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Encyclopedia > Rate of fluid flow

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. This article or section should be merged with Fluid mechanics Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. ... This article is in need of attention. ...

Given an area A, and a fluid flowing through it with uniform velocity v with an angle θ (away from the perpendicular), then the flux is This article explains the meaning of area as a physical quantity. ... This article is about velocity in physics. ... A perpendicular line. ...

In the special case where the flow is perpendicular to the area A (where θ = 0 and cosθ = 1) then the flux is

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: In mathematics, a surface integral is a definite integral taken over some surface that may be a curved set in space; it can be thought of as the double integral analog of the path 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 field v on that volume: In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky-Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ... In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in Euclidean space. ... Results from FactBites:

 U.S. Patent: 5024105 - Viscosity-insensitive variable-area flowmeter - June 18, 1991 (6938 words) The distance moved is proportional to the flow rate of liquid 4 and the annular area between the float 2 and the wall of tapered tube 3. The first flow obstructor is connected to the pressure sensor for (i) moving with the sensor to variable occlude the channel between the upstream and downstream locations, and (ii) receiving frictional force from the flowing fluid in the direction of the first flow obstructor's movement. The magnitude of fluid flow--which determines the displacement of the differential pressure sensor and the fluid flow obstructor attached thereto--may be indicated visually, or by a mechanical connection, or by, as is preferable, an electrical circuit.
 Low flow rate transducer construction - Patent 4173144 (2414 words) In such a construction, the fluid flow around the paddle wheel is essentially circumferential in that the fluid maintains a reactive contact with the paddle wheel for a substantial portion of the rotation of the wheel. The rate of rotation of the paddle wheel is optically sensed by means of a liquid source such as a light emitting diode mounted on one end wall of a cylindrical fluid chamber which cooperates with a photosensitive device such as a photo transistor mounted in the other end wall of the fluid chamber. Fluid enters the fluid chamber 24 through an inlet conduit 30 which terminates at the fluid chamber 24 in an inlet port 32 and fluid leaves the chamber through an outlet port 34 which communicates with an outlet conduit 36 arranged tangentially with respect to the cylindrical well of the fluid chamber 24.
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