📢Mass Density as the Integrating Factor

The solutions demonstrate how fundamental physical quantities in a continuous fluid are determined by integrating their respective densities over a given volume. In all cases, the mass density is crucial as it scales the quantity per unit mass to the quantity per unit volume. The total kinetic energy is a scalar, found by integrating the kinetic energy density. In contrast, both the total momentum and total angular momentum are vector quantities. Total momentum is the integral of the linear momentum density. Total angular momentum, which must be defined relative to a specific reference point, is the integral of the angular momentum density.

Fluid Mechanics Integrals for Mass and Motion | Proof and Derivationviadean on Notion