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{{Image|Venturi Tube.png|right|400px|Drawing of a classical Venturi tube per ASME Standard MFC-3M-1989.<ref name=ASME>ASME Standard MFC-3M-1989, ''Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi''', [[American Society of Mechanical Engineers]] (ASME), New York, 1989.</ref>}}


A '''Venturi tube''' (or simply a '''venturi''') is a section of [[Piping (engineering)|piping]] consisting of an inlet converging conical section leading to a small diameter cylindrical section called the ''throat'', followed by a diverging conical section leading to a cylindrical exit (see the adjacent drawing).
The [[Volume (science)|volumetric]] flow rate, '''''Q''''' (e.g., m<sup>3</sup>/s), of a fluid flowing through the venturi at any given point is the product of the cross-sectional area, '''''A''''' (e.g., m<sup>2</sup>) at that point multiplied by the fluid's linear [[velocity]], '''''v''''' (e.g., m/s), at that point. Since the volumetric flow rate is the same at any point within the venturi, the linear velocity of the fluid traveling through the smaller diameter throat of the venturi must increase which results in a decrease of [[pressure]] due to the [[conservation of energy]], one of the [[conservation laws]].
The gain in [[kinetic energy]] resulting from the increased linear velocity in the throat is offset (i.e., balanced) by the decrease of pressure in the throat. The reduction in pressure which occurs when the fluid flows through the throat is called the '''''Venturi effect''''' and is named after the Italian physicist [[Giovanni Battista Venturi]] (1746 - 1822) who first observed the effect.
Thus, referring to the adjacent drawing, the pressure '''''p<sub>2</sub>''''' and the cross-sectional area '''''A<sub>2</sub>''''' in the throat are smaller than the pressure '''''p<sub>1</sub>''''' and the cross-sectional area '''''A<sub>1</sub>''''' in the cylindrical inlet section. The linear velocity '''''v<sub>2</sub>''''' in the throat is higher than the linear velocity '''''v<sub>1</sub>''''' in the inlet section.
A venturi tube may also consist of non-cylindrical ducting rather than piping.
==Measuring fluid flow rate with a venturi==
===Incompressible fluid===
Venturi tubes are used to accurately measure the volumetric flow of an ideal fluid, meaning that the fluid satisfies these conditions:<ref>{{cite book|author=Raymond A. Serway, Chris Vuille and Jerry S. Faughn|title=College Physics|edition=8th Edition|publisher=Brooks Cole|year=2008|id=ISBN 0-495-38693-6}}</ref><ref name=FluidFlowParams>[http://www.docstoc.com/docs/18169711/Measurement-of-fluid-flow-parameters Fluid Flow Parameters]</ref>
*The fluid is nonviscous: There is no internal [[Sliding friction|friction]] between layers of the fluid.
*The fluid is incompressible: The [[Density (chemistry)|density]] of the fluid is constant (as is the case with liquids)
*The fluid flows without any [[turbulence]]: No element of the fluid has any angular velocity about its center, so there are no [[eddy current]]s present.
*The fluid flow is steady: The velocity, density and pressure at each point in the fluid does not change with time.
