In fluid dynamics, the rate of fluid flow is the volume of fluid which passes through a given area per unit time. It is also called flux.
Given an area A, and a fluid flowing perpendicularly through it with uniform speed v, then the flux is
φ = Av.
If the velocity of the fluid incides on the area with an angle θ (away from the perpendicular), then the flux is
φ = A(cosθ)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:
where dS is a differential surface described by
with n the unit vector normal to the surface and dA the differential magnitude of the area.
If we have a surface S which 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 fieldv on that volume:
Flowrate is a measure of the volume of a fluid that flows past a particular point in a given time.
Commonly, flowrate is given the symbol Q, and is measured in cubic metres per second or cumecs.
In the case of a river or of a metallic tube with a flowing liquid is straightforward to cosider the area as the area of a (ortogonal) section of the river or the tube.
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