Volumetric flow rate is defined by the limit
that is, the flow of volume of fluid  through a surface per unit time .
Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow.
IUPAC prefers the notation  and  for volumetric flow and mass flow respectively, to distinguish from the notation  for heat.