To obtain the volumetric flow rate of an incompressible fluid through a venturi, we start with this common form of the [[Bernoulli equation (fluid dynamics)|Bernoulli equation]] for fluid flow:
:&nbsp;<math>p_1 + \tfrac {1}{2}\, \rho_1\, v^2_1 + \rho_1\, g\, h_1 = p_2 + \tfrac {1}{2}\, \rho_2\, v^2_2 + \rho_2\, g\, h_2</math>
where '''''ρv<sup> 2</sup>/2''''' denotes [[kinetic energy]], '''''ρgh''''' denotes gravitational [[potential energy]] and:
:{|border="0" cellpadding="2"
|-
|align=right|<math>p</math>
|align=left|= the fluid's static pressure
|-
|align=right|<math>\rho</math>
|align=left|= the fluid's density
|-
|align=right|<math>v</math>
|align=left|= the fluid's linear velocity
|-
|align=right|<math>g</math>
|align=left|= the [[gravitational acceleration]]
|-
|align=right|<math>h</math>
|align=left|= the height of a given point (in the fluid flow) above any reference plane designated as having zero height
|}
For an incompressible fluid with a constant density and a venturi with a horizontal centerline, the equation simplifies to:
:&nbsp;<math>p_1 + \tfrac {1}{2}\, \rho\, v^2_1 = p_2 + \tfrac {1}{2}\, \rho\, v^2_2</math>
or to:
:&nbsp;<math>p_1 - p_2 = \tfrac {1}{2}\, \rho\, (v_2^2 - v_1^2)</math>
Since the volumetric flow rate '''''Q''''' is the same at all points in the venturi by the [[continuity equation]]:<ref>A continuity equation in physics is an equation describing the transport of some kind of conserved quantity. Continuity equations are the (stronger) local form of the [[conservation laws]]. A conserved quantity cannot increase or decrease, it can only move from place to place.</ref>
:&nbsp;<math>Q = A_1\, v_1 =A_2\, v_2</math>
then:
:&nbsp;<math>p_1 - p_2 = \tfrac {1}{2}\, \rho \left(\frac {Q^2}{A^2_2} - \frac {Q^2}{A^2_1}\right)</math>
which can be re-arranged to:
:&nbsp;<math>Q = A_2 \sqrt {\frac {2\, (p_1 - p_2)}{\rho \left (1 - \left [\frac {A_2}{A_1} \right ]^2 \right)}}</math>
The actual flow rate through a venturi tube is seldom equal to the theoretical flow rate  of an ideal fluid and
usually turns out to be less than the theoretical flow rate. In order to account for this
difference, a discharge coefficient C is introduced to obtain the final volumetric flow rate equation for an incompressible fluid flowing through a venturi tube with a horizontal centerline:
:&nbsp;<math>Q = C A_2 \sqrt {\frac {2\, (p_1 - p_2)}{\rho \left (1 - \left [\frac {A_2}{A_1} \right ]^2 \right)}}</math>
where:
:{|border="0" cellpadding="2"
|-
|align=right|<math>Q</math>
|align=left|= the volumetric flow rate of the fluid
|-
|align=right|<math>C</math>
|align=left|= the discharge coefficient = (actual flow rate)&thinsp;/&thinsp;(theoretical flow rate)
|-
|align=right|<math>A</math>
|align=left|= the cross-sectional area of the venturi in the indicated section of the venturi
|-
|align=right|<math>p</math>
|align=left|= the fluid's static pressure in the indicated section of the venturi
|-
|align=right|<math>\rho</math>
|align=left|= the fluid's density
|}
One method for determining the discharge coefficient is to calibrate the venturi tube on a test stand which is expensive and time consuming. A considerable number of test calibrations have been performed on various venturi tube geometries. As a result, the ASME Standard MFC-3M-1989<ref name=ASME/> provides these discharge coefficients for their specified venturi tube geometry (per the diagram at the top of this article) and for three types of fabrication:<ref name=ORO>[http://www.eng-software.com/products/methodology/ori_flo.pdf ORO-FLOW Users Guide]</ref><ref name=Flowel>[http://www.emersonprocess.com/metco/flowel/Download/Flowel3g%20Print.pdf Flowel 3.0 for Windows] Flow Element Sizing and Documentation</ref>
*For venturi tubes with a welded convergent cone: '''''C''''' = 0.984 (valid for fluid flow [[Reynolds number]]s between 2 × 10<sup>5</sup> and 6 × 10<sup>6</sup>
*For venturi tubes with an as-cast convergent cone: '''''C''''' = 0.984 (valid for fluid flow [[Reynolds number]]s between 2 × 10<sup>5</sup> and 6 × 10<sup>6</sup>
