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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 heta.

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_{S} \mathbf{v} \cdot d \mathbf{S}

where ''d''S is a differential surface described by:
: d\mathbf{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_S\mathbf{v}\cdot d\mathbf{S}=\iiint_V\left(
abla\cdot\mathbf{v} ight)dV.


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