Volumetric flow rate

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate, (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time; usually represented by the symbol Q. The SI unit is m³/s (cubic metres per second). Another unit used is sccm (standard cubic centimeters per minute).

In US Customary Units and British Imperial Units, volumetric flow rate is often expressed as ft³/s (cubic feet per second) or gallons per minute (either U.S. or imperial definitions).

Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m³/(m²·s), that is, m·s⁻¹. The integration of a flux over an area gives the volumetric flow rate.

Fundamental definition

Volumetric flow rate is defined by the limit:

I.e., the flow of volume of fluid V through a surface per unit time t.

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.