*For venturi tubes with a machined convergent cone: '''''C''''' = 0.995 (valid for fluid flow [[Reynolds number]]s between 2 × 10<sup>5</sup> and 2 × 10<sup>6</sup>
===Compressible fluid===
For compressible fluids (i.e., a [[gas]]es), the density is not constant. It will vary from the density '''''ρ<sub>1</sub>''''' at the venturi inlet to the density '''''ρ<sub>2</sub>''''' at the venturi throat. The equation for the mass flow rate of a compressible fluid through a venturi may be expressed as:<ref name=Perry>{{cite book|author=Don W. Green and Robert H. Perry|title=Perry's Chemical Engineers' Handbook|edition=6th Edition|publisher=McGraw-Hill|year=19845-13| id=ISBN 0-07-049479-7}} See equations 5-14 and 5-15 on pages 5-12 and 5-13.</ref><ref name=Finnemore>{{cite book|author=E. John Finnemore and Joseph P. Franzini|title=Fluid Mechanics with Engineering Applications|edition=10th Edition|publisher=McGraw-Hill|year=2003|id=ISBN 7-302-06344-3}} See pages 525-526</ref>
:&nbsp;<math>\dot {m} = Y C A_2\, \sqrt \frac {2\, \rho_1\, (p_1 - p_2)}{1 - \beta^4}= Y C A_2\, \sqrt \frac {2\, \rho_1\, (p_1 - p_2)}{1 - \left ( \frac {d}{D} \right )^4 }</math>
The expansion factor '''''Y''''' allows for the change in gas density as the gas expands adiabatically from the venturi inlet pressure to the reduced pressure at the venturi throat.  It may be calculated by using this equation:<ref name=Perry/><ref name=Finnemore/>
:&nbsp;<math>Y = \sqrt {\, r^{2/k} \left(\frac{k}{k-1}\right) \left(\frac {1 - r^{(k-1)/k)}} {1-r} \right ) \left (\frac{1 - \beta^4}{1 - \beta^4 r^{2/k}} \right)}</math>
where: 
:{|border="0" cellpadding="2"
|-
|align=right|<math>\dot m</math>
|align=left|= mass flow rate
|-
|align=right|<math>Y</math>
|align=left|= gas expansion factor
|-
|align=right|<math>C</math>
|align=left|= the discharge coefficient
|-
|align=right|<math>A_2</math>
|align=left|= cross-sectional area of the venturi's throat section
|-
|align=right|<math>\rho_1</math>
|align=left|= the gas density in the venturi's inlet section
|-
|align=right|<math>p_1</math>
|align=left|= the gas static pressure in the venturi's inlet section
|-
|align=right|<math>p_2</math>
|align=left|= the gas static pressure in the venturi's throat section
|-
|align=right|<math>\beta</math>
|align=left|= '''''d&thinsp;/&thinsp;D''''', the ratio of the venturi's throat diameter '''''d''''' to the venturi's inlet diameter '''''D'''''
|-
|align=right|<math>r</math>
|align=left|= '''''p<sub>2</sub>'''''&thinsp;/&thinsp;'''''p<sub>1</sub>'''''
|-
|align=right|<math>k</math>
|align=left|= the [[specific heat ratio]] of the gas
|}
==Other uses for a venturi==
Venturi tubes are used to create a low pressure or a partial vacuum in a great many applications (other than measuring flow rates) including the examples below as well as many others:
* [[Injector]]s or [[ejector]]s using [[steam]], [[water]], [[air]] or other motive fluid (liquid or gas) in a venturi to create a low pressure zone that draws in and entrains a suction fluid (liquid or gas).
* [[Water aspirators]] using water as a motive fluid to produce a partial [[vacuum]].
* [[Atomizer]]s  using air as a motive fluid to spray paint, perfume or other liquids.
* [[Eductor]]s using high-pressure water to create a partial vacuum to draw in and mix firefighting foam concentrate with the water.
* [[Carburetor]]s using a [[gasoline]] [[combustion engine]]'s intake air stream  as the motive fluid to entrain and mix gasoline into intake air.
* Compressed air as the motive fluid to create the vacuum for industrial [[vacuum cleaner]]s.
* [[Venturi scrubber]]s used in [[flue gas desulfurization]] systems.
* [[Sand blaster]]s using compressed air to draw in fine sand in and mix it with air.
* A [[diving regulator|scuba diving regulator]] to assist the flow of breathing air once it starts flowing.
* In [[Venturi mask]]s used in medical [[oxygen therapy]].
* The [[De Laval]] nozzles used in [[rocket engine]]s are essentially venturi tubes.
==References==
{{reflist}}

Revision as of 12:24, 20 March 2010

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