6492:
761:
must be acceptably circular, smooth and straight for stipulated distances. Sometimes when it is impossible to provide enough straight pipe, flow conditioners such as tube bundles or plates with multiple holes are inserted into the pipe to straighten and develop the flow profile, but even these require a further length of straight pipe before the orifice itself. Some standards and handbooks also provide for flows from or into large spaces rather than pipes, stipulating that the region before or after the plate is free of obstruction and abnormalities in the flow.
609:
possibilities. The edges may be rounded or conical, the plate may have an orifice the same size as the pipe except for a segment at top or bottom which is obstructed, the orifice may be installed eccentric to the pipe, and the pressure tappings may be at other positions. Variations on these possibilities are covered in various standards and handbooks. Each combination gives rise to different coefficients of discharge which can be predicted so long as various conditions are met, conditions which differ from one type to another.
4716:
4324:
598:
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.
53:(see drawing to the right) where the velocity reaches its maximum and the pressure reaches its minimum. Beyond that, the flow expands, the velocity falls and the pressure increases. By measuring the difference in fluid pressure across tappings upstream and downstream of the plate, the flow rate can be obtained from Bernoulli's equation using coefficients established from extensive research.
1516:
4711:{\displaystyle C=0.5961+0.0261\beta ^{2}-0.216\beta ^{8}+0.000521{\bigg (}{\frac {10^{6}\beta }{Re_{D}}}{\bigg )}^{0.7}+(0.0188+0.0063A)\beta ^{3.5}{\bigg (}{\frac {10^{6}}{Re_{D}}}{\bigg )}^{0.3}+(0.043+0.080\exp(-10{L_{1}})-0.123\exp(-7{L_{1}}))(1-0.11A){\frac {\beta ^{4}}{1-\beta ^{4}}}-0.031(M'_{2}-0.8{M'_{2}}^{1.1})\beta ^{1.3}}
3113:
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
689:
The simplest installations use single tappings upstream and downstream, but in some circumstances these may be unreliable; they might be blocked by solids or gas-bubbles, or the flow profile might be uneven so that the pressures at the tappings are higher or lower than the average in those planes. In
6296:
first drew attention to the fact that choked flow will not occur across a standard, thin, square-edged orifice.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
6152:
4110:
of the orifice plate, which depends upon the orifice type and the positions of the pressure tappings. With local pressure tappings (corner, flange and D+D/2), sharp-edged orifices have coefficients around 0.6 to 0.63, while the coefficients for conical entrance plates are in the range 0.73 to 0.734
48:
An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid (whether liquid or gaseous) passes through the orifice, its pressure builds up slightly upstream of the orifice but as the fluid is forced to converge to pass through the hole, the velocity increases
4126:
The equations provided in
American and European national and industry standards and the various coefficients used to differ from each other even to the extent of using different combinations of correction factors, but many are now closely aligned and give identical results; in particular, they use
2988:
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
760:
Standards and handbooks stipulate a well-developed flow profile; velocities will be lower at the pipe wall than in the centre but not eccentric or jetting. Similarly the flow downstream of the plate must be unobstructed, otherwise the downstream pressure will be affected. To achieve this, the pipe
597:
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
4105:
Flow rates through an orifice plate can be calculated without specifically calibrating the individual flowmeter so long as the construction and installation of the device complies with the stipulations of the relevant standard or handbook. The calculation takes account of the fluid and fluid
3875:
608:
Plates are commonly made with sharp-edged circular orifices and installed concentric with the pipe and with pressure tappings at one of three standard pairs of distances upstream and downstream of the plate; these types are covered by ISO 5167 and other major standards. There are many other
3733:
203:
1066:
926:
751:
of the pipe). Standards and handbooks stipulate that the upstream surface of the plate is particularly flat and smooth. Sometimes a small drain or vent hole is drilled through the plate where it meets the pipe, to allow condensate or gas bubbles to pass along the pipe.
4308:
612:
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.
3536:
3109:
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.
1329:
4122:
is also calculated. This factor is primarily a function of the ratio of the measured differential pressure to the fluid pressure and so can vary significantly as the flow rate varies, especially at high differential pressures and low static pressures.
3303:
For smaller values of β (such as restriction plates with β less than 0.25 and discharge from tanks), if the fluid is compressible, the rate of flow depends on whether the flow has become choked. If it is, then the flow may be calculated as shown at
1842:
2071:
690:
these situations multiple tappings can be used, arranged circumferentially around the pipe and joined by a piezometer ring, or (in the case of corner taps) annular slots running completely round the internal circumference of the orifice carrier.
6309:
ISO 5167-2 uses the terms (2.8-D/25.4) and (25.4/D) - which both convert D into inches - because in that one clause of the standard, 5.3.2.1, D is in millimetres. This article presents D in metres throughout, so the terms are (2.8-D/0.0254) and
3273:
1701:
5905:
The overall pressure loss caused by an orifice plate is less than the differential pressure measured across tappings near the plate. For sharp-edged plates such as corner, flange or D and D/2 tappings, it can be approximated by the equation
4111:
and for quarter-circle plates 0.77 to 0.85. The coefficients of sharp-edged orifices vary more with fluids and flow rates than the coefficients of conical-entrance and quarter-circle plates, especially at low flows and high viscosities.
704:
plates. In these, the leading edge is sharp and free of burrs and the cylindrical section of the orifice is short, either because the entire plate is thin or because the downstream edge of the plate is bevelled. Exceptions include the
3118:, nozzle, or venturi-nozzle does. Venturis also require much less straight pipe upstream. A venturi meter is more efficient, but usually more expensive and less accurate (unless calibrated in a laboratory) than an orifice plate.
2367:
5984:
1176:
3742:
4788:
5972:
5333:
2250:
4863:
790:(which expresses the conservation of energy of an incompressible fluid parcel as it moves between two points on the same streamline) can be rewritten without the gravitational potential energy term and reduced to:
3603:
4930:
94:
2148:
5050:
4206:
3308:(although the flow of real gases through thin-plate orifices never becomes fully choked By using a mechanical energy balance, compressible fluid flow in un-choked conditions may be calculated as:
1322:
1249:
3063:
4194:
3594:
547:
3313:
1511:{\displaystyle p_{1}-p_{2}={\frac {1}{2}}\cdot \rho \cdot {\bigg (}{\frac {q_{v}^{'}}{A_{2}}}{\bigg )}^{2}-{\frac {1}{2}}\cdot \rho \cdot {\bigg (}{\frac {q_{v}^{'}}{A_{1}}}{\bigg )}^{2}}
935:
795:
6372:
ISO 5167-1:2003 Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full - Part 1: General principles and requirements
5683:
6514:
682:
placed one pipe diameter upstream and at a position 0.3 to 0.9 diameters downstream, depending on the orifice type and size relative to the pipe, in the plane of minimum fluid pressure.
6199:
5191:
4992:
6269:
3983:
5124:
2459:
5738:
2871:
2823:
2546:
1951:
1880:
1554:
587:
38:
5365:
3957:
4131:
equation for the coefficient of discharge for sharp-edged orifice plates. The equations below largely follow the notation of the international standard ISO 5167 and use
3151:
1914:
1710:
674:
placed 2.5 pipe diameters upstream and 8 diameters downstream, at which point the measured differential is equal to the unrecoverable pressure loss caused by the orifice
5885:
5794:
4077:
3294:
3144:
414:
347:
5766:
686:
The measured differential pressure differs for each combination and so the coefficient of discharge used in flow calculations depends partly on the tapping positions.
449:
5822:
5087:
3908:
2409:
6599:
ISO 5167-2:2003 Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full - Part 2: Orifice plates
5708:
5633:
3126:
In general, equation (2) is applicable only for incompressible flows. It can be modified by introducing the expansibility factor, (also called the expansion factor)
3107:
2779:
279:
5595:
5560:
5525:
5490:
4042:
4015:
3014:
2973:
2945:
2906:
2691:
2656:
2585:
2498:
1944:
1561:
489:
244:
85:
5850:
5455:
5427:
5399:
4318:
Coefficient of discharge for sharp-edged orifice plates with corner, flange or D and D/2 tappings and no drain or vent hole (Reader-Harris/Gallagher equation):
3087:
2751:
2719:
2617:
2093:
379:
322:
302:
6147:{\displaystyle {\frac {\Delta {\bar {\omega }}}{\Delta p}}={\frac {{\sqrt {1-\beta ^{4}(1-C^{2})}}-C\beta ^{2}}{{\sqrt {1-\beta ^{4}(1-C^{2})}}+C\beta ^{2}}}}
2259:
3870:{\displaystyle q_{v}=C\;A_{2}\;{\sqrt {\gamma \;{\frac {p_{1}}{\rho _{1}}}\;{\bigg (}{\frac {2}{\gamma +1}}{\bigg )}^{\frac {\gamma +1}{\gamma -1}}}}}
4725:
5912:
5198:
2155:
6511:
4797:
633:
placed immediately upstream and downstream of the plate; convenient when the plate is provided with an orifice carrier incorporating tappings
3728:{\displaystyle q_{m}=C\;A_{2}\;{\sqrt {\gamma \;\rho _{1}\;p_{1}\;{\bigg (}{\frac {2}{\gamma +1}}{\bigg )}^{\frac {\gamma +1}{\gamma -1}}}}}
6451:
3296:
is 1.0 for incompressible fluids and it can be calculated for compressible gases using empirically determined formulae as shown below in
1075:
647:
placed one pipe diameter upstream and half a pipe diameter downstream of the plate; these can be installed by welding bosses to the pipe
6668:
729:
plate which has a bevelled leading edge and a very short cylindrical section. The orifices are normally concentric with the pipe (the
23:
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
198:{\displaystyle q_{m}={\frac {C_{d}}{\sqrt {1-\beta ^{4}}}}\;\epsilon \;{\frac {\pi }{4}}\;d^{2}\;{\sqrt {2\;\rho _{1}\Delta p\;}}}
6491:, Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989.
4303:{\displaystyle q_{m}={\frac {C}{\sqrt {1-\beta ^{4}}}}\;\epsilon \;{\frac {\pi }{4}}\;d^{2}\;{\sqrt {2\;\rho _{1}\Delta p\;}}}
2150:
to obtain the final equation for the volumetric flow of the fluid through the orifice which accounts for irreversible losses:
6678:
6657:
5140:
Expansibility factor, also called expansion factor, for sharp-edged orifice plates with corner, flange or D and D/2 tappings:
2098:
49:
and the fluid pressure decreases. A little downstream of the orifice the flow reaches its point of maximum convergence, the
616:
Orifice plates are also used to reduce pressure or restrict flow, in which case they are often called restriction plates.
