Mass flow rate ($\dot{M}={\int }_S\rho \mathbf{u}\cdot \mathbf{n}dS$)

The mass flow rate through an oriented cross-section is the integral of mass density times normal velocity. For constant density it is density times the volumetric flow rate. In a steady pipe without leaks, conservation of mass makes this rate independent of cross-section.

Coolant mass flow rate per open flow area, measured in $\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. A decrease in total flow does not establish a decrease in mass flux when the open area also changes.