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I've been learning Gauss' divergence theorem and I understand what "flux density" is when considering things like fluid transport or particle streams but I'm having trouble understanding what it means when talking about gravitational fields. I wonder if somebody can straighten me out.

Here's what I know:

For water flowing in a pipe, for example, the field under consideration would be called "volumetric flux density" and would have units of, say, liters per second per square meter. The "thing" that's flowing would be "water molecules".

For particles emitted by a radiation source, for example, the field under consideration would be called "particle intensity" and would have units of, say, particles per second per square meter. The "thing" that's flowing would be "particles".

Now here's where I have trouble:

For gravity the field would be called "gravitational field strength" or "gravitational flux density" and would have units of newtons per kilogram. But this looks completely different from the water and particle cases: there are no units indicating "something flowing per unit time per unit area".

I could play with the units to make it look like the water and particle cases:

N / kg = (kg m / s^2) / kg = m / s^2 = (m^3 / s) / s / m^2

So now I have something that looks like a "flux density" - I have "something" per second per unit area.

But what is this "something" that is "flowing" ? It has units of (m^3 / s) which is a volumetric flow. Does this "something" have a name? Thanks for reading this far. Hope someone can enlighten me.