4869:
3026:
4999:
4145:
3545:
498:
6559:
3531:{\displaystyle q_{m}=C\;A_{2}\;{\sqrt {2\;\rho _{1}\;p_{1}\;{\bigg (}{\frac {\gamma }{\gamma -1}}{\bigg )}{\bigg }}}}
1061:{\displaystyle p_{1}-p_{2}={\frac {1}{2}}\cdot \rho \cdot V_{2}^{'^{2}}-{\frac {1}{2}}\cdot \rho \cdot V_{1}^{'^{2}}}
921:{\displaystyle p_{1}+{\frac {1}{2}}\cdot \rho \cdot V_{1}^{'^{2}}=p_{2}+{\frac {1}{2}}\cdot \rho \cdot V_{2}^{'^{2}}}
356:, 1 for incompressible gases and most liquids, and decreasing with pressure ratio across the orifice, dimensionless
2254:
Multiplying by the density of the fluid to obtain the equation for the mass flow rate at any section in the pipe:
6722:
6224:
5641:
4106:
conditions, the pipe size, the orifice size and the measured differential pressure; it also takes account of the
3069:
and multiplying the coefficient of discharge by that parameter (as was done above) produces the flow coefficient
1254:
1181:
556:
in the pipe due to an orifice plate is lower than the measured differential pressure, typically by a factor of
6717:
6172:
4132:
655:
placed 25.4 mm (1 inch) upstream and downstream of the plate, normally within specialised pipe flanges.
6696:
6553:
Methods For The
Calculation Of Physical Effects Due To Releases Of Hazardous Substances (Liquids and Gases)
6555:, PGS2 CPR 14E, Chapter 2, The Netherlands Organization Of Applied Scientific Research, The Hague, 2005.
6384:
Experimental Fluid
Mechanics, Reader-Harris, ISBN 978-3-319-16879-1, 2015 edition, page 63, equation 2.13
5148:
3962:
624:
There are three standard positions for pressure tappings (also called taps), commonly named as follows:
2066:{\displaystyle q_{v}=C_{d}\;A_{2}\;{\sqrt {\frac {1}{1-\beta ^{4}}}}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
6448:
5716:
4948:
559:
6727:
6249:
3268:{\displaystyle q_{m}=\rho _{1}\;q_{v,1}=C\;\epsilon \;A_{2}\;{\sqrt {2\;\rho _{1}\;(p_{1}-p_{2})}}}
2591:
1837:{\displaystyle q_{v}^{'}=A_{2}\;{\sqrt {\frac {1}{1-(d/D)^{4}}}}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
787:
605:
if it has been calibrated with an appropriate fluid flow and a traceable flow measurement device.
6712:
5344:
5093:
3920:
2426:
1885:
5863:
5779:
4055:
3279:
3129:
3016:
is introduced. Methods exist for determining the coefficient of discharge as a function of the
2840:
2792:
2515:
1849:
1523:
392:
332:
5748:
1696:{\displaystyle q_{v}^{'}=A_{2}\;{\sqrt {\frac {2\;(p_{1}-p_{2})/\rho }{1-(A_{2}/A_{1})^{2}}}}}
431:
5807:
5059:
4107:
3893:
3089:. Methods also exist for determining the flow coefficient as a function of the beta function
2385:
1917:
5693:
5608:
3092:
2764:
264:
6254:
5573:
5538:
5503:
5468:
4020:
3993:
2992:
2958:
2923:
2884:
2669:
2634:
2563:
2476:
2465:
2415:
1922:
467:
461:
222:
63:
5835:
8:
6259:
3914:
775:
2362:{\displaystyle (2)\qquad q_{m}=\rho \;q_{v}=C\;A_{2}\;{\sqrt {2\;\rho \;(p_{1}-p_{2})}}}
6541:
5440:
5412:
5384:
3072:
2736:
2704:
2602:
2078:
364:
307:
287:
253:, dimensionless, typically between 0.6 and 0.85, depending on the orifice geometry and
786:
flow in a horizontal pipe (no change in elevation) with negligible frictional losses,
6674:
6653:
717:
orifice, which has a fully rounded leading edge and no cylindrical section, and the
6411:
2623:
748:
659:
These types are covered by ISO 5167 and other major standards. Other types include
735:
orifice is a specific exception) and circular (except in the specific case of the
6732:
6563:
6518:
6455:
6234:
3017:
6626:
Cunningham, R.G. (1951). "Orifice Meters with
Supercritical Compressible Flow".
5827:= isentropic exponent, often approximated by specific heat ratio, dimensionless
6264:
3115:
2552:
2504:
57:
6706:
779:
4783:{\displaystyle +0.011(0.75-\beta ){\bigg (}2.8-{\frac {D}{0.0254}}{\bigg )}}
783:
6495:
Click on PDF icon, wait and then scroll down to page 394 of 520 PDF pages.
5967:{\displaystyle {\frac {\Delta {\bar {\omega }}}{\Delta p}}=1-\beta ^{1.9}}
5328:{\displaystyle \epsilon =1-(0.351+0.256\beta ^{4}+0.93\beta ^{8}){\bigg }}
2245:{\displaystyle (1)\qquad q_{v}=C\;A_{2}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
6229:
3305:
6244:
4858:{\displaystyle A={\bigg (}{\frac {19000\beta }{Re_{D}}}{\bigg )}^{0.8}}
6556:
6601:. International Organization for Standardization (ISO). 1 March 2003.
6374:. International Organization for Standardization (ISO). 1 March 2003.
6239:
2950:= fluid downstream pressure, Pa with dimensions of kg/(m·s² )
6621:(6th ed.). The American Society of Mechanical Engineers (ASME).
5799:= expansibility factor, also called expansion factor, dimensionless
5530:= fluid absolute static pressure in plane of downstream tapping, Pa
1882:
gives the theoretical volume flow rate. Introducing the beta factor
4720:
and if D < 71.2mm in which case this further term is added to C:
2912:
2829:
2725:
1171:{\displaystyle q_{v}^{'}=A_{1}\cdot V_{1}^{'}=A_{2}\cdot V_{2}^{'}}
5495:= fluid absolute static pressure in plane of upstream tapping, Pa
6508:
Risk
Management Program Guidance For Offsite Consequence Analysis
5891:
4083:
2979:
2784:= ratio of orifice hole diameter to pipe diameter, dimensionless
420:
6270:
Advantages and disadvantages of orifice meter and venturi meter
6523:
4047:= mass and volumetric flow rate, respectively, kg/s and m³/s
6412:"Orifice Plates for Flow Measurement & Flow Restriction"
6510:, U.S. EPA publication EPA-550-B-99-009, April 1999.
6319:
ASME MFC-3M-2004 Sec. 2-4.3.2.2 stipulates a minimum of 0.8
4114:
For compressible flows such as flows of gases or steam, an
3598:
Under choked flow conditions, the fluid flow rate becomes:
2876:= theoretical fluid velocity through the orifice hole, m/s
5432:= internal orifice diameter under operating conditions, m
384:= internal orifice diameter under operating conditions, m
37:
6467:
6465:
6463:
6345:
454:= differential pressure measured across the orifice, Pa
6333:
5713:= diameter ratio of orifice diameter to pipe diameter,
5460:= internal pipe diameter under operating conditions, m
2143:{\displaystyle C={\frac {C_{d}}{\sqrt {1-\beta ^{4}}}}}
88:
measured in kg/s across an orifice can be described as
6460:
6175:
5987:
5915:
5866:
5838:
5810:
5782:
5751:
5719:
5696:
5644:
5611:
5576:
5541:
5506:
5471:
5443:
5415:
5387:
5347:
5339:
but for incompressible fluids, including most liquids
5201:
5151:
5096:
5062:
5002:
4951:
4872:
4800:
4728:
4327:
4209:
4148:
4058:
4023:
3996:
3965:
3923:
3896:
3745:
3606:
3548:
3316:
3282:
3154:
3132:
3095:
3075:
3029:
2995:
2961:
2926:
2887:
2843:
2795:
2767:
2739:
2707:
2672:
2637:
2605:
2566:
2518:
2479:
2429:
2388:
2262:
2158:
2101:
2081:
1954:
1925:
1888:
1852:
1713:
1564:
1526:
1332:
1257:
1184:
1078:
938:
798:
562:
501:
470:
434:
395:
367:
335:
310:
290:
267:
225:
97:
66:
6394:
6392:
6390:
4100:
6193:
6146:
5966:
5879:
5844:
5816:
5788:
5760:
5732:
5702:
5677:
5627:
5589:
5554:
5519:
5484:
5449:
5421:
5393:
5359:
5327:
5185:
5118:
5081:
5044:
4986:
4934:and only the three following pairs of values for L
4925:{\displaystyle M'_{2}={\frac {2L'_{2}}{1-\beta }}}
4924:
4857:
4782:
4710:
4302:
4188:
4071:
4036:
4009:
3977:
3951:
3902:
3869:
3727:
3588:
3530:
3288:
3267:
3138:
3101:
3081:
3057:
3008:
2967:
2939:
2900:
2865:
2817:
2773:
2745:
2713:
2685:
2650:
2611:
2579:
2540:
2492:
2453:
2403:
2361:
2244:
2142:
2087:
2065:
1938:
1908:
1874:
1836:
1695:
1548:
1510:
1316:
1243:
1170:
1060:
920:
698:Standards and handbooks are mainly concerned with
581:
541:
483:
443:
408:
373:
341:
316:
296:
273:
238:
197:
79:
6387:
5320:
5302:
5270:
5257:
4844:
4809:
4775:
4752:
4500:
4463:
4419:
4377:
3833:
3807:
3691:
3665:
3521:
3407:
3400:
3375:
3058:{\displaystyle {\frac {1}{\sqrt {1-\beta ^{4}}}}}
1497:
1456:
1421:
1380:
6704:
6568:
6493:Handbook of Chemical Hazard Analysis, Appendix B
6433:Flow of Fluids Through Valves, Fittings and Pipe
5045:{\displaystyle L_{1}=L'_{2}={\frac {0.0254}{D}}}
4189:{\displaystyle q_{v}={\frac {q_{m}}{\rho _{1}}}}
3589:{\displaystyle q_{v}={\frac {q_{m}}{\rho _{1}}}}
542:{\displaystyle q_{v}={\frac {q_{m}}{\rho _{1}}}}
6489:Handbook of Chemical Hazard Analysis Procedures
2696:= cross-sectional area of the orifice hole, m²
3146:to account for the compressibility of gasses.
2075:And finally introducing the meter coefficient
16:Device for measuring or restricting fluid flow
747:orifice, in which the plate obstructs just a
250:
6643:(2nd ed.). London: E. & F. N. Spon.
6593:
6591:
6589:
6587:
6585:
6583:
6535:
6546:
6366:
6364:
6362:
6360:
6157:
5678:{\displaystyle {\frac {4q_{m}}{\pi \mu D}}}
5369:
4313:
3878:
2370:
207:
6666:
6625:
6529:
6484:
6482:
6480:
6471:
6293:
5404:= coefficient of discharge, dimensionless
4297:
4280:
4274:
4263:
4252:
4248:
3804:
3779:
3773:
3762:
3662:
3651:
3640:
3634:
3623:
3372:
3361:
3350:
3344:
3333:
3233:
3222:
3216:
3205:
3201:
3178:
2915:, Pa with dimensions of kg/(m·s² )
2327:
2323:
2317:
2306:
2289:
2202:
2196:
2185:
2023:
2017:
1989:
1978:
1794:
1788:
1746:
1605:
1597:
553:
192:
175:
169:
158:
147:
143:
6580:
6512:Guidance for Offsite Consequence Analysis
3297:
1317:{\displaystyle V_{2}^{'}=q_{v}^{'}/A_{2}}
1244:{\displaystyle V_{1}^{'}=q_{v}^{'}/A_{1}}
353:
6667:Perry, Robert H.; Green, Don W. (1984).
