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| [[Image:Orifice.png|thumb|300px|right|Flat-plate, sharp-edge orifice]]
| | == zoals muffins en pannenkoeken Ray Ban Winkels Den Haag == |
| [[Image:Blende eng.png|thumb|176px|right|ISO 5167 Orifice Plate]]
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| An '''orifice plate''' is a device used for measuring flow rate, for reducing pressure or for restricting flow (in the latter two cases it is often called a '''restriction plate'''). Either a volumetric or mass flow rate may be determined, depending on the calculation associated with the orifice plate. It uses the same principle as a [[Venturi effect|Venturi]] nozzle, namely [[Bernoulli's principle]] which states that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa.
| | '. Ik wakker in een klein stadje genaamd Columbia elke ochtend om 4:30 in mijn kingsize bed, en flip op CNN als ik klaar. Dit omvat het nemen van een douche, klaarmaken een pot . Reden waarom Internet uitwisselingen gebeuren is dat er een behoefte, zei ze. Moet een noodzaak om een mandaat om verbinding te verbinden zijn. Dat een zeer belangrijk onderscheid. <br><br>Ik maak de meeste van de afgebeelde gebakken producten (zoals muffins en pannenkoeken) van tevoren en bewaar ze in onze vriezer. Dus als ik het inpakken schoolmaaltijden de avond voordat ik trek gewoon wat ik nodig heb, zodat het kan 's nachts ontdooien in de koelkast. Bijna alle van de recepten die ik gebruikte is te vinden op de blog gebruik het zoekvak in de rechterbovenhoek van de pagina om te vinden wat u zoekt!.. <br><br>Restaurants kan niet opladen je veel voor deze bescheiden tarief. Om Krik de prijs [http://www.eurocallis.com/import_data2013/frame.php?rayban=191-Ray-Ban-Winkels-Den-Haag Ray Ban Winkels Den Haag] zal veel [http://www.vibesconsultancy.nl/nl/database/list.asp?b=115-New-Balance-574 New Balance 574] bedrijven gaan ervan uit dat u wenst een volledige plaat maaltijd. Niet alleen krijg je een stijve factuur, maar u zult verspillen veel. Net in van mijn wandeling. Was zo warm en er maar wist in die gebruikelijke 4,5 mijl te krijgen. Mijn knie begon mij dwars ongeveer een mijl afstand van het huis, niet zeker wat is er met dat! Moest [http://www.vibesconsultancy.nl/nl/database/list.asp?b=149-New-Balance-Amsterdam New Balance Amsterdam] het grootste deel van de weg naar huis lopen vanaf daar. <br><br>Deze aanpak geeft geen informatie op de startpagina, zoals weerberichten of nieuwsberichten, maar als ik het type "Boston weer", kan ik een weerbericht te krijgen binnen een of twee klikken. CNN probeert zoveel mogelijk informatie te verstrekken over hun voorpagina, dat is waarschijnlijk [http://www.sebuma.nl/Images/js/client.asp?a=7 Abercrombie And Fitch] een goed idee voor een nieuwsorganisatie. E! Online houdt van Flash-animaties, maar in de tijd die het kost hun 300kb pagina te laden, ik ben in slaap gevallen.. <br><br>Application des lois sur les droits de proprit intellectuelle. Pour votre communicatie, nous sommes votre oplossing! Contactez nous pour recevoir un devis gratuit! Hulp la Production. Cration de site internet. JASON ACIDRE is wereldwijd bekend om zijn online marketing blog op Kaiserthesage en is ook columnist voor Technorati's Business Channel, waar hij covers en deelt zijn meningen over tech startups, evenals in online marketing. Hij is de mede oprichter en CEO van Xight Interactive, een van de toonaangevende online marketing bureaus in Azië als het gaat om innovatieve strategieën, gevestigd in de Filippijnen. Hij begon zijn carrière in digitale marketing in het begin van 2010, en heeft nu gewerkt met een aantal van de grootste merken op het web als een marketing consultant en strateeg ...<ul> |
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| ==Description==
| | <li>[http://www.isanya.net/forum.php?mod=viewthread&tid=124174&fromuid=11564 http://www.isanya.net/forum.php?mod=viewthread&tid=124174&fromuid=11564]</li> |
| An orifice plate is a thin plate with a hole in the middle. It is usually placed in a pipe in which fluid flows. When the fluid reaches the orifice plate, the fluid is forced to converge to go through the small hole; the point of maximum convergence actually occurs shortly downstream of the physical orifice, at the so-called vena contracta point (see drawing to the right). As it does so, the velocity and the pressure changes. Beyond the vena contracta, the fluid expands and the velocity and pressure change once again. By measuring the difference in fluid pressure between the normal pipe section and at the vena contracta, the volumetric and mass flow rates can be obtained from Bernoulli's equation.
