 Volumetric flow rate

The volumetric flow rate measures volume crossing an oriented surface per unit time: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 ${\mathrm{m}}^3{\mathrm{s}}^{-1}$. 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.