6444:
6442:
6357:
6305:
6303:
5900:
36:
6638:
6503:
6501:
6477:
6339:
6297:is reduced below the critical pressure.
6194:{\displaystyle \Delta {\bar {\omega }}}
5855:= dynamic viscosity of the fluid, Pa.s
5135:
4094:and other symbols are defined as above
2661:= cross-sectional area of the pipe, m²
6705:
6647:
6435:. Ipswich: Crane. 1988. pp. 2–14.
6398:
6351:
769:
254:
6650:Flow Measurement Engineering Handbook
6439:
6300:
284:= diameter ratio of orifice diameter
6670:Perry's Chemical Engineers' Handbook
6616:
6574:
6498:
5894:in plane of upstream tapping, kg/m³
3121:
619:
423:in plane of upstream tapping, kg/m³
5186:{\displaystyle p_{2}/p_{1}>0.75}
13:
6176:
6008:
5991:
5936:
5919:
5752:
4291:
3978:{\displaystyle \gamma \approx 1.4}
2756:= diameter of the orifice hole, m
435:
186:
14:
6744:
4101:Computation according to ISO 5167
4086:under upstream conditions, kg/m³
6697:Online Orifice Plate Calculator
6689:
6673:(Sixth ed.). McGraw Hill.
6313:
6287:
6225:Accidental release source terms
6212:and other symbols are as above
2272:
2168:
6425:
6404:
6378:
6185:
6120:
6101:
6060:
6041:
6000:
5928:
5733:{\displaystyle {\frac {d}{D}}}
5252:
5214:
4987:{\displaystyle L_{1}=L'_{2}=0}
4747:
4735:
4695:
4651:
4610:
4595:
4592:
4589:
4568:
4553:
4532:
4514:
4448:
4433:
4129:Reader-Harris/Gallagher (1998)
3506:
3494:
3490:
3461:
3441:
3412:
3260:
3234:
2354:
2328:
2269:
2263:
2229:
2203:
2165:
2159:
2050:
2024:
1821:
1795:
1775:
1760:
1680:
1651:
1632:
1606:
592:
582:{\displaystyle 1-\beta ^{1.9}}
32:
1:
6641:Flow Measurement & Meters
6617:Bean, Howard S., ed. (1983).
6449:Lecture, University of Sydney
6275:
2828:= theoretical upstream fluid
2555:(at any cross-section), kg/s
2507:(at any cross-section), kg/s
2468:(at any cross-section), m³/s
2418:(at any cross-section), m³/s
601:An orifice plate is called a
6326:
6204:= overall pressure loss, Pa
5771:= differential pressure, Pa
3065:is often referred to as the
7:
6218:
6208:
6168:
6160:
5859:
5831:
5803:
5775:
5744:
5689:
5604:
5569:
5534:
5499:
5464:
5436:
5408:
5380:
5372:
5360:{\displaystyle \epsilon =1}
5193:(at least - standards vary)
5119:{\displaystyle L'_{2}=0.47}
4090:
4051:
3989:
3952:{\displaystyle c_{p}/c_{v}}
3889:
3881:
3067:velocity of approach factor
2954:
2919:
2880:
2836:
2788:
2760:
2732:
2700:
2665:
2630:
2598:
2559:
2511:
2472:
2454:{\displaystyle q_{v}^{'}{}}
2422:
2381:
2373:
427:
388:
360:
328:
260:
218:
210:
10:
6749:
6648:Miller, Richard W (1996).
6609:
6211:
6203:
5889:
5854:
5826:
5798:
5770:
5712:
5637:
5599:
5564:
5529:
5494:
5459:
5431:
5403:
4093:
4081:
4046:
3912:
2977:
2949:
2910:
2875:
2827:
2783:
2755:
2723:
2695:
2660:
2621:
2589:
2550:
2502:
2463:
2413:
1909:{\displaystyle \beta =d/D}
778:(constant fluid density),
774:By assuming steady-state,
453:
418:
383:
351:
283:
248:
6652:. New York: McGraw-Hill.
5880:{\displaystyle \rho _{1}}
5789:{\displaystyle \epsilon }
4072:{\displaystyle \rho _{1}}
3289:{\displaystyle \epsilon }
3139:{\displaystyle \epsilon }
2866:{\displaystyle V_{2}^{'}}
2818:{\displaystyle V_{1}^{'}}
2541:{\displaystyle q_{m}^{'}}
1875:{\displaystyle q_{v}^{'}}
1846:The above expression for
1549:{\displaystyle q_{v}^{'}}
764:
409:{\displaystyle \rho _{1}}
342:{\displaystyle \epsilon }
6542:Section 3 -- Choked Flow
6280:
6250:Restrictive flow orifice
5761:{\displaystyle \Delta p}
5638:= pipe Reynolds number,
5600:= volume flow rate, m/s
4314:Coefficient of discharge
4108:coefficient of discharge
2592:coefficient of discharge
1070:By continuity equation:
693:
444:{\displaystyle \Delta p}
251:coefficient of discharge
5817:{\displaystyle \kappa }
5565:= mass flow rate, kg/s
5082:{\displaystyle L_{1}=1}
4792:In the equation for C,
3903:{\displaystyle \gamma }
2404:{\displaystyle q_{v}{}}
755:
679:Vena contracta tappings
6723:Mechanical engineering
6472:Perry & Green 1984
6195:
6148:
5968:
5881:
5846:
5818:
5790:
5762:
5734:
5704:
5703:{\displaystyle \beta }
5679:
5629:
5628:{\displaystyle Re_{D}}
5591:
5556:
5521:
5486:
5451:
5423:
5395:
5361:
5329:
5187:
5120:
5083:
5046:
4988:
4926:
4859:
4784:
4712:
4304:
4190:
4073:
4038:
4011:
3979:
3953:
3904:
3871:
3729:
3590:
3532:
3290:
3269:
3140:
3103:
3102:{\displaystyle \beta }
3083:
3059:
3010:
2969:
2941:
2902:
2867:
2819:
2775:
2774:{\displaystyle \beta }
2747:
2715:
2687:
2652:
2613:
2581:
2542:
2494:
2455:
2405:
2363:
2246:
2144:
2089:
2067:
1940:
1910:
1876:
1838:
1697:
1550:
1512:
1318:
1245:
1172:
1062:
922:
583:
543:
485:
445:
410:
375:
343:
318:
298:
275:
274:{\displaystyle \beta }
240:
199:
81:
45:
41:Orifice plate showing
6196:
6149:
5969:
5901:Overall pressure loss
5882:
5847:
5819:
5791:
5763:
5735:
5705:
5680:
5630:
5592:
5590:{\displaystyle q_{v}}
5557:
5555:{\displaystyle q_{m}}
5522:
5520:{\displaystyle p_{2}}
5487:
5485:{\displaystyle p_{1}}
5452:
5424:
5396:
5362:
5330:
5188:
5121:
5084:
5047:
4989:
4927:
4860:
4785:
4713:
4305:
4191:
4074:
4039:
4037:{\displaystyle q_{v}}
4012:
4010:{\displaystyle q_{m}}
3980:
3954:
3905:
3872:
3730:
3591:
3533:
3291:
3270:
3141:
3104:
3084:
3060:
3011:
3009:{\displaystyle C_{d}}
2970:
2968:{\displaystyle \rho }
2942:
2940:{\displaystyle p_{2}}
2903:
2901:{\displaystyle p_{1}}
2868:
2820:
2776:
2748:
2716:
2688:
2686:{\displaystyle A_{2}}
2653:
2651:{\displaystyle A_{1}}
2614:
2582:
2580:{\displaystyle C_{d}}
2543:
2495:
2493:{\displaystyle q_{m}}
2456:
2406:
2364:
2247:
2145:
2090:
2068:
1941:
1939:{\displaystyle C_{d}}
1918:discharge coefficient
1911:
1877:
1839:
1698:
1551:
1513:
1319:
1246:
1173:
1063:
923:
584:
554:overall pressure loss
544:
486:
484:{\displaystyle q_{v}}
446:
411:
376:
344:
319:
299:
276:
241:
239:{\displaystyle C_{d}}
200:
82:
80:{\displaystyle q_{m}}
40:
6718:Chemical engineering
6255:Rocket engine nozzle
6173:
5985:
5913:
5864:
5845:{\displaystyle \mu }
5836:
5808:
5780:
5749:
5717:
5694:
5642:
5609:
5574:
5539:
5504:
5469:
5441:
5413:
5385:
5345:
5199:
5149:
5136:Expansibility factor
5094:
5060:
5054:D and D/2 tappings:
5000:
4949:
4870:
4798:
4726:
4325:
4207:
4146:
4116:expansibility factor
4056:
4021:
3994:
3963:
3921:
3894:
3743:
3604:
3546:
3314:
3280:
3152:
3130:
3093:
3073:
3027:
2993:
2959:
2924:
2885:
2841:
2793:
2765:
2737:
2705:
2670:
2635:
2603:
2564:
2516:
2477:
2466:volumetric flow rate
2427:
2416:volumetric flow rate
2386:
2260:
2156:
2099:
2095:which is defined as
2079:
1952:
1923:
1886:
1850:
1711:
1562:
1524:
1330:
1255:
1182:
1076:
936:
796:
788:Bernoulli's equation
560:
499:
468:
432:
393:
365:
354:expansibility factor
333:
308:
288:
265:
223:
95:
64:
6639:Linford, A (1961).
6532:, pp. 625–638.
6354:, pp. 7.1–7.3.
5109:
5028:
4977:
4907:
4885:
4687:
4666:
3915:heat capacity ratio
2862:
2814:
2537:
2448:
1871:
1732:
1583:
1545:
1481:
1405:
1298:
1276:
1225:
1203:
1167:
1132:
1097:
1057:
1009:
917:
856:
770:Incompressible flow
492:measured in m/s is
6562:2007-08-09 at the
6517:2006-02-24 at the
6454:2007-05-29 at the
6191:
6144:
5964:
5877:
5842:
5814:
5786:
5758:
5730:
5700:
5675:
5625:
5587:
5552:
5517:
5482:
5447:
5419:
5391:
5357:
5325:
5183:
5116:
5097:
5079:
5042:
5016:
4984:
4965:
4922:
4895:
4873:
4855:
4780:
4708:
4675:
4654:
4300:
4186:
4069:
4034:
4007:
3975:
3959:), dimensionless (
3949:
3900:
3867:
3725:
3586:
3528:
3286:
3265:
3136:
3099:
3079:
3055:
3006:
2965:
2937:
2898:
2863:
2844:
2815:
2796:
2771:
2743:
2711:
2683:
2648:
2609:
2577:
2538:
2519:
2490:
2451:
2430:
2401:
2359:
2242:
2140:
2085:
2063:
1936:
1906:
1872:
1853:
1834:
1714:
1693:
1565:
1546:
1527:
1508:
1463:
1387:
1314:
1280:
1258:
1241:
1207:
1185:
1168:
1149:
1114:
1079:
1058:
1032:
984:
918:
892:
831:
603:calibrated orifice
579:
539:
481:
441:
406:
371:
339:
314:
294:
271:
236:
195:
77:
46:
6680:978-0-07-049479-4
6659:978-0-07-042366-4
6342:, pp. 85–86.