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| | | <li>[http://sns.daredu.com/home.php?mod=space&uid=6795 http://sns.daredu.com/home.php?mod=space&uid=6795]</li> |
| ==Uses==
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| Orifice plates are most commonly used to measure flow rates in pipes, when the fluid is single-phase (rather than being a mixture of gases and liquids, or of liquids and solids) and well-mixed, the flow is continuous rather than pulsating, the fluid occupies the entire pipe (precluding silt or trapped gas), the flow profile is even and well-developed and the fluid and flow rate meet certain other conditions. Under these circumstances and when the orifice plate is constructed and installed according to appropriate standards, the flow rate can easily be determined using published formulae based on substantial research and published in industry, national and international standards. <ref>{{cite book|last=Miller|first=Richard W|title=Flow Measurement Engineering Handbook|year=1996|publisher=McGraw-Hill|location=New York|isbn=0-07-042366-0}}</ref>
| | <li>[http://usa.publishkaro.com/index.php?page=item&id=132572 http://usa.publishkaro.com/index.php?page=item&id=132572]</li> |
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| Once the orifice plate is designed and installed, the flow rate can often be indicated with an acceptably low uncertainty simply by taking the square root of the differential pressure across the orifice's pressure tappings and applying an appropriate constant. Even compressible flows of gases that vary in pressure and temperature may be measured with acceptable uncertainty by merely taking the square roots of the absolute pressure and/or temperature, depending on the purpose of the measurement and the costs of ancillary instrumentation.
| | <li>[http://cgmoxin.com/home.php?mod=space&uid=514 http://cgmoxin.com/home.php?mod=space&uid=514]</li> |
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| Orifice plates are also used to reduce pressure or restrict flow, in which case they are often called restriction plates.<ref>{{cite web|title=Orifice Plates for Flow Measurement & Flow Restriction|url=http://www.wermac.org/specials/orificeplate.html|accessdate=1 February 2014}}</ref> <ref>{{cite book|title=Flow of Fluids Through Valves, Fittings and Pipe|publisher=Crane|location=Ipswich|page=2-14|year=1988}}</ref>
| | </ul> |
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| ==Incompressible flow through an orifice==
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| By assuming steady-state, [[Incompressible flow|incompressible]] (constant fluid density), [[Inviscid flow|inviscid]], [[Laminar flow|laminar]] flow in a horizontal pipe (no change in elevation) with negligible frictional losses, [[Bernoulli's principle|Bernoulli's equation]] reduces to an equation relating the conservation of energy between two points on the same streamline:
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| <math>P_1 + \frac{1}{2}\cdot\rho\cdot V_1^2 = P_2 + \frac{1}{2}\cdot\rho\cdot V_2^2 </math>
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| or:
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| <math>P_1 - P_2 = \frac{1}{2}\cdot\rho\cdot V_2^2 - \frac{1}{2}\cdot\rho\cdot V_1^2 </math>
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| By continuity equation:
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| <math>Q = A_1\cdot V_1 = A_2\cdot V_2</math> or <math>V_1 = Q/A_1</math> and <math>V_2 = Q/A_2</math> :
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| <math>P_1 - P_2 = \frac{1}{2}\cdot\rho\cdot \bigg(\frac{Q}{A_2}\bigg)^2 - \frac{1}{2}\cdot\rho\cdot\bigg(\frac{Q}{A_1}\bigg)^2 </math>
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| Solving for <math>Q_{}</math>:
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| <math>Q = A_2\;\sqrt{\frac{2\;(P_1-P_2)/\rho}{1-(A_2/A_1)^2}}</math>
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| and:
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| <math>Q = A_2\;\sqrt{\frac{1}{1-(d_2/d_1)^4}}\;\sqrt{2\;(P_1-P_2)/\rho}</math>
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| The above expression for <math>Q</math> gives the theoretical volume flow rate. Introducing the beta factor <math>\beta = d_2/d_1</math> as well as the coefficient of discharge <math>C_d</math>:
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| <math>Q = C_d\; A_2\;\sqrt{\frac{1}{1-\beta^4}}\;\sqrt{2\;(P_1-P_2)/\rho}</math>
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| And finally introducing the meter coefficient <math>C</math> which is defined as <math>C = \frac{C_d}{\sqrt{1-\beta^4}}</math> to obtain the final equation for the volumetric flow of the fluid through the orifice:
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| <math>(1)\qquad Q = C\;A_2\;\sqrt{2\;(P_1-P_2)/\rho}</math>
