10.5433PressureDifferential Meters1.01.40.95Square-edgedorificed.0.900 to 0.2Ld,= 0.4 0.85= 0.6= 0.70.80Nozzleo0.8Venturi meterdoOto0.0.75Ed=0.5Aoeosuee=0.60.70=0.7L10.750.65：=0.8= 0.850.60LL0.55LLL0.500.45L0.400.0 0.20.40.60.81.0(Pi-P2)/piFigure10.6Expansionfactorsforcommonobstructionmeterswithk=Cp/cy=1.4.(CourtesyofAmericanSocietyofMechanical Engineers,NewYork,NY;compiledandreprintedfromreference1.)nozzlecontraction isthatofthequadrantof anellipse,withthemajoraxis aligned with theflow axisas shown in Figure 10.9.The nozzle is typically installed inline,but can also be used at the inlet toandtheoutletfromaplenumorreservoirorattheoutletofapipe.Pressuretapsareusuallylocated(1) at one pipe diameter upstream of the nozzle inlet and at the nozzle throat using either wall orthroat taps, or (2) d and d/2 wall taps located one pipe diameter upstream and one-half diameterdownstream of the upstream nozzle face.The flow rate is determined from Equation 10.12 withvalues for Ao and β based on the throat diameter.Typical values for the flow coefficient andexpansionfactoraregiveninFigures10.10and10.6.Therelativeinstrumentsystematicuncertaintyat95%confidenceforthedischargecoefficientisabout2%of Candfortheexpansionfactoris about[2(pi-p2)/p,J% of Y (3).Thepermanent loss associated with a flow nozzle is largerthan for a comparable venturi but significantly smaller than for an orifice (Fig.10.7)for the samepressure drop
E1C10 09/14/2010 13:4:37 Page 433 nozzle contraction is that of the quadrant of an ellipse, with the major axis aligned with the flow axis, as shown in Figure 10.9. The nozzle is typically installed inline, but can also be used at the inlet to and the outlet from a plenum or reservoir or at the outlet of a pipe. Pressure taps are usually located (1) at one pipe diameter upstream of the nozzle inlet and at the nozzle throat using either wall or throat taps, or (2) d and d/2 wall taps located one pipe diameter upstream and one-half diameter downstream of the upstream nozzle face. The flow rate is determined from Equation 10.12 with values for Ao and b based on the throat diameter. Typical values for the flow coefficient and expansion factor are given in Figures 10.10 and 10.6. The relative instrument systematic uncertainty at 95% confidence for the discharge coefficient is about 2% of C and for the expansion factor is about ½2ðp1 p2Þ=p1% of Y (3). The permanent loss associated with a flow nozzle is larger than for a comparable venturi but significantly smaller than for an orifice (Fig. 10.7) for the same pressure drop. 1.0 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.0 0.2 0.4 0.6 0.8 1.0 Expansion factor, Y ( p1 – p2)/p1 = 0.6 = 0.7 = 0.8 k = 1.4 Square-edged orifice Nozzle or Venturi meter do d1 = 0 to 0.2 = 0.75 = 0.85 = 0.5 = 0.7 = 0.8 = 0.6 do d1 β = = 0 to 0.2 = 0.4 Figure 10.6 Expansion factors for common obstruction meters with k ¼ cp=cv ¼ 1:4. (Courtesy of American Society of Mechanical Engineers, New York, NY; compiled and reprinted from reference 1.) 10.5 Pressure Differential Meters 433
434Chapter10FlowMeasurements100V1-β*(1 -C-)-Cp2(Ap)loss=1-β19 (orifice)ApV1-β*(1-C-)+Cp2=1 +0.014β 2.06β2+1.18β3(nozzle)80 0 ng sSquare-edged orifice60Flownozzle4015°Figure10.7Thepermanentpressure loss associated with20(Ap)iens70=0.436-0.86β+0.59p2flowthroughcommonobstruc-ApVenturition meters.(Courtesy of=0.218-0.42β+0.38p2American Society of Mechani-cal Engineers, New York, NY:1111A0.20.40.60.81.0compiled and reprinted fromβreference 1.)ConvergentThroatentranceDivergentCylindricalinletoutlet中-·21do7°or15°中P2Pie(Ap)ho0Figure 10.8 The Herschel venturi meter with the associated flow pressure drop along its axis
E1C10 09/14/2010 13:4:38 Page 434 0.2 0.4 0.6 0.8 15° 7° Venturi Flow nozzle Square-edged orifice = 0.436 – 0.86 + 0.59 2 = 0.218 – 0.42 + 0.38 2 (Δp)loss Δp 1.0 0 20 40 60 80 100 Overall pressure loss, (Δp)loss (% of pressure differential) β β β β β = 1 + 0.014 – 2.06 2 + 1.18β3 β β (nozzle) = ≈ (orifice) 1 – (1 – C2) 4 1 – 1.9 – (1 – C2) + C 2 1 – 4 C 2 (Δp)loss Δp Figure 10.7 The permanent pressure loss associated with flow through common obstruction meters. (Courtesy of American Society of Mechanical Engineers, New York, NY; compiled and reprinted from reference 1.) x 0 ( p)loss Relative pressure drop Cylindrical inlet Convergent entrance Divergent outlet Throat d 7° or 15° d1 0 p1 p2 21° d1 Figure 10.8 The Herschel venturi meter with the associated flow pressure drop along its axis. 434 Chapter 10 Flow Measurements
43510.5PressureDifferentialMetersThroatpressuretapfdoUpstreamPiPipe flangespressure tape(Ap)nssFigure 10.9 The ASME long-radius nozzle with the associated flow pressure drop along its axis.The idea of using a nozzleas a flowmeter was firstproposed in1891by JohnRipleyFreeman(1855-1932),an inspector and engineeremployed by a fireinsurance firm.His workrequired tedious tests to quantify pressure losses in pipes, hoses, and fittings.He noted aconsistent relationship between pressure drop and flow ratethrough fire nozzles at higherflowrates.Example10.3The U-tube manometerfilled with manometer fluid (of specific gravity Sm)of Figure10.11 is usedtomeasurethepressuredropacross anobstructionmeter.Afluidhaving specificgravitySflowsthrough the meter.Determine a relationship between the meter flow rate and the measuredmanometerdeflection,H
E1C10 09/14/2010 13:4:38 Page 435 The idea of using a nozzle as a flow meter was first proposed in 1891 by John Ripley Freeman (1855–1932), an inspector and engineer employed by a fire insurance firm. His work required tedious tests to quantify pressure losses in pipes, hoses, and fittings. He noted a consistent relationship between pressure drop and flow rate through fire nozzles at higher flow rates. Example 10.3 The U-tube manometer filled with manometer fluid (of specific gravity Sm) of Figure 10.11 is used to measure the pressure drop across an obstruction meter. A fluid having specific gravity S flows through the meter. Determine a relationship between the meter flow rate and the measured manometer deflection, H. Relative pressure drop 0 Throat pressure tap Upstream pressure tap Pipe flanges Δp (Δp)loss p2 p2 p1 d0 d1 d0 2 3 r1 Figure 10.9 The ASME long-radius nozzle with the associated flow pressure drop along its axis. 10.5 Pressure Differential Meters 435