= Volumetric flow rate
{title2=$Q$}
{wiki}
= Volume flux
{synonym}
The <volumetric flow rate> measures <volume> crossing an oriented surface per unit <time>:
$$
Q=\int_A\mathbf v\cdot\mathbf n\,dA.
$$
For a planar cross-section of area $A$, define the mean normal <velocity> $\bar U=A^{-1}\int_A\mathbf v\cdot\mathbf n\,dA$; then $Q=A\bar U$ exactly. The units are $\mathrm{m^3\,s^{-1}}$. A nonuniform velocity profile changes the mean, rather than invalidating this definition.
In steady <incompressible flow> without leaks or branches, <mass conservation> makes $Q$ the same at every pipe section. In a compressible stream the conserved quantity is <mass flow rate>, and $Q$ can change as <mass density> changes. Collecting discharged liquid for a measured interval gives an elementary flow-rate measurement, provided the collection captures the full flow and the volume is interpreted at the appropriate conditions.
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