Editing Venturi effect

{{Short description|Reduced pressure caused by a flow restriction in a tube or pipe}}
{{Lead too short|date=February 2024}}
[[File:Venturi5.svg|thumb|300x300px|The upstream [[static pressure]] (1) is higher than in the constriction (2), and the [[fluid]] [[speed]] at "1" is lower than at "2", because the cross-sectional area at "1" is greater than at "2".]]
[[File:VenturiFlow.png|right|thumb|A flow of air through a [[pitot tube]] Venturi meter, showing the columns connected in a [[manometer]] and partially filled with water. The meter is "read" as a differential pressure head in cm or inches of water.]]
[[File:Venturi Tube en.webm|thumb|Video of a Venturi meter used in a lab experiment]]
[[File:Venturi.gif|thumb|Idealized flow in a Venturi tube]]

The '''Venturi effect''' is the reduction in [[fluid 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 Italian [[physicist]] [[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 a [[vacuum ejector]]).

==Background==
In [[inviscid flow|inviscid]] [[fluid dynamics]], an incompressible fluid's [[velocity]] must ''increase'' as it passes through a constriction in accord with the [[Continuity equation#Fluid dynamics|principle of mass continuity]], while its [[static pressure]] must ''decrease'' in accord with the principle of [[Mechanical energy#Conservation of mechanical energy|conservation of mechanical energy]] ([[Bernoulli's principle]]) or according to the [[Euler equations (fluid dynamics)|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 plate]]s.

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

<math display="block">p_1 - p_2 = \frac{\rho}{2} (v_2^2 - v_1^2),</math>

where <math>\rho</math> is the [[density]] of the fluid, <math>v_1</math> is the (slower) fluid velocity where the pipe is wider, and <math>v_2</math> 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 will also increase the local sonic velocity, thus allowing increased mass flow rate, but only if the nozzle area is also increased to compensate for the resulting decrease in density.

===Expansion of the section===

The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is a shortened expansion in the tube section, turbulence is more likely to appear, and the theorem will not hold. 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==
[[File:Green Hope High School (Physics Laboratory Venturi Tube) 2006.jpg|thumb|right|Venturi tube demonstration apparatus built out of PVC pipe and operated with a vacuum pump]]
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===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 undue [[aerodynamic drag]], a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees.<ref>{{cite book|last1=Nasr|first1=G. G.|last2=Connor|first2=N. E.|title=Natural Gas Engineering and Safety Challenges: Downstream Process, Analysis, Utilization and Safety|date=2014|publisher=Springer|isbn=9783319089485|page=183|chapter-url=https://books.google.com/books?id=C-01BAAAQBAJ&pg=PA183|language=en|chapter=5.3 Gas Flow Measurement}}</ref>

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|date=April 2016}}

===Orifice plate===
Venturi tubes are more expensive to construct than simple [[orifice plate]]s, and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss.<ref name="wolfram">{{cite web |url= http://demonstrations.wolfram.com/TheVenturiEffect/|title= The Venturi effect |publisher=Wolfram Demonstrations Project |access-date=2009-11-03 }}</ref>

==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]], <math>\scriptstyle Q</math>, using [[Bernoulli's principle]].

Since
<math display="block">\begin{align}
          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{align}</math>

then
<math display="block">
  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}}
</math>
<!-- The equation for flow needs a term for time which is not accounted for as it is written. -->
<!-- The explanation of how to mix fluids needs help; specifically the system used. -->
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. See [[Aspirator (pump)|aspirator]] and [[pressure head]] for discussion of this type of [[siphon]].

===Differential pressure===
{{main|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 in [[metrology]] 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 by [[Clemens Herschel]] who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century.<ref>Herschel, Clemens. (1898). ''Measuring Water.'' Providence, RI:Builders Iron Foundry.</ref> While working for the [[Holyoke Water Power Company]], Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on the [[Holyoke Canal System]], first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter to [[William Unwin]] in a letter dated June 5, 1888.<ref>{{cite journal|page=254|volume=136|issue=3433|date=August 17, 1935|journal=Nature|doi=10.1038/136254a0|title=Invention of the Venturi Meter|bibcode=1935Natur.136Q.254.|doi-access=free}}</ref>

=== Compensation for temperature, pressure, and mass ===

Fundamentally, pressure-based meters measure [[kinetic energy]] density. [[Bernoulli's equation]] (used above) relates this to [[mass density]] and volumetric flow:

<math>\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</math>

where constant terms are absorbed into ''k''. Using the definitions of density (<math>m=\rho V</math>), [[molar concentration]] (<math>n=C V</math>), and [[molar mass]] (<math>m=M n</math>), one can also derive mass flow or molar flow (i.e. standard volume flow):

<math>\begin{align}\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{align}</math>

However, measurements outside the design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. The [[ideal gas law]] is used to relate actual values to [[Standard state|design values]]:

<math>C = \frac{P}{RT} = \frac{\left(\frac{P}{P^\ominus}\right)}{\left(\frac{T}{T^\ominus}\right)} C^\ominus</math>
<math>\rho = \frac{MP}{RT} = \frac{\left(\frac{M}{M^\ominus} \frac{P}{P^\ominus}\right)}{\left(\frac{T}{T^\ominus}\right)} \rho^\ominus.</math>