6216:
6215:
6188:
6142:
6123:
6063:
6015:
6003:
5943:
5931:
5898:
5897:
5728:
5673:
5450:{\displaystyle D}
5422:{\displaystyle d}
5394:{\displaystyle C}
5315:
5297:
5040:
4996:flange tappings:
4945:corner tappings:
4920:
4839:
4771:
4643:
4495:
4414:
4298:
4261:
4246:
4245:
4184:
4138:Volume flow rate:
4098:
4097:
3865:
3862:
3828:
3802:
3723:
3720:
3686:
3584:
3526:
3396:
3263:
3122:Compressible flow
3082:{\displaystyle C}
3053:
3052:
2986:
2985:
2911:= fluid upstream
2746:{\displaystyle d}
2714:{\displaystyle D}
2612:{\displaystyle C}
2357:
2240:
2138:
2137:
2088:{\displaystyle C}
2061:
2015:
2014:
1832:
1786:
1785:
1691:
1690:
1492:
1443:
1416:
1367:
1178: or
1021:
973:
881:
820:
620:Pressure tappings
537:
458:
457:
374:{\displaystyle d}
317:{\displaystyle D}
304:to pipe diameter
297:{\displaystyle d}
193:
156:
141:
140:
26:restriction plate
6740:
6684:
6663:
6644:
6635:
6622:
6603:
6602:
6595:
6578:
6572:
6566:
6550:
6544:
6539:
6533:
6527:
6521:
6505:
6496:
6486:
6475:
6469:
6458:
6446:
6437:
6436:
6429:
6423:
6422:
6420:
6418:
6408:
6402:
6396:
6385:
6382:
6376:
6375:
6368:
6355:
6349:
6343:
6337:
6320:
6317:
6311:
6307:
6298:
6291:
6260:Torricelli's law
6200:
6198:
6197:
6192:
6190:
6189:
6181:
6158:
6153:
6151:
6150:
6145:
6143:
6141:
6140:
6139:
6124:
6119:
6118:
6100:
6099:
6084:
6081:
6080:
6079:
6064:
6059:
6058:
6040:
6039:
6024:
6021:
6016:
6014:
6006:
6005:
6004:
5996:
5989:
5973:
5971:
5970:
5965:
5963:
5962:
5944:
5942:
5934:
5933:
5932:
5924:
5917:
5886:
5884:
5883:
5878:
5876:
5875:
5851:
5849:
5848:
5843:
5823:
5821:
5820:
5815:
5795:
5793:
5792:
5787:
5767:
5765:
5764:
5759:
5740:, dimensionless
5739:
5737:
5736:
5731:
5729:
5721:
5709:
5707:
5706:
5701:
5685:, dimensionless
5684:
5682:
5681:
5676:
5674:
5672:
5661:
5660:
5659:
5646:
5634:
5632:
5631:
5626:
5624:
5623:
5596:
5594:
5593:
5588:
5586:
5585:
5561:
5559:
5558:
5553:
5551:
5550:
5526:
5524:
5523:
5518:
5516:
5515:
5491:
5489:
5488:
5483:
5481:
5480:
5456:
5454:
5453:
5448:
5428:
5426:
5425:
5420:
5400:
5398:
5397:
5392:
5370:
5366:
5364:
5363:
5358:
5334:
5332:
5331:
5326:
5324:
5323:
5317:
5316:
5308:
5306:
5305:
5298:
5296:
5295:
5286:
5285:
5276:
5274:
5273:
5261:
5260:
5251:
5250:
5235:
5234:
5192:
5190:
5189:
5184:
5176:
5175:
5166:
5161:
5160:
5125:
5123:
5122:
5117:
5105:
5088:
5086:
5085:
5080:
5072:
5071:
5051:
5049:
5048:
5043:
5041:
5033:
5024:
5012:
5011:
4993:
4991:
4990:
4985:
4973:
4961:
4960:
4931:
4929:
4928:
4923:
4921:
4919:
4908:
4903:
4890:
4881:
4864:
4862:
4861:
4856:
4854:
4853:
4848:
4847:
4840:
4838:
4837:
4836:
4823:
4815:
4813:
4812:
4789:
4787:
4786:
4781:
4779:
4778:
4772:
4764:
4756:
4755:
4717:
4715:
4714:
4709:
4707:
4706:
4694:
4693:
4688:
4683:
4662:
4644:
4642:
4641:
4640:
4624:
4623:
4614:
4588:
4587:
4586:
4552:
4551:
4550:
4510:
4509:
4504:
4503:
4496:
4494:
4493:
4492:
4479:
4478:
4469:
4467:
4466:
4460:
4459:
4429:
4428:
4423:
4422:
4415:
4413:
4412:
4411:
4398:
4394:
4393:
4383:
4381:
4380:
4368:
4367:
4352:
4351:
4309:
4307:
4306:
4301:
4299:
4290:
4289:
4276:
4273:
4272:
4262:
4254:
4247:
4244:
4243:
4228:
4224:
4219:
4218:
4195:
4193:
4192:
4187:
4185:
4183:
4182:
4173:
4172:
4163:
4158:
4157:
4120:expansion factor
4078:
4076:
4075:
4070:
4068:
4067:
4043:
4041:
4040:
4035:
4033:
4032:
4016:
4014:
4013:
4008:
4006:
4005:
3984:
3982:
3981:
3976:
3958:
3956:
3955:
3950:
3948:
3947:
3938:
3933:
3932:
3909:
3907:
3906:
3901:
3879:
3876:
3874:
3873:
3868:
3866:
3864:
3863:
3861:
3850:
3839:
3837:
3836:
3829:
3827:
3813:
3811:
3810:
3803:
3801:
3800:
3791:
3790:
3781:
3775:
3772:
3771:
3755:
3754:
3734:
3732:
3731:
3726:
3724:
3722:
3721:
3719:
3708:
3697:
3695:
3694:
3687:
3685:
3671:
3669:
3668:
3661:
3660:
3650:
3649:
3636:
3633:
3632:
3616:
3615:
3595:
3593:
3592:
3587:
3585:
3583:
3582:
3573:
3572:
3563:
3558:
3557:
3537:
3535:
3534:
3529:
3527:
3525:
3524:
3518:
3517:
3513:
3488:
3487:
3478:
3473:
3472:
3457:
3456:
3452:
3439:
3438:
3429:
3424:
3423:
3411:
3410:
3404:
3403:
3397:
3395:
3381:
3379:
3378:
3371:
3370:
3360:
3359:
3346:
3343:
3342:
3326:
3325:
3295:
3293:
3292:
3287:
3274:
3272:
3271:
3266:
3264:
3259:
3258:
3246:
3245:
3232:
3231:
3218:
3215:
3214:
3194:
3193:
3177:
3176:
3164:
3163:
3145:
3143:
3142:
3137:
3108:
3106:
3105:
3100:
3088:
3086:
3085:
3080:
3064:
3062:
3061:
3056:
3054:
3051:
3050:
3035:
3031:
3015:
3013:
3012:
3007:
3005:
3004:
2974:
2972:
2971:
2966:
2946:
2944:
2943:
2938:
2936:
2935:
2907:
2905:
2904:
2899:
2897:
2896:
2872:
2870:
2869:
2864:
2861:
2860:
2852:
2824:
2822:
2821:
2816:
2813:
2812:
2804:
2780:
2778:
2777:
2772:
2752:
2750:
2749:
2744:
2720:
2718:
2717:
2712:
2692:
2690:
2689:
2684:
2682:
2681:
2657:
2655:
2654:
2649:
2647:
2646:
2626:, dimensionless
2624:flow coefficient
2618:
2616:
2615:
2610:
2594:, dimensionless
2586:
2584:
2583:
2578:
2576:
2575:
2547:
2545:
2544:
2539:
2536:
2535:
2527:
2499:
2497:
2496:
2491:
2489:
2488:
2460:
2458:
2457:
2452:
2450:
2447:
2446:
2438:
2410:
2408:
2407:
2402:
2400:
2398:
2397:
2371:
2368:
2366:
2365:
2360:
2358:
2353:
2352:
2340:
2339:
2319:
2316:
2315:
2299:
2298:
2282:
2281:
2251:
2249:
2248:
2243:
2241:
2236:
2228:
2227:
2215:
2214:
2198:
2195:
2194:
2178:
2177:
2149:
2147:
2146:
2141:
2139:
2136:
2135:
2120:
2119:
2118:
2109:
2094:
2092:
2091:
2086:
2072:
2070:
2069:
2064:
2062:
2057:
2049:
2048:
2036:
2035:
2019:
2016:
2013:
2012:
2011:
1992:
1991:
1988:
1987:
1977:
1976:
1964:
1963:
1945:
1943:
1942:
1937:
1935:
1934:
1915:
1913:
1912:
1907:
1902:
1881:
1879:
1878:
1873:
1870:
1869:
1861:
1843:
1841:
1840:
1835:
1833:
1828:
1820:
1819:
1807:
1806:
1790:
1787:
1784:
1783:
1782:
1770:
1749:
1748:
1745:
1744:
1731:
1730:
1722:
1702:
1700:
1699:
1694:
1692:
1689:
1688:
1687:
1678:
1677:
1668:
1663:
1662:
1643:
1639:
1631:
1630:
1618:
1617:
1600:
1599:
1596:
1595:
1582:
1581:
1573:
1555:
1553:
1552:
1547:
1544:
1543:
1535:
1517:
1515:
1514:
1509:
1507:
1506:
1501:
1500:
1493:
1491:
1490:
1480:
1479:
1471:
1462:
1460:
1459:
1444:
1436:
1431:
1430:
1425:
1424:
1417:
1415:
1414:
1404:
1403:
1395:
1386:
1384:
1383:
1368:
1360:
1355:
1354:
1342:
1341:
1323:
1321:
1320:
1315:
1313:
1312:
1303:
1297:
1296:
1288:
1275:
1274:
1266:
1250:
1248:
1247:
1242:
1240:
1239:
1230:
1224:
1223:
1215:
1202:
1201:
1193:
1177:
1175:
1174:
1169:
1166:
1165:
1157:
1145:
1144:
1131:
1130:
1122:
1110:
1109:
1096:
1095:
1087:
1067:
1065:
1064:
1059:
1056:
1055:
1054:
1053:
1040:
1022:
1014:
1008:
1007:
1006:
1005:
992:
974:
966:
961:
960:
948:
947:
927:
925:
924:
919:
916:
915:
914:
913:
900:
882:
874:
869:
868:
855:
854:
853:
852:
839:
821:
813:
808:
807:
726:conical entrance
701:sharp-edged thin
588:
586:
585:
580:
578:
577:
548:
546:
545:
540:
538:
536:
535:
526:
525:
516:
511:
510:
