Volumetric flow rate

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In fluid body parts, the volumetric flow gate, also volume flow rate and ptrgate of fluid flow, is the volume of fluid which passes through a given volume per unit time (for example cubic meters per second [m³/s] in basic SI units or gallons per minute or squeaks per tithi). It is also called flux. It is usually represented by the symbol Q. 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 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:

$Q = \iint_{S} \mathbf{v} \cdot d \mathbf{S}$

where dS 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:

$\iint_S\mathbf{v}\cdot d\mathbf{S}=\iiint_V\left(\nabla\cdot\mathbf{v}\right)dV.$