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:

<math> Q = A \cdot v \cdot \cos \theta. </math>

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

<math> Q = A \cdot v. </math>

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:

<math> Q = \iint_{S} \mathbf{v} \cdot d \mathbf{S} </math>

where dS is a differential surface described by:

<math> d\mathbf{S} = \mathbf{n} \, dA </math>

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:

<math>\iint_S\mathbf{v}\cdot d\mathbf{S}=\iiint_V\left(\nabla\cdot\mathbf{v}\right)dV.</math>

See also

• Discharge (hydrology)
• Mass flow rate
• Flowmeterca:Cabal hidràulic

en:Discharge (hydrology) eo:Debito es:caudal fa:بده fr:Débit gl:Caudal (fluído) hu:Vízhozam it:Portata nl:Debiet pl:Przepływ rzeki pt:Caudal