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Buoyant Vacuums?
Name: Steve T.
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: Thursday, April 25, 2002
Question:
is it possible to take advantage of the fact that a
vacuum is lighter than helium by creating an envelope that was engineered
to be very light while also strong enough to resist acute internal
strain? could purging a container like this cause it to float?
Replies:
Good question. I made an estimate with some excitement, but the
answer to your question is no (if by floating, you mean in the
atmosphere). Steel vessels can be easily constructed that float in
water, as is obvious from any visit to any harbor. They take
advantage of the fact that water is some 833 times as dense as air is
near the earth's surface (1.3 kg/m^3).
To make an estimate of the feasibility of the idea, three equations
are needed:
B = 4/3 pi r^3 dair, M = 4 pi r^2 t dsteel,
F = A S
pi r^2 patm = 2 pi r t S
Here B is the mass of air displaced by a steel sphere of radius r in
air of density dair. pi = 3.14.
M is the mass of the sphere given by the area of the sphere times its
wall thickness times the density of steel, dsteel.
The third equation estimates the thickness of the wall required to
withstand the force of atmospheric pressure (patm) which must be
withstood by the steel around a diameter. A is the area of this steel
(circumference times thickness) and S is the maximum compressive
stress that can be withstood by the steel.
Putting these equations together, I get:
B/M = (2 S dair)/(3 patm dsteel) = 0.56
I used dair = 1.3 kg/m^3, patm = 1.0 x 10^5 N/m^2,
dsteel = 7800 kg/m^3, and S = 5 x 10^8 N/m^2.
Notice that the buoyant force is only a little more than half the
weight of the steel sphere. As the equation shows, this can be
improved by using a stronger material (S), and/or a less dense
material (dsteel). dair and patm obviously cannot be changed.
For a 10m diameter steel sphere, B = 680 kg and M = 1215 kg.
Best, Dick Plano...
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