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Volumetric flow rate
From Wikipedia, the free encyclopedia
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:
In the special case where the flow is perpendicular to the area A, that is, θ = 0, the volumetric flow rate is:
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:
where dS is a differential surface described by:
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:
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