Volumetric flow rate can also be defined by
where
:  = flow velocity,
:  = cross-sectional vector area/surface.
The above equation is only true for uniform or homogeneous flow velocity and a flat or planar cross section. In general, including spatially variable or non-homogeneous flow velocity and curved surfaces, the equation becomes a surface integral:
This is the definition used in practice. The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through, , and a unit vector normal to the area, . The relation is .