490:
488:
487:
482:
480:
479:
462:volume flow rate
450:
448:
447:
442:
415:
413:
412:
407:
405:
404:
380:
378:
377:
372:
348:
346:
345:
340:
324:, dimensionless
323:
321:
320:
315:
303:
301:
300:
295:
280:
278:
277:
272:
245:
243:
242:
237:
235:
234:
208:
204:
202:
201:
196:
194:
185:
184:
171:
168:
167:
157:
149:
142:
139:
138:
123:
122:
121:
112:
107:
106:
86:
84:
83:
78:
76:
75:
56:In general, the
6748:
6747:
6743:
6742:
6741:
6739:
6738:
6737:
6728:Control devices
6703:
6702:
6701:
6692:
6687:
6681:
6660:
6612:
6607:
6606:
6597:
6596:
6581:
6573:
6569:
6564:Wayback Machine
6551:
6547:
6540:
6536:
6530:Cunningham 1951
6528:
6524:
6519:Wayback Machine
6506:
6499:
6487:
6478:
6470:
6461:
6456:Wayback Machine
6447:
6440:
6431:
6430:
6426:
6416:
6414:
6410:
6409:
6405:
6397:
6388:
6383:
6379:
6370:
6369:
6358:
6350:
6346:
6338:
6334:
6329:
6324:
6323:
6318:
6314:
6308:
6301:
6294:Cunningham 1951
6292:
6288:
6283:
6278:
6235:De Laval nozzle
6221:
6180:
6179:
6174:
6171:
6170:
6135:
6131:
6114:
6110:
6095:
6091:
6083:
6082:
6075:
6071:
6054:
6050:
6035:
6031:
6023:
6022:
6020:
6007:
5995:
5994:
5990:
5988:
5986:
5983:
5982:
5978:
5958:
5954:
5935:
5923:
5922:
5918:
5916:
5914:
5911:
5910:
5903:
5871:
5867:
5865:
5862:
5861:
5837:
5834:
5833:
5809:
5806:
5805:
5781:
5778:
5777:
5750:
5747:
5746:
5720:
5718:
5715:
5714:
5695:
5692:
5691:
5662:
5655:
5651:
5647:
5645:
5643:
5640:
5639:
5619:
5615:
5610:
5607:
5606:
5581:
5577:
5575:
5572:
5571:
5546:
5542:
5540:
5537:
5536:
5511:
5507:
5505:
5502:
5501:
5476:
5472:
5470:
5467:
5466:
5442:
5439:
5438:
5414:
5411:
5410:
5386:
5383:
5382:
5346:
5343:
5342:
5319:
5318:
5307:
5301:
5300:
5299:
5291:
5287:
5281:
5277:
5275:
5269:
5268:
5256:
5255:
5246:
5242:
5230:
5226:
5200:
5197:
5196:
5171:
5167:
5162:
5156:
5152:
5150:
5147:
5146:
5141:
5138:
5101:
5095:
5092:
5091:
5067:
5063:
5061:
5058:
5057:
5032:
5020:
5007:
5003:
5001:
4998:
4997:
4969:
4956:
4952:
4950:
4947:
4946:
4941:
4937:
4909:
4899:
4891:
4889:
4877:
4871:
4868:
4867:
4849:
4843:
4842:
4841:
4832:
4828:
4824:
4816:
4814:
4808:
4807:
4799:
4796:
4795:
4774:
4773:
4763:
4751:
4750:
4727:
4724:
4723:
4702:
4698:
4689:
4679:
4674:
4673:
4658:
4636:
4632:
4625:
4619:
4615:
4613:
4582:
4578:
4577:
4546:
4542:
4541:
4505:
4499:
4498:
4497:
4488:
4484:
4480:
4474:
4470:
4468:
4462:
4461:
4455:
4451:
4424:
4418:
4417:
4416:
4407:
4403:
4399:
4389:
4385:
4384:
4382:
4376:
4375:
4363:
4359:
4347:
4343:
4326:
4323:
4322:
4316:
4285:
4281:
4275:
4268:
4264:
4253:
4239:
4235:
4223:
4214:
4210:
4208:
4205:
4204:
4200:
4199:Mass flow rate:
4178:
4174:
4168:
4164:
4162:
4153:
4149:
4147:
4144:
4143:
4139:
4103:
4063:
4059:
4057:
4054:
4053:
4028:
4024:
4022:
4019:
4018:
4001:
3997:
3995:
3992:
3991:
3964:
3961:
3960:
3943:
3939:
3934:
3928:
3924:
3922:
3919:
3918:
3895:
3892:
3891:
3851:
3840:
3838:
3832:
3831:
3830:
3817:
3812:
3806:
3805:
3796:
3792:
3786:
3782:
3780:
3774:
3767:
3763:
3750:
3746:
3744:
3741:
3740:
3709:
3698:
3696:
3690:
3689:
3688:
3675:
3670:
3664:
3663:
3656:
3652:
3645:
3641:
3635:
3628:
3624:
3611:
3607:
3605:
3602:
3601:
3578:
3574:
3568:
3564:
3562:
3553:
3549:
3547:
3544:
3543:
3520:
3519:
3509:
3493:
3489:
3483:
3479:
3474:
3468:
3464:
3448:
3444:
3440:
3434:
3430:
3425:
3419:
3415:
3406:
3405:
3399:
3398:
3385:
3380:
3374:
3373:
3366:
3362:
3355:
3351:
3345:
3338:
3334:
3321:
3317:
3315:
3312:
3311:
3281:
3278:
3277:
3254:
3250:
3241:
3237:
3227:
3223:
3217:
3210:
3206:
3183:
3179:
3172:
3168:
3159:
3155:
3153:
3150:
3149:
3131:
3128:
3127:
3124:
3094:
3091:
3090:
3074:
3071:
3070:
3046:
3042:
3030:
3028:
3025:
3024:
3018:Reynolds number
3000:
2996:
2994:
2991:
2990:
2960:
2957:
2956:
2931:
2927:
2925:
2922:
2921:
2892:
2888:
2886:
2883:
2882:
2854:
2853:
2848:
2842:
2839:
2838:
2806:
2805:
2800:
2794:
2791:
2790:
2766:
2763:
2762:
2738:
2735:
2734:
2728:of the pipe, m
2706:
2703:
2702:
2677:
2673:
2671:
2668:
2667:
2642:
2638:
2636:
2633:
2632:
2604:
2601:
2600:
2571:
2567:
2565:
2562:
2561:
2529:
2528:
2523:
2517:
2514:
2513:
2484:
2480:
2478:
2475:
2474:
2449:
2440:
2439:
2434:
2428:
2425:
2424:
2399:
2393:
2389:
2387:
2384:
2383:
2348:
2344:
2335:
2331:
2318:
2311:
2307:
2294:
2290:
2277:
2273:
2261:
2258:
2257:
2232:
2223:
2219:
2210:
2206:
2197:
2190:
2186:
2173:
2169:
2157:
2154:
2153:
2131:
2127:
2114:
2110:
2108:
2100:
2097:
2096:
2080:
2077:
2076:
2053:
2044:
2040:
2031:
2027:
2018:
2007:
2003:
1996:
1990:
1983:
1979:
1972:
1968:
1959:
1955:
1953:
1950:
1949:
1930:
1926:
1924:
1921:
1920:
1916:as well as the
1898:
1887:
1884:
1883:
1863:
1862:
1857:
1851:
1848:
1847:
1824:
1815:
1811:
1802:
1798:
1789:
1778:
1774:
1766:
1753:
1747:
1740:
1736:
1724:
1723:
1718:
1712:
1709:
1708:
1683:
1679:
1673:
1669:
1664:
1658:
1654:
1644:
1635:
1626:
1622:
1613:
1609:
1601:
1598:
1591:
1587:
1575:
1574:
1569:
1563:
1560:
1559:
1537:
1536:
1531:
1525:
1522:
1521:
1502:
1496:
1495:
1494:
1486:
1482:
1473:
1472:
1467:
1461:
1455:
1454:
1435:
1426:
1420:
1419:
1418:
1410:
1406:
1397:
1396:
1391:
1385:
1379:
1378:
1359:
1350:
1346:
1337:
1333:
1331:
1328:
1327:
1308:
1304:
1299:
1290:
1289:
1284:
1268:
1267:
1262:
1256:
1253:
1252:
1235:
1231:
1226:
1217:
1216:
1211:
1195:
1194:
1189:
1183:
1180:
1179:
1159:
1158:
1153:
1140:
1136:
1124:
1123:
1118:
1105:
1101:
1089:
1088:
1083:
1077:
1074:
1073:
1049:
1045:
1042:
1041:
1036:
1013:
1001:
997:
994:
993:
988:
965:
956:
952:
943:
939:
937:
934:
933:
909:
905:
902:
901:
896:
873:
864:
860:
848:
844:
841:
840:
835:
812:
803:
799:
797:
794:
793:
772:
767:
758:
745:
739:
733:
727:
721:
715:
709:
702:
696:
680:
672:
666:
665:2½D and 8D taps
653:
645:
639:
631:
622:
595:
573:
569:
561:
558:
557:
531:
527:
521:
517:
515:
506:
502:
500:
497:
496:
475:
471:
469:
466:
465:
433:
430:
429:
400:
396:
394:
391:
390:
366:
363:
362:
334:
331:
330:
309:
306:
305:
289:
286:
285:
266:
263:
262:
230:
226:
224:
221:
220:
180:
176:
170:
163:
159:
148:
134:
130:
117:
113:
111:
102:
98:
96:
93:
92:
71:
67:
65:
62:
61:
35:
27:
17:
12:
11:
5:
6746:
6736:
6735:
6730:
6725:
6720:
6715:
6713:Fluid dynamics
6700:
6699:
6693:
6691:
6688:
6686:
6685:
6679:
6664:
6658:
6645:
6636:
6623:
6613:
6611:
6608:
6605:
6604:
6579:
6567:
6545:
6534:
6522:
6497:
6476:
6459:
6438:
6424:
6403:
6386:
6377:
6356:
6344:
6331:
6330:
6328:
6325:
6322:
6321:
6312:
6299:
6285:
6284:
6282:
6279:
6277:
6274:
6273:
6272:
6267:
6265:Venturi effect
6262:
6257:
6252:
6247:
6242:
6237:
6232:
6227:
6220:
6217:
6214:
6213:
6210:
6206:
6205:
6202:
6187:
6184:
6178:
6166:
6165:
6162:
6156:
6155:
6138:
6134:
6130:
6127:
6122:
6117:
6113:
6109:
6106:
6103:
6098:
6094:
6090:
6087:
6078:
6074:
6070:
6067:
6062:
6057:
6053:
6049:
6046:
6043:
6038:
6034:
6030:
6027:
6019:
6013:
