If we model an object as a collection of point particles, there is another level

Question

If we model an object as a collection of point particles, there is another level of modeling that is needed. Do these point particles maintain a definite relative position to each other or can their relative positions change? If the point particles maintain a definite relative position to each other, then we say that the object is a rigid body. If not, we may say that the object is a fluid. The main purpose of this is to formulate a statement of the conservation of mass as a fluid flows. Theoretical physicists must figure out ways to mathematically describe philosophical ideas when modeling systems. We have the basic belief that as a fluid flows, the mass of the fluid must be conserved. This is not as easy to describe for fluids as for rigid bodies because for rigid bodies, the mass in any part of the body remains intact in the same space as the object moves. This is not the case for fluids. How do we formulate the conservation of mass for fluids?

Explanation / Answer

Considering a given volume element, we can say that the amount of fluid entering that volume element must be equal to the amount of fluid coming out of the volume, given that there is no source or sink in the volume element. If there is a source or sink in the region, then we can account for it by adding a mathematical term called divergence.

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