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

<math>\begin{align}\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{align}</math>

''Q'', ''m'', or ''n'' are easily isolated by dividing and taking the [[square 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:

<math>\begin{align}\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{align}</math>

==Examples==
{{excessive examples|section|date=February 2024}}

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

===Machines===
* During [[Underway replenishment]] the [[helmsman]] of each ship must constantly steer away from the other ship due to the Venturi effect, otherwise they will collide.
* Cargo [[Eductor-jet pump|eductors]] on oil product and chemical ship tankers
* [[Inspirator]]s mix air and flammable gas in [[Grill (cooking)|grills]], [[gas stove]]s and [[Bunsen burner]]s
* [[Water aspirators]] produce a partial vacuum using the kinetic energy from the faucet water pressure
* [[Steam injector#Vacuum ejectors|Steam siphons]] use the kinetic energy from the steam pressure to create a partial vacuum
* [[Atomizer nozzle|Atomizers]] disperse perfume or spray paint (i.e. from a spray gun or [[airbrush]])
* [[Carburetor]]s often use the effect to force [[gasoline]] 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 from [[Bernoulli's principle]].
* [[Cylinder head]]s 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 aerator]]s infuse air into wine as it is poured into a glass
* [[Protein skimmer]]s filter saltwater [[aquarium|aquaria]]
* [[Automated pool cleaner]]s use pressure-side water flow to collect sediment and debris
* [[Clarinet]]s use a reverse taper to speed the air down the tube, enabling better tone, response and intonation<ref>{{Cite web|url=https://www.face2fire.com/venturi-or-air-circulation-thats-the-question/|title=Venturi or air circulation?, that's the question.|last=Blasco|first=Daniel Cortés|website=face2fire|language=es|access-date=2019-07-14}}</ref>
* The [[leadpipe]] of a [[trombone]], affecting the [[timbre]]
* Industrial [[vacuum cleaner]]s use compressed air
* [[Venturi scrubber]]s are used to clean [[flue gas]] emissions
* Injectors (also called ejectors) are used to add chlorine gas to [[water treatment]] [[Water chlorination|chlorination]] systems
* [[Injector|Steam injectors]] use the Venturi effect and the [[latent heat]] of evaporation to deliver feed water to a [[steam 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.
* A [[diving regulator|scuba diving regulator]] uses the Venturi effect to assist maintaining the flow of gas once it starts flowing
* In [[recoilless rifle]]s to decrease the recoil of firing
* The [[Diffuser (automotive)|diffuser]] on an automobile
* Race cars utilising [[Ground effect (cars)|ground effect]] to increase [[downforce]] and thus become capable of higher cornering speeds
* Foam proportioners used to induct [[fire 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-speed [[wind tunnel]]s 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.<ref>{{cite book |last1=Anderson |first1=John |title=Fundamentals of Aerodynamics |date=2017 |publisher=McGraw-Hill Education |location=New York, NY |isbn=978-1-259-12991-9 |page=218 |edition=6th}}</ref>

===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 original [[World Trade Center (1973–2001)|World Trade Center]] was an extreme example of the phenomenon, which made the ground level plaza notoriously windswept.<ref>{{Cite news|title=At New Trade Center, Seeking Lively (but Secure) Streets |work=The New York Times |url = https://www.nytimes.com/2006/12/07/nyregion/07blocks.html?fta=y |date=December 7, 2006 |author=Dunlap, David W}}</ref> In fact, some gusts were so high that pedestrian travel had to be aided by ropes.<ref>{{Cite news|title=Girding Against Return of the Windy City in Manhattan |work=The New York Times |url = https://www.nytimes.com/2004/03/25/nyregion/25blocks.html |date=March 25, 2004 |author=Dunlap, David W}}</ref>
* In the south of Iraq, near the modern town of [[Nasiriyah]], a 4000-year-old flume structure has been discovered at the ancient site of [[Girsu]]. This construction by the ancient [[Sumerians]] 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 the [[British Museum]] confirmed the finding.

===Nature===
* In windy mountain passes, resulting in erroneous [[pressure altimeter]] readings<ref>{{cite video | year = 1971 | title = Dusk to Dawn | medium = educational film | publisher = Federal Aviation Administration | url = https://archive.org/details/gov.ntis.ava20333vnb1 | minutes = 17| id = AVA20333VNB1}}</ref>
*The [[mistral wind]] in southern France increases in speed through the [[Rhone valley]].

==See also==
* [[Joule–Thomson effect]]
* [[Venturi flume]]
* [[Parshall flume]]

==References==
{{reflist}}

==External links==
{{commons category}}
*[https://www.youtube.com/watch?v=oUd4WxjoHKY 3D animation of the Differential Pressure Flow Measuring Principle (Venturi meter)]
*{{cite web |url= http://www.ce.utexas.edu/prof/KINNAS/319LAB/Applets/Venturi/venturi.html|title= Venturi Tube Simulation|author= UT Austin |access-date=2009-11-03 }}
*[https://www.youtube.com/watch?v=fT2KhJ8W-Kg Use of the Venturi effect for gas pumps to know when to turn off (video)]

[[Category:Fluid dynamics]]