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| Multiplying by the density of the fluid to obtain the equation for the mass flow rate at any section in the pipe:<ref name=Sydney>[http://www.aeromech.usyd.edu.au/aero/cvanalysis/node3.shtml#node43 Lecture, University of Sydney]</ref><ref name=Perry>{{cite book|author=Perry, Robert H. and Green, Don W.|title=[[Perry's Chemical Engineers' Handbook]]|edition=Sixth Edition|publisher=McGraw Hill|year=1984|isbn=0-07-049479-7}}</ref><ref name=Hazards>''Handbook of Chemical Hazard Analysis Procedures'', Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989. [http://nepis.epa.gov/Exe/ZyNET.exe/10003MK5.TXT?ZyActionD=ZyDocument&Client=EPA&Index=1986+Thru+1990&Docs=&Query=&Time=&EndTime=&SearchMethod=1&TocRestrict=n&Toc=&TocEntry=&QField=pubnumber%5E%22OSWERHCHAP%22&QFieldYear=&QFieldMonth=&QFieldDay=&UseQField=pubnumber&IntQFieldOp=1&ExtQFieldOp=1&XmlQuery=&File=D%3A%5Czyfiles%5CIndex%20Data%5C86thru90%5CTXT%5C00000003%5C10003MK5.TXT&User=ANONYMOUS&Password=anonymous&SortMethod=h%7C-&MaximumDocuments=10&FuzzyDegree=0&ImageQuality=r75g8/r75g8/x150y150g16/i425&Display=p%7Cf&DefSeekPage=x&SearchBack=ZyActionL&Back=ZyActionS&BackDesc=Results%20page&MaximumPages=1&ZyEntry=1&SeekPage=x Handbook of Chemical Hazard Analysis, Appendix B] Click on PDF icon, wait and then scroll down to page 391 of 520 PDF pages.</ref><ref name=Risk>''Risk Management Program Guidance For Offsite Consequence Analysis'', U.S. EPA publication EPA-550-B-99-009, April 1999. [http://yosemite.epa.gov/oswer/ceppoweb.nsf/vwResourcesByFilename/oca-all.pdf/$file/oca-all.pdf?OpenElement Guidance for Offsite Consequence Analysis]</ref>
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| <math>(2)\qquad \dot{m} = \rho\;Q = C\;A_2\;\sqrt{2\;\rho\;(P_1-P_2)}</math>
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| {| border="0" cellpadding="2"
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| |-
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| |align=right|where:
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| |-
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| !align=right|''<math>Q_{}</math>''
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| |align=left|= [[volumetric flow rate]] (at any cross-section), m³/s
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| |-
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| !align=right|''<math>\dot{m}</math>''
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| |align=left|= [[mass flow rate]] (at any cross-section), kg/s
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| |-
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| !align=right|''<math>C_d</math>'' | |
| |align=left|= [[coefficient of discharge]], dimensionless
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| |-
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| !align=right|''<math>C</math>''
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| |align=left|= orifice [[flow coefficient]], dimensionless
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| |-
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| !align=right|''<math>A_1</math>''
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| |align=left|= cross-sectional area of the pipe, m²
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| |-
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| !align=right|''<math>A_2</math>''
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| |align=left|= cross-sectional area of the orifice hole, m²
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| |-
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| !align=right|''<math>d_1</math>''
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| |align=left|= [[diameter]] of the pipe, m
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| |-
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| !align=right|''<math>d_2</math>''
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| |align=left|= diameter of the orifice hole, m
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| |-
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| !align=right|''<math>\beta</math>'' | |
| |align=left|= ratio of orifice hole diameter to pipe diameter, dimensionless
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| |-
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| !align=right|''<math>V_1</math>''
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| |align=left|= upstream fluid [[velocity]], m/s
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| |-
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| !align=right|''<math>V_2</math>''
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| |align=left|= fluid velocity through the orifice hole, m/s
