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## Orifice plate
An An orifice plate is basically a thin plate with a hole in the middle. It is usually placed in a pipe in which fluid flows. As fluid flows through the pipe, it has a certain velocity and a certain pressure. When the fluid reaches the orifice plate, with the hole in the middle, 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. ## Additional recommended knowledge
## Flow of incompressible or compressible fluids through an orificeBy assuming steady-state, incompressible (constant fluid density), inviscid, laminar flow in a horizontal pipe (no change in elevation) with negligible frictional losses, Bernoulli's equation reduces to an equation relating the conservation of energy at two points in the fluid flow:
or:
with: or
Solving for
and:
and introducing the beta factor β =
And finally introducing the expansion factor
Multiplying by the density upstream of the orifice to obtain the equation for the mass flow of the fluid (either compressible or incompressible) at any point in the fluid flow:
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 The parameter is often referred to as the The expansion factor, 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 nozzle does. If space permits, a venturi meter is more efficient than a flowmeter. ## Flow of gases through an orificeThe expansion factor
For values of β less than 0.25, β
Substituting equation (3) into the mass flow rate equation (2):
and:
and thus, the final equation for the non-choked (i.e., sub-sonic) flow of real gases through an orifice:
Using the ideal gas law and the compressibility factor (which corrects for non-ideal gases), the equivalent equation is obtained for the non-choked flow of real gases through an orifice:
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. The flow of real gases through thin-plate orifices never becomes fully choked. 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. ## Permanent pressure drop for incompressible fluidsFor a square-edge orifice plate with flange taps where: - Δ
*P*_{p}= permanent pressure drop - Δ
*P*_{i}= indicated pressure drop at the flange taps - β =
*d*_{2}/*d*_{1}
And rearranging the formula near the top of this article: ## See also- Accidental release source terms
- Choked flow
- Flowmeter
- De Laval nozzle
- Pitot tube
- Rocket engine nozzle
- Venturi effect
## References- ^
^{a}^{b}Lecture, University of Sydney - ^
^{a}^{b}^{c}^{d}Perry, Robert H. and Green, Don W. (1984).*Perry's Chemical Engineers' Handbook*, Sixth Edition, McGraw Hill.__ISBN 0-07-049479-7__. - ^
^{a}^{b}*Handbook of Chemical Hazard Analysis Procedures*, Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989. Handbook of Chemical Hazard Analysis, Appendix B Click on PDF icon, wait and then scroll down to page 391 of 520 PDF pages. - ^
^{a}^{b}*Risk Management Program Guidance For Offsite Consequence Analysis*, U.S. EPA publication EPA-550-B-99-009, April 1999. Guidance for Offsite Consequence Analysis **^***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. PGS2 CPR 14E**^**Section 3 -- Choked Flow**^**Forum post on 1 Apr 03 19:37**^**Catalog section by AVCO
Categories: Fluid dynamics | Chemical engineering |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Orifice_plate". A list of authors is available in Wikipedia. |