VOLUMETRIC FLOW RATE

In fluid dynamics and hydrometry, the 'volumetric flow rate', also 'volume flow rate' and '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:
:$Q\; =\; A\; cdot\; v\; cdot\; cos\; heta.$
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 ''d'''S' 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:
:$iint\_Smathbf\{v\}cdot\; dmathbf\{S\}=iiint\_Vleft($
ablacdotmathbf{v}
ight)dV.

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See also

See also

★ Air to cloth ratio

★ Discharge (hydrology)

★ Flowmeter

★ Flux (transport definition)

★ Mass flow rate

★ Orifice plate