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Venturi effect

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Reduced pressure caused by a flow restriction in a tube or pipe

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The upstreamstatic pressure (1) is higher than in the constriction (2), and thefluid speed at "1" is lower than at "2", because the cross-sectional area at "1" is greater than at "2".

A flow of air through a Venturi meter, showing the columns connected in amanometer and partially filled with water. The meter is "read" as a differential pressure head in cm or inches of water.

Video of a Venturi meter used in a lab experiment

Idealized flow in a Venturi tube

TheVenturi effect is the reduction influid pressure that results when a moving fluid speeds up as it flows from one section of a pipe to a smaller section. The Venturi effect is named after its discoverer, the Italianphysicist Giovanni Battista Venturi, and was first published in 1797.

The effect has various engineering applications, as the reduction in pressure inside the constriction can be used both for measuring the fluid flow and for moving other fluids (e.g. in avacuum ejector).

Background

Ininviscid fluid dynamics, an incompressible fluid'svelocity mustincrease as it passes through a constriction in accord with theprinciple of mass continuity, while itsstatic pressure mustdecrease in accord with the principle ofconservation of mechanical energy (Bernoulli's principle) or according to theEuler equations. Thus, any gain inkinetic energy a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss inpotential 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 variousflow measurement devices such as Venturi meters, Venturi nozzles andorifice 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 theoreticalstatic pressure drop at the constriction is given by

$p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),$

where $\rho$ is thedensity of the fluid, $v_{1}$ is the (slower) fluid velocity where the pipe is wider, and $v_{2}$ 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 ofchoked flow, where thefluid velocity approaches the localspeed 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.

Themass 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 ade 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 never compared with them.

Experimental apparatus

Venturi tube demonstration apparatus built out of PVC pipe and operated with a vacuum pump

A pair of Venturi tubes on a light aircraft, used to provide airflow for air-driven gyroscopic instruments

Venturi tubes

The simplest apparatus is a tubular setup known as a Venturi tube or simply a Venturi (plural: "Venturis" or occasionally "Venturies"). Fluid flows through a length of pipe of varying diameter. To avoid undueaerodynamic drag, a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees.^[1]

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.^{[citation needed]}

Orifice plate

Venturi tubes are more expensive to construct than simpleorifice plates, and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss.^[2]

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 thevolumetric flow rate, $\scriptstyle Q$ , usingBernoulli's principle.

Since ${\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}$

then $Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}$ A Venturi can also be used to mix a liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a Venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a Venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. Seeaspirator andpressure head for discussion of this type ofsiphon.

Differential pressure

Main article:Pressure head

As fluid flows through a Venturi, the expansion and compression of the fluids cause the pressure inside the Venturi to change. This principle can be used inmetrology for gauges calibrated for differential pressures. This type of pressure measurement may be more convenient, for example, to measure fuel or combustion pressures in jet or rocket engines.

The first large-scale Venturi meters to measure liquid flows were developed byClemens Herschel who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century.^[3] While working for theHolyoke Water Power Company, Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on theHolyoke Canal System, first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter toWilliam Unwin in a letter dated June 5, 1888.^[4]

Compensation for temperature, pressure, and mass

Fundamentally, pressure-based meters measurekinetic energy density.Bernoulli's equation (used above) relates this tomass density and volumetric flow:

$\Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}$

where constant terms are absorbed intok. Using the definitions of density ( $m=\rho V$ ),molar concentration ( $n=CV$ ), andmolar mass ( $m=Mn$ ), one can also derive mass flow or molar flow (i.e. standard volume flow):

${\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}$

However, measurements outside the design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. Theideal gas law is used to relate actual values todesign values:

$C={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }$ $\rho ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.$

Substituting these two relations into the pressure-flow equations above yields the fully compensated flows:

${\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}$

Q,m, orn are easily isolated by dividing and taking thesquare root. Note that pressure-, temperature-, and mass-compensation is required for every flow, regardless of the end units or dimensions. Also we see the relations:

${\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}$

Examples

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The Venturi effect may be observed or used in the following:

