The volumetric flow rate in fluid dynamics and hydrometry, (also known as volume flow rate or rate of fluid flow) is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m³ s^-1] in SI units, or cubic feet per second [cu ft/s]). It is usually represented by the symbol Q.

Volumetric flow rate should not be confused with volumetric flux, 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. Volumetric flow rate is also linked to viscosity.

Given an area A, and a fluid flowing through it with uniform velocity v with an angle θ away from the perpendicular to A, the flow rate is:

$Q\; =\; A\; cdot\; v\; cdot\; cos\; theta.$

In the special case where the flow is perpendicular to the area A, that is, θ = 0, the volumetric flow rate is:

$Q\; =\; A\; cdot\; v.$

If the velocity of the fluid through the area is non-uniform (or if the area is non-planar) then the rate of fluid flow can be calculated by means of a surface integral:

$Q\; =\; iint\_\{S\}\; mathbf\{v\}\; cdot\; d\; mathbf\{S\}$

where dS is a differential surface described by:

$dmathbf\{S\}\; =\; mathbf\{n\}\; ,\; dA$

with n the unit surface normal and dA the differential magnitude of the area.

If a surface S encloses a volume V, the divergence theorem states that the rate of fluid flow through the surface is the integral of the divergence of the velocity vector field v on that volume:

$iint\_Smathbf\{v\}cdot\; dmathbf\{S\}=iiint\_Vleft(nablacdotmathbf\{v\}right)dV.$

See also

• Air to cloth ratio
• Darcy's law
• Discharge (hydrology)
• Flowmeter
• Flux (transport definition)
• Mass flow rate
• Orifice plate
• Poiseuille's law
• Units of flow