This is an interesting question, we know that for water the pressure would be equal throughout the material.
I would think in a powder the frictional forced between the particles would cause the material to bind on the outside therefor bridging the forces around the inside. This would cause less pressure on the inside and more on the outside.
I agree with this. I think the pressure would be at most = to pressure applied to outside, actual pressure depending on nature of powder (pressure = if it behaves like a liquid). It's easy to imagine a powder that bridges completely, like a 3-dimensional arch all round, if the particles are correctly shaped. This would support the applied pressure and there would be no pressure at the centre.
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Give masochists a fair crack of the whip
Powder is of course a mixture of gas and solid particles as the pressure increased the properties of the mixture would change from that of a gas to that of a solid as a greater area of the particles come in contact with each other.
Assuming the pressure was raised slowly this would be a uniform process throughout the mixture but if the commpression was rapid the pressure increase would propergate through the mixture as a wavefront at the speed of sound in the mixture which of course would change as the
properties of the mixture
changed from that of a gas
to that of a solid.
(this caused a lot of problems to the manhatten project and they had to do a lot of experiments but I do not know how much of the results were published)
if the pressure was not sufficient to compress the solid like materiel one could visulise an outer shell of solid materiel with a centre of powder but I do not think this would be a stable state and not likley to arise in practice
I believe that syphrum is basically correct - slow compression should result in uniform deformation and therefore uniform pressure - unless the powder can align along the surface of the container, in which case it could indeed form a stable protective shell.
If the compression is applied rapidly, it will propagate as a wave. Regardless of variations in the powder properties during compression, this should result in the greatest pressure occuring near the centre of the sphere - but
random effects and gravity mean that the peak pressure will not normally be exactly at the center, and
reflections at phase-changes and the aforementioned random scatter could mean that the peak pressure could be way lower than simple theory would predict.
I find this discussion fascinating as the only application I know for symetrical spherical compression is to make a plutomium bomb.
About thirty years ago there was slow motion Xray film shown on the TV of tests performed by the Manhatten team to develop the 'Big boy' bomb, many test explosions were carried out and eventualy symetrical compression of the core was achieved, this is very difficult to achieve as the North Korean team found out when their test detonation was only a partial success.
I cannot visulise such film being shown on the TV today with all the hysteria about 'rogue states' getting bombs
There is a technique known as "inertial confinement fusion", where laser pulses were used to create a spherical shock waves to create a very high temperature plasma. I believe that steady-state plasmas show more promise at the moment (but don't hold your breath). Other proposed applications have inlcuded diamond creation, but presses are adequate for industrial-grade diamond and CVD can provide higher quality material for heat-sinks, windows, etc. I heard that similar methods were proposed to produce other specialist materials, including Borazon (cubic BN), but I don't know what are the present techniques.