, and assuming worst case
elastic collision, is 2.A.rho.v^2. Normalize A to get pressure,
assume rho is atmospheric density at RT (the in-rushing air is from
the atmosphere, approx 1 gram per 1000 cc). What is a reasonable v?
Not large, intuition tells me 10cm/sec into a vacuum is a reasonable
guess. My calculation of collision pressure is 2e-6 N/cm^2, or 3e-6
psig. The more likely inelastic collision (cf wind against a sail),
and compression effects make this even smaller (right?). Even if I
increased v by 3 orders of magnitude, I'm still relatively small at
0.3 psig. Please check my math and try not to embarrass me too much
if you find a mistake :-)


> But one thing's for sure, the membrane will see
> a lot more that 1 atm pressure.  As an approximation,
> analyze it in the linear regime.  Take 1 atm as
> the "at rest" position.  Then the initial condition
> is a very loud sound wave (negative 1 atm [gauge]
> sound pressure).  This sound wave will reflect off
> the membrane.  During the time of this reflection,
> the incident wave and the reflected wave will
> both be at the surface, so there will be a plus 1
> atm [gauge] sound pressure, i.e. 2 atm [absolute].

I'm having a hard time figuring if this is really an equivalent
problem. Generating a sound wave of any magnitude will of course have
an effect; if I fling a small dirt particle at it I can break the
window also. Given my air example above, where is the source for such
an impulse to travel through the air filling the chamber so it may
bounce off the membrane?


Stefan Jeglinski