6010:
6002:
5999:
5993:
5975:
5974:
5961:
5957:
5953:
5950:
5947:
5941:
5938:
5930:
5927:
5921:
5902:
5899:
5896:
5895:
5888:
5874:
5870:
5857:
5856:
5853:
5841:
5829:
5828:
5825:
5813:
5801:
5800:
5797:
5785:
5773:
5772:
5769:
5757:
5754:
5742:
5741:
5727:
5724:
5711:
5699:
5687:
5686:
5671:
5668:
5665:
5658:
5654:
5650:
5636:
5622:
5618:
5614:
5602:
5601:
5598:
5584:
5580:
5567:
5566:
5563:
5549:
5545:
5532:
5531:
5528:
5514:
5510:
5497:
5496:
5493:
5479:
5475:
5462:
5461:
5458:
5446:
5434:
5433:
5430:
5418:
5406:
5405:
5402:
5390:
5378:
5377:
5374:
5368:
5367:
5356:
5353:
5350:
5340:
5336:
5335:
5322:
5314:
5311:
5304:
5294:
5290:
5284:
5280:
5272:
5267:
5264:
5259:
5254:
5249:
5245:
5241:
5238:
5233:
5229:
5225:
5222:
5219:
5216:
5213:
5210:
5207:
5204:
5194:
5182:
5179:
5174:
5170:
5165:
5159:
5155:
5137:
5134:
5133:
5132:
5131:
5130:
5129:
5128:
5127:
5126:
5115:
5112:
5108:
5104:
5100:
5089:
5078:
5075:
5070:
5066:
5052:
5039:
5036:
5031:
5027:
5023:
5019:
5015:
5010:
5006:
4994:
4983:
4980:
4976:
4972:
4968:
4964:
4959:
4955:
4939:
4935:
4932:
4918:
4915:
4912:
4906:
4902:
4898:
4894:
4888:
4884:
4880:
4876:
4865:
4852:
4846:
4835:
4831:
4827:
4822:
4819:
4811:
4806:
4803:
4790:
4777:
4770:
4767:
4762:
4759:
4754:
4749:
4746:
4743:
4740:
4737:
4734:
4731:
4721:
4718:
4705:
4701:
4697:
4692:
4686:
4682:
4678:
4672:
4669:
4665:
4661:
4657:
4653:
4650:
4647:
4639:
4635:
4631:
4628:
4622:
4618:
4612:
4609:
4606:
4603:
4600:
4597:
4594:
4591:
4585:
4581:
4576:
4573:
4570:
4567:
4564:
4561:
4558:
4555:
4549:
4545:
4540:
4537:
4534:
4531:
4528:
4525:
4522:
4519:
4516:
4513:
4508:
4502:
4491:
4487:
4483:
4477:
4473:
4465:
4458:
4454:
4450:
4447:
4444:
4441:
4438:
4435:
4432:
4427:
4421:
4410:
4406:
4402:
4397:
4392:
4388:
4379:
4374:
4371:
4366:
4362:
4358:
4355:
4350:
4346:
4342:
4339:
4336:
4333:
4330:
4315:
4312:
4311:
4310:
4296:
4293:
4288:
4284:
4279:
4271:
4267:
4260:
4257:
4251:
4242:
4238:
4234:
4231:
4227:
4222:
4217:
4213:
4197:
4196:
4181:
4177:
4171:
4167:
4161:
4156:
4152:
4102:
4099:
4096:
4095:
4092:
4088:
4087:
4080:
4066:
4062:
4049:
4048:
4045:
4031:
4027:
4004:
4000:
3987:
3986:
3974:
3971:
3968:
3946:
3942:
3937:
3931:
3927:
3911:
3899:
3887:
3886:
3883:
3860:
3857:
3854:
3849:
3846:
3843:
3835:
3826:
3823:
3820:
3816:
3809:
3799:
3795:
3789:
3785:
3778:
3770:
3766:
3761:
3758:
3753:
3749:
3718:
3715:
3712:
3707:
3704:
3701:
3693:
3684:
3681:
3678:
3674:
3667:
3659:
3655:
3648:
3644:
3639:
3631:
3627:
3622:
3619:
3614:
3610:
3581:
3577:
3571:
3567:
3561:
3556:
3552:
3523:
3516:
3512:
3508:
3505:
3502:
3499:
3496:
3492:
3486:
3482:
3477:
3471:
3467:
3463:
3460:
3455:
3451:
3447:
3443:
3437:
3433:
3428:
3422:
3418:
3414:
3409:
3402:
3394:
3391:
3388:
3384:
3377:
3369:
3365:
3358:
3354:
3349:
3341:
3337:
3332:
3329:
3324:
3320:
3285:
3262:
3257:
3253:
3249:
3244:
3240:
3236:
3230:
3226:
3221:
3213:
3209:
3204:
3200:
3197:
3192:
3189:
3186:
3182:
3175:
3171:
3167:
3162:
3158:
3135:
3123:
3120:
3098:
3078:
3049:
3045:
3041:
3038:
3034:
3023:The parameter
3003:
2999:
2984:
2983:
2976:
2964:
2952:
2951:
2948:
2934:
2930:
2917:
2916:
2909:
2895:
2891:
2878:
2877:
2874:
2859:
2856:
2851:
2847:
2834:
2833:
2826:
2811:
2808:
2803:
2799:
2786:
2785:
2782:
2770:
2758:
2757:
2754:
2742:
2730:
2729:
2722:
2710:
2698:
2697:
2694:
2680:
2676:
2663:
2662:
2659:
2645:
2641:
2628:
2627:
2620:
2608:
2596:
2595:
2588:
2574:
2570:
2557:
2556:
2553:mass flow rate
2551:= theoretical
2549:
2534:
2531:
2526:
2522:
2509:
2508:
2505:mass flow rate
2501:
2487:
2483:
2470:
2469:
2464:= theoretical
2462:
2445:
2442:
2437:
2433:
2420:
2419:
2412:
2396:
2392:
2379:
2378:
2375:
2356:
2351:
2347:
2343:
2338:
2334:
2330:
2326:
2322:
2314:
2310:
2305:
2302:
2297:
2293:
2288:
2285:
2280:
2276:
2271:
2268:
2265:
2239:
2235:
2231:
2226:
2222:
2218:
2213:
2209:
2205:
2201:
2193:
2189:
2184:
2181:
2176:
2172:
2167:
2164:
2161:
2134:
2130:
2126:
2123:
2117:
2113:
2107:
2104:
2084:
2060:
2056:
2052:
2047:
2043:
2039:
2034:
2030:
2026:
2022:
2010:
2006:
2002:
1999:
1995:
1986:
1982:
1975:
1971:
1967:
1962:
1958:
1933:
1929:
1905:
1901:
1897:
1894:
1891:
1868:
1865:
1860:
1856:
1831:
1827:
1823:
1818:
1814:
1810:
1805:
1801:
1797:
1793:
1781:
1777:
1773:
1769:
1765:
1762:
1759:
1756:
1752:
1743:
1739:
1735:
1729:
1726:
1721:
1717:
1686:
1682:
1676:
1672:
1667:
1661:
1657:
1653:
1650:
1647:
1642:
1638:
1634:
1629:
1625:
1621:
1616:
1612:
1608:
1604:
1594:
1590:
1586:
1580:
1577:
1572:
1568:
1542:
1539:
1534:
1530:
1505:
1499:
1489:
1485:
1478:
1475:
1470:
1466:
1458:
1453:
1450:
1447:
1442:
1439:
1434:
1429:
1423:
1413:
1409:
1402:
1399:
1394:
1390:
1382:
1377:
1374:
1371:
1366:
1363:
1358:
1353:
1349:
1345:
1340:
1336:
1311:
1307:
1302:
1295:
1292:
1287:
1283:
1279:
1273:
1270:
1265:
1261:
1238:
1234:
1229:
1222:
1219:
1214:
1210:
1206:
1200:
1197:
1192:
1188:
1164:
1161:
1156:
1152:
1148:
1143:
1139:
1135:
1129:
1126:
1121:
1117:
1113:
1108:
1104:
1100:
1094:
1091:
1086:
1082:
1052:
1048:
1044:
1039:
1035:
1031:
1028:
1025:
1020:
1017:
1012:
1004:
1000:
996:
991:
987:
983:
980:
977:
972:
969:
964:
959:
955:
951:
946:
942:
912:
908:
904:
899:
895:
891:
888:
885:
880:
877:
872:
867:
863:
859:
851:
847:
843:
838:
834:
830:
827:
824:
819:
816:
811:
806:
802:
776:incompressible
771:
768:
766:
763:
757:
754:
743:
737:
731:
725:
719:
713:
708:quarter-circle
707:
700:
695:
692:
684:
683:
678:
675:
670:
664:
657:
656:
651:
648:
643:
638:D and D/2 taps
637:
634:
629:
621:
618:
594:
591:
576:
572:
568:
565:
550:
549:
534:
530:
524:
520:
514:
509:
505:
478:
474:
456:
455:
452:
440:
437:
425:
424:
417:
403:
399:
386:
385:
382:
370:
358:
357:
350:
338:
326:
325:
313:
293:
282:
270:
258:
257:
247:
233:
229:
216:
215:
212:
206:
205:
191:
188:
183:
179:
174:
166:
162:
155:
152:
146:
137:
133:
129:
126:
120:
116:
110:
105:
101:
74:
70:
58:mass flow rate
51:vena contracta
43:vena contracta
34:
31:
25:
15:
9:
6:
4:
3:
2:
6745:
6734:
6731:
6729:
6726:
6724:
6721:
6719:
6716:
6714:
6711:
6710:
6708:
6698:
6695:
6694:
6682:
6676:
6672:
6671:
6665:
6661:
6655:
6651:
6646:
6642:
6637:
6633:
6629:
6624:
6620:
6615:
6614:
6600:
6594:
6592:
6590:
6588:
6586:
6584:
6576:
6571:
6565:
6561:
6558:
6554:
6549:
6543:
6538:
6531:
6526:
6520:
6516:
6513:
6509:
6504:
6502:
6494:
6490:
6485:
6483:
6481:
6473:
6468:
6466:
6464:
6457:
6453:
6450:
6445:
6443:
6434:
6428:
6413:
6407:
6400:
6395:
6393:
6391:
6381:
6373:
6367:
6365:
6363:
6361:
6353:
6348:
6341:
6336:
6332:
6316:
6306:
6304:
6295:
6290:
6286:
6271:
6268:
6266:
6263:
6261:
6258:
6256:
6253:
6251:
6248:
6246:
6243:
6241:
6238:
6236:
6233:
6231:
6228:
6226:
6223:
6222:
6207:
6201:
6182:
6167:
6163:
6159:
6136:
6132:
6128:
6125:
6115:
6111:
6107:
6104:
6096:
6092:
6088:
6085:
