- Volumetric flow rate
The

**volumetric flow rate**influid dynamics andhydrometry , (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 examplecubic meters per second [m^{3}s^{-1}] inSI 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 m^{3}/(m^{2}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 toviscosity .Given an

area "A", and a fluid flowing through it with uniformvelocity "v" with an angle θ away from theperpendicular 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 unitsurface 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 thedivergence of the velocityvector field **v**on that volume::$iint\_Smathbf\{v\}cdot\; dmathbf\{S\}=iiint\_Vleft(\; ablacdotmathbf\{v\}\; ight)dV.$

**ee also***

Air to cloth ratio

*Darcy's law

*Discharge (hydrology)

*Flowmeter

*Flux (transport definition)

*Mass flow rate

*Orifice plate

*Poiseuille's law

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