Volumetric flow rate ($Q$)

The volumetric flow rate is the volume of fluid crossing a section per unit time, $Q={\int }_A\mathbf{u}\cdot \mathbf{n}dA$.

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.

For a flow invariant in one horizontal direction, the volume flux per unit width is the velocity integrated across the flow depth. It has dimensions of area per unit time.

A discharge coefficient multiplies an ideal inviscid opening-flow rate to represent contraction and dissipative losses. Its value depends on the opening geometry and flow regime.