6076:
6072:
6068:
6065:
6055:
6051:
6047:
6044:
6036:
6032:
6028:
6025:
6017:
6011:
5997:
5981:
5980:
5979:
5959:
5955:
5951:
5948:
5945:
5939:
5925:
5909:
5908:
5907:
5893:
5887:
5872:
5868:
5858:
5852:
5839:
5830:
5824:
5811:
5802:
5796:
5783:
5774:
5768:
5755:
5743:
5725:
5722:
5710:
5697:
5688:
5669:
5666:
5663:
5656:
5652:
5648:
5635:
5620:
5616:
5612:
5603:
5597:
5582:
5578:
5568:
5562:
5547:
5543:
5533:
5527:
5512:
5508:
5498:
5492:
5477:
5473:
5463:
5457:
5444:
5435:
5429:
5416:
5407:
5401:
5388:
5379:
5375:
5371:
5354:
5351:
5348:
5341:
5338:
5337:
5312:
5309:
5292:
5288:
5282:
5278:
5265:
5262:
5247:
5243:
5239:
5236:
5231:
5227:
5223:
5220:
5217:
5211:
5208:
5205:
5202:
5195:
5180:
5177:
5172:
5168:
5163:
5157:
5153:
5144:
5143:
5142:
5113:
5110:
5106:
5102:
5098:
5090:
5076:
5073:
5068:
5064:
5056:
5055:
5053:
5037:
5034:
5029:
5025:
5021:
5017:
5013:
5008:
5004:
4995:
4981:
4978:
4974:
4970:
4966:
4962:
4957:
4953:
4944:
4943:
4933:
4916:
4913:
4910:
4904:
4900:
4896:
4892:
4886:
4882:
4878:
4874:
4866:
4850:
4833:
4829:
4825:
4820:
4817:
4804:
4801:
4794:
4793:
4791:
4768:
4765:
4760:
4757:
4744:
4741:
4738:
4732:
4729:
4722:
4719:
4703:
4699:
4690:
4684:
4680:
4676:
4670:
4667:
4663:
4659:
4655:
4648:
4645:
4637:
4633:
4629:
4626:
4620:
4616:
4607:
4604:
4601:
4598:
4583:
4579:
4574:
4571:
4565:
4562:
4559:
4556:
4547:
4543:
4538:
4535:
4529:
4526:
4523:
4520:
4517:
4511:
4506:
4489:
4485:
4481:
4475:
4471:
4456:
4452:
4445:
4442:
4439:
4436:
4430:
4425:
4408:
4404:
4400:
4395:
4390:
4386:
4372:
4369:
4364:
4360:
4356:
4353:
4348:
4344:
4340:
4337:
4334:
4331:
4328:
4321:
4320:
4319:
4294:
4286:
4282:
4277:
4269:
4265:
4258:
4255:
4249:
4240:
4236:
4232:
4229:
4225:
4220:
4215:
4211:
4203:
4202:
4201:
4179:
4175:
4169:
4165:
4159:
4154:
4150:
4142:
4141:
4140:
4136:
4134:
4130:
4124:
4121:
4117:
4112:
4109:
4089:
4085:
4079:
4064:
4060:
4050:
4044:
4029:
4025:
4002:
3998:
3988:
3972:
3969:
3966:
3944:
3940:
3935:
3929:
3925:
3916:
3910:
3897:
3888:
3884:
3880:
3877:
3858:
3855:
3852:
3847:
3844:
3841:
3824:
3821:
3818:
3814:
3797:
3793:
3787:
3783:
3776:
3768:
3764:
3759:
3756:
3751:
3747:
3738:
3735:
3716:
3713:
3710:
3705:
3702:
3699:
3682:
3679:
3676:
3672:
3657:
3653:
3646:
3642:
3637:
3629:
3625:
3620:
3617:
3612:
3608:
3599:
3596:
3579:
3575:
3569:
3565:
3559:
3554:
3550:
3541:
3538:
3514:
3510:
3503:
3500:
3497:
3484:
3480:
3475:
3469:
3465:
3458:
3453:
3449:
3445:
3435:
3431:
3426:
3420:
3416:
3392:
3389:
3386:
3382:
3367:
3363:
3356:
3352:
3347:
3339:
3335:
3330:
3327:
3322:
3318:
3309:
3307:
3301:
3299:
3283:
3275:
3255:
3251:
3247:
3242:
3238:
3228:
3224:
3219:
3211:
3207:
3202:
3198:
3195:
3190:
3187:
3184:
3180:
3173:
3169:
3165:
3160:
3156:
3147:
3133:
3119:
3117:
3111:
3096:
3076:
3068:
3047:
3043:
3039:
3036:
3032:
3021:
3019:
3001:
2997:
2981:
2975:
2962:
2953:
2947:
2932:
2928:
2918:
2914:
2908:
2893:
2889:
2879:
2873:
2857:
2855:
2849:
2845:
2835:
2831:
2825:
2809:
2807:
2801:
2797:
2787:
2781:
2768:
2759:
2753:
2740:
2731:
2727:
2721:
2708:
2699:
2693:
2678:
2674:
2664:
2658:
2643:
2639:
2629:
2625:
2619:
2606:
2597:
2593:
2587:
2572:
2568:
2558:
2554:
2548:
2532:
2530:
2524:
2520:
2510:
2506:
2500:
2485:
2481:
2471:
2467:
2461:
2443:
2441:
2435:
2431:
2421:
2417:
2411:
2394:
2390:
2380:
2376:
2372:
2369:
2349:
2345:
2341:
2336:
2332:
2324:
2320:
2312:
2308:
2303:
2300:
2295:
2291:
2286:
2283:
2278:
2274:
2266:
2255:
2252:
2237:
2233:
2224:
2220:
2216:
2211:
2207:
2199:
2191:
2187:
2182:
2179:
2174:
2170:
2162:
2151:
2132:
2128:
2124:
2121:
2115:
2111:
2105:
2102:
2082:
2073:
2058:
2054:
2045:
2041:
2037:
2032:
2028:
2020:
2008:
2004:
2000:
1997:
1993:
1984:
1980:
1973:
1969:
1965:
1960:
1956:
1947:
1931:
1927:
1919:
1903:
1899:
1895:
1892:
1889:
1866:
1864:
1858:
1854:
1844:
1829:
1825:
1816:
1812:
1808:
1803:
1799:
1791:
1779:
1771:
1767:
1763:
1757:
1754:
1750:
1741:
1737:
1733:
1727:
1725:
1719:
1715:
1706:
1703:
1684:
1674:
1670:
1665:
1659:
1655:
1648:
1645:
1640:
1636:
1627:
1623:
1619:
1614:
1610:
1602:
1592:
1588:
1584:
1578:
1576:
1570:
1566:
1557:
1540:
1538:
1532:
1528:
1518:
1503:
1487:
1483:
1476:
1474:
1468:
1464:
1451:
1448:
1445:
1440:
1437:
1432:
1427:
1411:
1407:
1400:
1398:
1392:
1388:
1375:
1372:
1369:
1364:
1361:
1356:
1351:
1347:
1343:
1338:
1334:
1325:
1309:
1305:
1300:
1293:
1291:
1285:
1281:
1277:
1271:
1269:
1263:
1259:
1236:
1232:
1227:
1220:
1218:
1212:
1208:
1204:
1198:
1196:
1190:
1186:
1162:
1160:
1154:
1150:
1146:
1141:
1137:
1133:
1127:
1125:
1119:
1115:
1111:
1106:
1102:
1098:
1092:
1090:
1084:
1080:
1071:
1068:
1050:
1046:
1043:
1037:
1033:
1029:
1026:
1023:
1018:
1015:
1010:
1002:
998:
995:
989:
985:
981:
978:
975:
970:
967:
962:
957:
953:
949:
944:
940:
931:
928:
910:
906:
903:
897:
893:
889:
886:
883:
878:
875:
870:
865:
861:
857:
849:
845:
842:
836:
832:
828:
825:
822:
817:
814:
809:
804:
800:
791:
789:
785:
781:
777:
762:
753:
750:
746:
740:
734:
728:
722:
720:conical inlet
716:
714:quadrant-edge
710:
703:
691:
687:
681:
676:
673:
671:recovery taps
667:
662:
661:
660:
654:
649:
646:
640:
635:
632:
627:
626:
625:
617:
614:
610:
606:
604:
599:
590:
574:
570:
566:
563:
555:
532:
528:
522:
518:
512:
507:
503:
495:
494:
493:
491:
476:
472:
463:
451:
438:
426:
422:
416:
401:
397:
387:
381:
368:
359:
355:
349:
336:
327:
311:
291:
281:
268:
259:
256:
252:
246:
231:
227:
217:
213:
209:
189:
181:
177:
172:
164:
160:
153:
150:
144:
135:
131:
127:
124:
118:
114:
108:
103:
99:
91:
90:
89:
87:
72:
68:
59:
54:
52:
44:
39:
30:
28:
22:
21:orifice plate
6690:Online Tools
6669:
6649:
6640:
6631:
6627:
6619:Fluid Meters
6618:
6598:
6570:
6557:PGS2 CPR 14E
6552:
6548:
6537:
6525:
6507:
6488:
6432:
6427:
6415:. Retrieved
6406:
6380:
6371:
6347:
6340:Linford 1961
6335:
6315:
6289:
6169:
5976:
5904:
5860:
5832:
5804:
5776:
5745:
5690:
5605:
5570:
5535:
5500:
5465:
5437:
5409:
5381:
5139:
4317:
4198:
4137:
4128:
4125:
4119:
4115:
4113:
4104:
4052:
3990:
3890:
3739:
3736:
3600:
3597:
3542:
3539:
3310:
3302:
3276:
3148:
3125:
3112:
3066:
3022:
2987:
2955:
2920:
2881:
2837:
2789:
2761:
2733:
2701:
2666:
2631:
2599:
2560:
2512:
2473:
2423:
2382:
2256:
2253:
2152:
2074:
1948:
1845:
1707:
1704:
1558:
1520:Solving for
1519:
1326:
1072:
1069:
932:
929:
792:
773:
759:
742:
736:
730:
724:
718:
712:
706:
699:
697:
688:
685:
677:
669:
663:
658:
650:
642:
636:
628:
623:
615:
611:
607:
602:
600:
596:
551:
464:
459:
428:
389:
361:
329:
261:
219:
60:
55:
50:
47:
42:
24:
20:
18:
6628:Trans. ASME
6399:Miller 1996
6352:Miller 1996
6310:(0.0254/D).
6230:Choked flow
4942:are valid:
4082:= real gas
3306:choked flow
3298:computation
652:Flange taps
644:radius taps
630:Corner taps
593:Application
33:Description
6707:Categories
6634:: 625–638.
