To first reply, yes, the outer sphere is constant.
It matters. Adiabatic compression is taking place. Even though it matters, such effect will be taken into account once I have a rate equation in terms of mass.
The effect will reflect on density.
Mass is the product of density and volume.
Mass flow rate is the product density, velocity, and cross-sectional area. (It's the derivative of mass with respect to time.)
Bare with the syntax please...
Looking at a sphere within a larger sphere, the volume of the difference is...