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| |-
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| !align=right|''<math>P_1</math>''
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| |align=left|= fluid upstream [[pressure]], Pa with dimensions of kg/(m·s² )
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| |-
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| !align=right|''<math>P_2</math>''
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| |align=left|= fluid downstream pressure, Pa with dimensions of kg/(m·s² )
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| |-
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| !align=right|''<math>\rho</math>'' | |
| |align=left|= fluid [[density]], kg/m³
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| |}
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| Deriving the above equations used the cross-section of the orifice opening and is not as realistic as using the minimum cross-section at the vena contracta. In addition, frictional losses may not be negligible and viscosity and turbulence effects may be present. For that reason, the coefficient of discharge <math>C_d</math> is introduced. Methods exist for determining the coefficient of discharge as a function of the [[Reynolds number]].<ref name=Perry/>
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| The parameter <math>\sqrt{1-\beta^4}</math> is often referred to as the ''velocity of approach factor''<ref name=Sydney/> and dividing the coefficient of discharge by that parameter (as was done above) produces the flow coefficient <math>C</math>. Methods also exist for determining the flow coefficient as a function of the beta function <math>\beta</math> and the location of the downstream pressure sensing tap. For rough approximations, the flow coefficient may be assumed to be between 0.60 and 0.75. For a first approximation, a flow coefficient of 0.62 can be used as this approximates to fully developed flow.
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| An orifice only works well when supplied with a fully developed flow profile. This is achieved by a long upstream length (20 to 40 pipe diameters, depending on Reynolds number) or the use of a flow conditioner. Orifice plates are small and inexpensive but do not recover the pressure drop as well as a [[venturi effect|venturi]] nozzle does. If space permits, a venturi meter is more efficient than an orifice plate.
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| ==Flow of gases through an orifice==
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| In general, equation (2) is applicable only for incompressible flows. It can be modified by introducing the expansion factor <math>Y</math> to account for the compressibility of gases.
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| <math>(3)\qquad \dot{m} = \rho_1\;Q = C\;Y\;A_2\;\sqrt{2\;\rho_1\;(P_1-P_2)}</math>
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| <math>Y</math> is 1.0 for incompressible fluids and it can be calculated for compressible gases.<ref name=Perry/>
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| ===Calculation of expansion factor===
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| For flow measurement purposes, the expansion factor <math>Y</math>, which allows for the change in the density of an ideal gas as it expands [[isentropic process|isentropically]], is given by the empirical formula:<ref name=Perry/>
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| <math>(4)\qquad Y =\;1-\bigg(\frac{1-r}{k}\bigg)\bigg(0.41+0.35\beta^4\bigg)</math>
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| {| border="0" cellpadding="2"
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| |-
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| |align=right|where:
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| |-
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| !align=right|''<math>Y</math>''
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| |align=left|= Expansion factor, dimensionless
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| |-
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| !align=right|''<math>r</math>
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| |align=left|= <math>P_2/P_1</math>
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| |-
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| !align=right|''<math>k</math>
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| |align=left|= [[specific heat]] ratio (<math>c_p/c_v</math>), dimensionless
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| |}
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| and the pressures are measured at orifice plate tappings (such as flange, corner or D+D/2), β is in the range 0.2 to 0.75 and certain other conditions are met.
