The Venturi effect is the reduction in fluid pressure that results when a moving fluid speeds up as it is funneled from one section of a pipe to another, smaller section. As the fluid flows into a smaller area, the fluid's velocity increases, while the static pressure decreases. The Venturi effect is an example of Bernoulli's principle. The Venturi effect is named after its discoverer, the Italian Physicist Giovanni Battista Venturi, and was first published in 1797. The effect has various applications in engineering, architecture, and everyday objects such as atomizer nozzles and wine aerators. The reduction in pressure inside the constriction can be used both for measuring the fluid flow and for moving other fluids (e.g. in a vacuum ejector).
Background In inviscid fluid dynamics, an incompressible fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must decrease in accord with the principle of conservation of mechanical energy (Bernoulli's principle) or according to the Euler equations. Thus, any gain in kinetic energy a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss in potential energy. By measuring the pressure difference without needing to measure the actual pressures at the two points, the flow rate can be determined, as in various flow measurement devices such as Venturi meters, Venturi nozzles and orifice plates. Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low-speed flow of gas) along a streamline, the theoretical static pressure drop at the constriction is given by
p 1 − p 2 = ρ 2 ( v 2 2 − v 1 2 ) , {\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),}
where ρ {\displaystyle \rho } is the density of the fluid, v 1 {\displaystyle v_{1}} is the (slower) fluid velocity where the pipe is wider, and v 2 {\displaystyle v_{2}} is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). The static pressure at each position is measured using a small tube either outside and ending at the wall or into the pipe with the small tube end face parallel with the flow direction.
Choked flow The limiting case of the Venturi effect is when a fluid reaches the state of choked flow, where the fluid velocity approaches the local speed of sound of the fluid. When a fluid system is in a state of choked flow, a further decrease in the downstream pressure environment will not lead to an increase in velocity, unless the fluid is compressed. The mass flow rate for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a de Laval nozzle. Increasing source temperature can also increase the local sonic velocity, thus allowing increased mass flow rate.
Expansion of the section The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is a shortening expansion in the tube section, turbulence is more likely to appear, and the variation from the theorem will increase. Generally in Venturi tubes, the pressure in the entrance is compared to the pressure in the middle section and the output section is not compared with them.
Experimental apparatus
Venturi tubes The simplest apparatus is a tubular setup known as a Venturi tube or simply a Venturi (plural: "Venturis" or occasionally "Venturies"). Fluid first flows through a length of converging tube and then often flows into a diverging tube. To avoid undue aerodynamic drag, a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees. Venturi tubes are often used in processes where permanent pressure loss is not tolerable and where maximum accuracy is needed in case of highly viscous liquids.
Orifice plate Venturi tubes are more expensive to construct than simple orifice plates, and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss.
Instrumentation and measurement Both Venturi tubes and orifice plates are used in industrial applications and in scientific laboratories for measuring the flow rate of liquids.
Flow rate A Venturi can be used to measure the volumetric flow rate, Q {\displaystyle \scriptstyle Q} , using Bernoulli's principle. Since
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