6417:1 February
6276:References
6245:Pitot tube
2989:discharge
2622:= orifice
6575:Bean 1983
6327:Citations
6240:Flowmeter
6186:¯
6183:ω
6177:Δ
6133:β
6108:−
6093:β
6089:−
6073:β
6066:−
6048:−
6033:β
6029:−
6009:Δ
6001:¯
5998:ω
5992:Δ
5956:β
5952:−
5937:Δ
5929:¯
5926:ω
5920:Δ
5869:ρ
5840:μ
5812:κ
5784:ϵ
5753:Δ
5698:β
5667:μ
5664:π
5349:ϵ
5313:κ
5266:−
5244:β
5228:β
5212:−
5203:ϵ
4917:β
4914:−
4821:β
4761:−
4745:β
4742:−
4700:β
4668:−
4646:−
4634:β
4630:−
4617:β
4602:−
4572:−
4566:
4557:−
4536:−
4530:
4453:β
4396:β
4361:β
4354:−
4345:β
4292:Δ
4283:ρ
4256:π
4250:ϵ
4237:β
4233:−
4176:ρ
4127:the same
4061:ρ
3985:for air)
3970:≈
3967:γ
3898:γ
3856:−
3853:γ
3842:γ
3819:γ
3794:ρ
3777:γ
3714:−
3711:γ
3700:γ
3677:γ
3643:ρ
3638:γ
3576:ρ
3515:γ
3498:γ
3459:−
3454:γ
3390:−
3387:γ
3383:γ
3353:ρ
3284:ϵ
3248:−
3225:ρ
3203:ϵ
3170:ρ
3134:ϵ
3097:β
3044:β
3040:−
2963:ρ
2769:β
2342:−
2325:ρ
2287:ρ
2238:ρ
2217:−
2129:β
2125:−
2059:ρ
2038:−
2005:β
2001:−
1890:β
1830:ρ
1809:−
1758:−
1649:−
1641:ρ
1620:−
1452:⋅
1449:ρ
1446:⋅
1433:−
1376:⋅
1373:ρ
1370:⋅
1344:−
1147:⋅
1112:⋅
1030:⋅
1027:ρ
1024:⋅
1011:−
982:⋅
979:ρ
976:⋅
950:−
890:⋅
887:ρ
884:⋅
829:⋅
826:ρ
823:⋅
738:segmental
732:eccentric
571:β
567:−
529:ρ
436:Δ
398:ρ
337:ϵ
269:β
187:Δ
178:ρ
151:π
145:ϵ
132:β
128:−
6560:Archived
6515:Archived
6452:Archived
6219:See also
5890:= fluid
5107:′
5026:′
4975:′
4905:′
4883:′
4685:′
4664:′
4373:0.000521
2982:, kg/m³
2978:= fluid
2913:pressure
2858:′
2830:velocity
2810:′
2726:diameter
2533:′
2444:′
1867:′
1728:′
1579:′
1541:′
1477:′
1401:′
1324: :
1294:′
1272:′
1221:′
1199:′
1163:′
1128:′
1093:′
1047:′
999:′
907:′
846:′
780:inviscid
419:= fluid
255:tappings
6610:Sources
6209:
6164:
5892:density
5376:
5373:where:
4135:units.
4091:
4084:density
3885:
3882:where:
3116:venturi
2980:density
2377:
2374:where:
784:laminar
749:segment
421:density
214:
211:where:
6733:Piping
6677:
6656:
6161:where
6154:
5035:0.0254
4938:and L'
4769:0.0254
4443:0.0063
4437:0.0188
4341:0.0261
4335:0.5961
2832:, m/s
765:Theory
6281:Notes
5224:0.256
5218:0.351
4818:19000
4733:0.011
4649:0.031
4560:0.123
4524:0.080
4518:0.043
4357:0.216
1705:and:
744:chord
694:Plate
6675:ISBN
6654:ISBN
6419:2014
5240:0.93
5181:0.75
5178:>
5114:0.47
4739:0.75
4605:0.11
3540:and
1251:and
930:or:
756:Pipe
552:The
460:The
29:).
19:An
5960:1.9
5145:if
4851:0.8
4758:2.8
4704:1.3
4691:1.1
4671:0.8
4563:exp
4527:exp
4507:0.3
4457:3.5
4426:0.7
4118:or
3973:1.4
3737:or
741:or
723:or
711:or
668:or
641:or
575:1.9
6709::
6632:73
6630:.
6582:^
6500:^
6479:^
6462:^
6441:^
6389:^
6359:^
6302:^
5977:or
4539:10
4472:10
4387:10
4133:SI
4017:,
3913:=
3300:.
3020:.
2724:=
2590:=
2503:=
2414:=
1946::
1556::
782:,
589:.
352:=
249:=
6683:.
6662:.
6577:.
6474:.
6421:.
6401:.
6137:2
6129:C
6126:+
6121:)
6116:2
6112:C
6105:1
6102:(
6097:4
6086:1
6077:2
6069:C
6061:)
6056:2
6052:C
6045:1
6042:(
6037:4
6026:1
6018:=
6012:p
5949:1
5946:=
5940:p
5873:1
5756:p
5726:D
5723:d
5670:D
5657:m
5653:q
5649:4
5621:D
5617:e
5613:R
5583:v
5579:q
5548:m
5544:q
5513:2
5509:p
5478:1
5474:p
5445:D
5417:d
5389:C
5355:1
5352:=
5321:]
5310:1
5303:)
5293:1
5289:p
5283:2
5279:p
5271:(
5263:1
5258:[
5253:)
5248:8
5237:+
5232:4
5221:+
5215:(
5209:1
5206:=
5173:1
5169:p
5164:/
5158:2
5154:p
5111:=
5103:2
5099:L
5077:1
5074:=
5069:1
5065:L
5038:D
5030:=
5022:2
5018:L
5014:=
5009:1
5005:L
4982:0
4979:=
4971:2
4967:L
4963:=
4958:1
4954:L
4940:2
4936:1
4911:1
4901:2
4897:L
4893:2
4887:=
4879:2
4875:M
4845:)
4834:D
4830:e
4826:R
4810:(
4805:=
4802:A
4776:)
4766:D
4753:(
4748:)
4736:(
4730:+
4696:)
4681:2
4677:M
4660:2
4656:M
4652:(
4638:4
4627:1
4621:4
4611:)
4608:A
4599:1
4596:(
4593:)
4590:)
4584:1
4580:L
4575:7
4569:(
4554:)
4548:1
4544:L
4533:(
4521:+
4515:(
4512:+
4501:)
4490:D
4486:e
4482:R
4476:6
4464:(
4449:)
4446:A
4440:+
4434:(
4431:+
4420:)
4409:D
4405:e
4401:R
4391:6
4378:(
4370:+
4365:8
4349:2
4338:+
4332:=
4329:C
4295:p
4287:1
4278:2
4270:2
4266:d
4259:4
4241:4
4230:1
4226:C
4221:=
4216:m
4212:q
4180:1
4170:m
4166:q
4160:=
4155:v
4151:q
4065:1
4030:v
4026:q
4003:m
3999:q
3945:v
3941:c
3936:/
3930:p
3926:c
3917:(
3859:1
3848:1
3845:+
3834:)
3825:1
3822:+
3815:2
3808:(
3798:1
3788:1
3784:p
3769:2
3765:A
3760:C
3757:=
3752:v
3748:q
3717:1
3706:1
3703:+
3692:)
3683:1
3680:+
3673:2
3666:(
3658:1
3654:p
3647:1
3630:2
3626:A
3621:C
3618:=
3613:m
3609:q
3580:1
3570:m
3566:q
3560:=
3555:v
3551:q
3522:]
3511:/
3507:)
3504:1
3501:+
3495:(
3491:)
3485:1
3481:p
3476:/
3470:2
3466:p
3462:(
3450:/
3446:2
3442:)
3436:1
3432:p
3427:/
3421:2
3417:p
3413:(
3408:[
3401:)
3393:1
3376:(
3368:1
3364:p
3357:1
3348:2
3340:2
3336:A
3331:C
3328:=
3323:m
3319:q
3261:)
3256:2
3252:p
3243:1
3239:p
3235:(
3229:1
3220:2
3212:2
3208:A
3199:C
3196:=
3191:1
3188:,
3185:v
3181:q
3174:1
3166:=
3161:m
3157:q
3077:C
3048:4
3037:1
3033:1
3002:d
2998:C
2933:2
2929:p
2894:1
2890:p
2850:2
2846:V
2802:1
2798:V
2741:d
2709:D
2679:2
2675:A
2644:1
2640:A
2607:C
2573:d
2569:C
2525:m
2521:q
2486:m
2482:q
2436:v
2432:q
2395:v
2391:q
2355:)
2350:2
2346:p
2337:1
2333:p
2329:(
2321:2
2313:2
2309:A
2304:C
2301:=
2296:v
2292:q
2284:=
2279:m
2275:q
2270:)
2267:2
2264:(
2234:/
2230:)
2225:2
2221:p
2212:1
2208:p
2204:(
2200:2
2192:2
2188:A
2183:C
2180:=
2175:v
2171:q
2166:)
2163:1
2160:(
2133:4
2122:1
2116:d
2112:C
2106:=
2103:C
2083:C
2055:/
2051:)
2046:2
2042:p
2033:1
2029:p
2025:(
2021:2
2009:4
1998:1
1994:1
1985:2
1981:A
1974:d
1970:C
1966:=
1961:v
1957:q
1932:d
1928:C
1904:D
1900:/
1896:d
1893:=
1859:v
1855:q
1826:/
1822:)
1817:2
1813:p
1804:1
1800:p
1796:(
1792:2
1780:4
1776:)
1772:D
1768:/
1764:d
1761:(
1755:1
1751:1
1742:2
1738:A
1734:=
1720:v
1716:q
1685:2
1681:)
1675:1
1671:A
1666:/
1660:2
1656:A
1652:(
1646:1
1637:/
1633:)
1628:2
1624:p
1615:1
1611:p
1607:(
1603:2
1593:2
1589:A
1585:=
1571:v
1567:q
1533:v
1529:q
1504:2
1498:)
1488:1
1484:A
1469:v
1465:q
1457:(
1441:2
1438:1
1428:2
1422:)
1412:2
1408:A
1393:v
1389:q
1381:(
1365:2
1362:1
1357:=
1352:2
1348:p
1339:1
1335:p
1310:2
1306:A
1301:/
1286:v
1282:q
1278:=
1264:2
1260:V
1237:1
1233:A
1228:/
1213:v
1209:q
1205:=
1191:1
1187:V
1155:2
1151:V
1142:2
1138:A
1134:=
1120:1
1116:V
1107:1
1103:A
1099:=
1085:v
1081:q
1051:2
1038:1
1034:V
1019:2
1016:1
1003:2
990:2
986:V
971:2
968:1
963:=
958:2
954:p
945:1
941:p
911:2
898:2
894:V
879:2
876:1
871:+
866:2
862:p
858:=
850:2
837:1
833:V
818:2
815:1
810:+
805:1
801:p
564:1
533:1
523:m
519:q
513:=
508:v
504:q
477:v
473:q
439:p
402:1
369:d
312:D
292:d
232:d
228:C
190:p
182:1
173:2
165:2
161:d
154:4
136:4
125:1
119:d
115:C
109:=
104:m
100:q
73:m
69:q
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