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| For smaller values of β (such as restriction plates and discharge from tanks but not generally in flow measurement), Y may be calculated from first principles and the effect of β neglected, giving:
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| <math>\dot{m} = C\;A_2\;\sqrt{2\;\rho_1\;\bigg (\frac{k}{k-1}\bigg)\bigg[\frac{(P_2/P_1)^{2/k}-(P_2/P_1)^{(k+1)/k}}{1-P_2/P_1}\bigg](P_1-P_2)}</math> | |
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| and:
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| <math>\dot{m} = C\;A_2\;\sqrt{2\;\rho_1\;\bigg (\frac{k}{k-1}\bigg)\bigg[\frac{(P_2/P_1)^{2/k}-(P_2/P_1)^{(k+1)/k}}{(P_1-P_2)/P_1}\bigg](P_1-P_2)}</math>
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| and thus, the final equation for approximating the non-choked (i.e., sub-sonic) flow of ideal gases through an orifice for values of β less than 0.25:
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| <math>(5)\qquad \dot{m} = C\;A_2\;\sqrt{2\;\rho_1\;P_1\;\bigg (\frac{k}{k-1}\bigg)\bigg[(P_2/P_1)^{2/k}-(P_2/P_1)^{(k+1)/k}\bigg]}</math>
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| Using the [[ideal gas law]] and the [[compressibility factor]] (which corrects for non-ideal gases), a practical equation is obtained for the non-choked flow of [[real gas]]es through an orifice for values of β less than 0.25:<ref name=Hazards/><ref name=Risk/><ref name=Netherlands>''Methods For The Calculation Of Physical Effects Due To Releases Of Hazardous Substances (Liquids and Gases)'', PGS2 CPR 14E, Chapter 2, The Netherlands Organization Of Applied Scientific Research, The Hague, 2005. [http://vrom.nl/pagina.html?id=20725 PGS2 CPR 14E]</ref>
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| <math>(6)\qquad \dot{m} = C\;A_2\;P_1\;\sqrt{\frac{2\;M}{Z\;R\;T_1}\bigg(\frac{k}{k-1}\bigg)\bigg[(P_2/P_1)^{2/k}-(P_2/P_1)^{(k+1)/k}\bigg]}</math>
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| Remembering that <math> Q_1= \frac{\dot{m}}{\rho_1} </math> and <math> \rho_1 = M\;\frac{P_1}{Z\;R\;T_1}</math> (ideal gas law and the compressibility factor)
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| <math>(8)\qquad Q_1 = C\;A_2\;\sqrt{2\;\frac{Z\;R\;T_1}{M}\bigg(\frac{k}{k-1}\bigg)\bigg[(P_2/P_1)^{2/k}-(P_2/P_1)^{(k+1)/k}\bigg]}</math>
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| {| border="0" cellpadding="2"
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| |-
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| |align=right|where:
| |
| |
| |
| |-
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| !align=right|''<math>k</math>
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| |align=left|= [[specific heat]] ratio (<math>c_p/c_v</math>), dimensionless
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| |-
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| !align=right|''<math>\dot{m}</math>''
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| |align=left|= [[mass flow rate]] at any section, kg/s
| |
| |-
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| !align=right|''<math> Q_1 </math>''
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| |align=left|= upstream real gas flow rate, m³/s
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| |-
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| !align=right|''<math>C</math>''
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| |align=left|= orifice flow coefficient, dimensionless
| |
| |-
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| !align=right|''<math>A_2</math>''
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| |align=left|= cross-sectional area of the orifice hole, m²
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| |-
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| !align=right|''<math>\rho_1</math>''
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| |align=left|= upstream real gas [[density]], kg/m³
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| |-
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| !align=right|''<math>P_1</math>''
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| |align=left|= upstream gas [[pressure]], Pa with dimensions of kg/(m·s²)
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| |-
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| !align=right|''<math>P_2</math>''
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| |align=left|= downstream pressure, Pa with dimensions of kg/(m·s²)
| |
| |-
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| !align=right|''<math>M</math>''
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| |align=left|= the gas [[molar mass]], kg/mol
| |
| |-
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| !align=right|''<math>R</math>''
| |
| |align=left|= the [[Gas constant|Universal Gas Law Constant]] = 8.3145 J/(mol·K)
