"Robert J. Chassell" wrote:
...
> For those figuring out the air pressure question, would there be
> differences if
>
> a) the structure was disc like, completely open on the inside
> (other than support structures)
>
> b) wheel like, with the rim having air and four (or x) spokes open
> all the way to the axis
>
> As far as I know, A and B are identical from a presssure point of view
> since the columns of air go to the center, and Pascal discovered that
> the height of the column is what counts. Is that right?
Yes. Pretend that the air is still. Then putting in
partitions between the columns should have no effect. So it's fair to
do any column in isolation.
>
> c) wheel like, with only the rim having air, the spokes separate
> from the rim
>
> In this configuration, the relevant maximum height is, I think, the
> ceiling. Perhaps I am wrong -- does someone know?
I'm not sure what you are saying. It is fair to take the
solution for a cylinder and restrict it to the part of a cylinder
that you have. You can see this by looking at B. The short columns
must have the same pressure distribution as the long columns in the
spokes, since they are in equilibrium with each other at any given
height. Now C is nothing but short columns--again nothing changes.
>
> Hmm... would the pressure at the ceiling be the same as the pressure
> at that altitude in an `open' configuration? Or would it be lower
> because there is no weight of air above the ceiling. Or would it be
> higher because the ceiling holds it in?
Same. But the space would be more "pressurized", as opposed
to having pressure come from a column of air. I'm not sure this
makes a difference to your intuition.
Or use Eric's argument. It works the same regardless of
which parts of the cylinder have air.
Anyway, you take the general solution, and then use the
pressure at some point as an initial condition to get the specific
solution for the pressure distribution.
---David
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