Machines

DuringUnderway replenishment thehelmsman of each ship must constantly steer away from the other ship due to the Venturi effect, otherwise they will collide.
Cargoeductors on oil product and chemical ship tankers
Inspirators mix air and flammable gas ingrills,gas stoves andBunsen burners
Water aspirators produce a partial vacuum using the kinetic energy from the faucet water pressure
Steam siphons use the kinetic energy from the steam pressure to create a partial vacuum
Atomizers disperse perfume or spray paint (i.e. from a spray gun orairbrush)
Carburetors can use the effect to forcegasoline into an engine's intake air stream at the throat by the difference between the pressure there and at the upstream start of the converging wall (which is fed to the float bowl). In other carburetors ambient air pressure can be fed to the float bowl, in which case the effect comes fromBernoulli's principle.
Cylinder heads in piston engines have multiple Venturi areas like the valve seat and the port entrance, although these are not part of the design intent, merely a byproduct and any venturi effect is without specific function.
Wine aerators infuse air into wine as it is poured into a glass
Protein skimmers filter saltwateraquaria
Automated pool cleaners use pressure-side water flow to collect sediment and debris
Clarinets use a reverse taper to speed the air down the tube, enabling better tone, response and intonation^[5]
Theleadpipe of atrombone, affecting thetimbre
Industrialvacuum cleaners use compressed air
Venturi scrubbers are used to cleanflue gas emissions
Injectors (also called ejectors) are used to add chlorine gas towater treatment chlorination systems
Steam injectors use the Venturi effect and thelatent heat of evaporation to deliver feed water to asteam locomotive boiler.
Sandblasting nozzles accelerate and air and media mixture
Bilge water can be emptied from a moving boat through a small waste gate in the hull. The air pressure inside the moving boat is greater than the water sliding by beneath.
Ascuba diving regulator uses the Venturi effect to assist maintaining the flow of gas once it starts flowing
Inrecoilless rifles to decrease the recoil of firing
Thediffuser on an automobile
Race cars utilisingground effect to increasedownforce and thus become capable of higher cornering speeds
Foam proportioners used to inductfire fighting foam concentrate into fire protection systems
Trompe air compressors entrain air into a falling column of water
The bolts in some brands of paintball markers
Low-speedwind tunnels can be considered very large Venturi because they take advantage of the Venturi effect to increase velocity and decrease pressure to simulate expected flight conditions.^[6]

Architecture

Hawa Mahal of Jaipur, also utilizes the Venturi effect, by allowing cool air to pass through, thus making the whole area more pleasant during the high temperatures in summer.
Large cities where wind is forced between buildings - the gap between the Twin Towers of the originalWorld Trade Center was an extreme example of the phenomenon, which made the ground level plaza notoriously windswept.^[7] In fact, some gusts were so high that pedestrian travel had to be aided by ropes.^[8]
In the south of Iraq, near the modern town ofNasiriyah, a 4000-year-old flume structure has been discovered at the ancient site ofGirsu. This construction by the ancientSumerians forced the contents of a nineteen kilometre canal through a constriction to enable the side-channeling of water off to agricultural lands from a higher origin than would have been the case without the flume. A recent dig by archaeologists from theBritish Museum confirmed the finding.

Nature

In windy mountain passes, resulting in erroneouspressure altimeter readings^[9]
Themistral wind in southern France increases in speed through theRhone valley.

See also

References

^Nasr, G. G.; Connor, N. E. (2014)."5.3 Gas Flow Measurement".Natural Gas Engineering and Safety Challenges: Downstream Process, Analysis, Utilization and Safety. Springer. p. 183.ISBN 9783319089485.
^"The Venturi effect". Wolfram Demonstrations Project. Retrieved2009-11-03.
^Herschel, Clemens. (1898).Measuring Water. Providence, RI:Builders Iron Foundry.
^"Invention of the Venturi Meter".Nature.136 (3433): 254. August 17, 1935.Bibcode:1935Natur.136Q.254..doi:10.1038/136254a0.
^Blasco, Daniel Cortés."Venturi or air circulation?, that's the question".face2fire (in Spanish). Retrieved2019-07-14.^{[permanent dead link]}
^Anderson, John (2017).Fundamentals of Aerodynamics (6th ed.). New York, NY: McGraw-Hill Education. p. 218.ISBN 978-1-259-12991-9.
^Dunlap, David W (December 7, 2006)."At New Trade Center, Seeking Lively (but Secure) Streets".The New York Times.
^Dunlap, David W (March 25, 2004)."Girding Against Return of the Windy City in Manhattan".The New York Times.
^Dusk to Dawn (educational film). Federal Aviation Administration. 1971. 17 minutes in. AVA20333VNB1.

External links

Wikimedia Commons has media related toVenturi effect.

3D animation of the Differential Pressure Flow Measuring Principle (Venturi meter)
UT Austin."Venturi Tube Simulation". Retrieved2009-11-03.
Use of the Venturi effect for gas pumps to know when to turn off (video)

Retrieved from "https://en.wikipedia.org/w/index.php?title=Venturi_effect&oldid=1315530001"

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