| |
| |-
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| !align=right|''<math>T_1</math>''
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| |align=left|= absolute upstream gas temperature, K
| |
| |-
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| !align=right|''<math>Z</math>''
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| |align=left|= the gas compressibility factor at <math>P_1</math> and <math>T_1</math>, dimensionless
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| |}
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| A detailed explanation of choked and non-choked flow of gases, as well as the equation for the choked flow of gases through restriction orifices, is available at [[Choked flow]].
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| The flow of real gases through thin-plate orifices never becomes fully choked. Cunningham (1951) first drew attention to the fact that choked flow will not occur across a standard, thin, square-edged orifice.<ref name=thin_plate_2>Cunningham, R.G., "Orifice Meters with Supercritical Compressible Flow", Trans. ASME, Vol. 73, pp. 625-638, 1951</ref>
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| The mass flow rate through the orifice continues to increase as the downstream pressure is lowered to a perfect vacuum, though the mass flow rate increases slowly as the downstream pressure is reduced below the critical pressure.<ref name=thin_plate_1>[http://www.engsoft.co.kr/download_e/steam_flow_e.htm Section 3 -- Choked Flow]</ref>
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| ==Permanent pressure drop for incompressible fluids==
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| For a square-edge orifice plate with flange taps:<ref name=avcovalve>[http://www.avcovalve.com/products/pdfs/Orifice%20Plates.pdf Catalog section by AVCO]</ref>
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| :<math>\frac{\Delta P_p}{\Delta P_i} =
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| 1 - 0.24 \beta - 0.52 \beta ^2 - 0.16 \beta ^3
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| </math>
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| where:
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| :<math>\Delta P_p</math> = permanent pressure drop
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| :<math>\Delta P_i</math> = indicated pressure drop at the flange taps
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| :<math>\beta = d_2 / d_1</math>
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| And rearranging the formula near the top of this article:
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| :<math>
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| \Delta P_i = P_1 - P_2 = \frac
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| {Q^2 ~\rho~ (1 - \beta ^4)}
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| {2 ~C_d^2~ A_2^2}
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| = \frac
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| {Q^2 ~\rho~ (1 - \beta ^4)}
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| {2 ~C_d^2 ~A_1^2 ~\beta ^4}
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| </math> | |
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| ==See also==
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| *[[Accidental release source terms]]
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| *[[Choked flow]]
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| *[[De Laval nozzle]]
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| *[[Flowmeter]]
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| *[[Pitot tube]]
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| *[[Restrictive flow orifice]]
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| *[[Rocket engine nozzle]]
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| *[[Venturi effect]]
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| ==References==
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| {{Reflist|2}}
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| ==External links==
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| * [http://tierling.home.texas.net/ Tierling Orifice flow calculators]
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| * [http://www.lenoxlaser.com/index.php?dispatch=pages.view&page_id=43 Lenox Laser Orifice Calculator]
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| [[Category:Fluid dynamics]]
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| [[Category:Chemical engineering]]
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| [[Category:Mechanical engineering]]
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| [[Category:Control devices]]
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| [[Category:Piping]]
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