Volumetric flow rate

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In fluid dynamics, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given area per unit time. It is also called flux. It is usually represented by the symbol Q.

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 flux 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 flux 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_ \mathbf \cdot d \mathbf ]

where dS is a differential surface described by:

[ d\mathbf = \mathbf \, 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_S\mathbf\cdot d\mathbf=\iiint_V\left(\nabla\cdot\mathbf\right)dV.]

Volumetric flow rate

See also