Hi, I'm trying to learn about the 'continuity equation' at the moment in fluid dynamics, and according to this page, it is based on the idea of a control volume, of arbitrary sides, Δx, Δy, and Δz, somewhere in the middle of a fluid stream:

...they then explain how the sum of mass flow rates into, and out of, each face of the cube will be equal to the rate at which mass accumulates within the it. According to them, the rate of mass entering a face of the cube, is a product of density, velocity, and the face area.

My first question...

How can they use density interchangeably with mass in their equations? Since density equals mass/volume, then for density and mass to be numerically equal, then the volume must be equal to 1 (it must be a unit volume). So using SI units, (expressing the mass in kg) then the unit volume must be 1m^3, but if Δx, Δy, and Δz, are supposed to be very tiny dimensions, then how can this be the case?.... I mean the entire amount of mass occupying a cubic metre, is not passing through a face of this tiny cube is it? only a tiny amount.

Hopefully you understand my question, if not just ask, and I'll try to rephrase,

thanks, bit4bit.