# Ball in water (in free fall)

The pressure within the bulk of the water is constant. Accordingly, the pressure gradient is zero within the bulk of the water. That is what I mean when I say that there is no gradient within the bulk of the water. It is not clear whether you disagree with this.
That depends, if it's just the bulk of the water aboard the ISS as a floating sphere and in the absence of forces that may create a gradient then I agree. Once a bubble of air is introduced into the sphere then to be honest I am not so sure the parameters remain the same.
You will end up haveing two different substances with different properties and densities one on the inside of the sphere of water as air and another on the outside of the sphere also as air.
Also two layers of surface tension.

jbriggs444
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That depends, if it's just the bulk of the water aboard the ISS as a floating sphere and in the absence of forces that may create a gradient then I agree. Once a bubble of air is introduced into the sphere then to be honest I am not so sure the parameters remain the same.

You will end up haveing two different substances with different properties and densities one on the inside of the sphere of water as air and another on the outside of the sphere also as air.
Also two layers of surface tension.

Now consider a small parcel of water somewhere between the outer surface where water meets air and the inner surface where water meets air. Further suppose that this parcel of water is under a pressure higher than a neighboring parcel.

Under this scenario, the water between those two regions will be under a net force away from the high pressure region and toward the low pressure region, yes?

And this water will undergo an acceleration away from the high pressure region and toward the low pressure region, yes?

And the resulting influx of water will increase the pressure in the low pressure region and decrease the pressure in the high pressure region, yes?

So the only stable static arrangment must be one in which the pressure throughout the bulk of the water is constant.

One quibble is that there can be stable dynamic arrangements, e.g. a whirlpool or a compression wave, but those will tend to decay over time, so let's agree to consider only a static equilibrium.

The same reasoning applies for the air in the cabin and for the air in the embedded bubble.