Appendix - Intergraph Smart Instrumentation - 13.1 - Reference - Hexagon PPM

Integraph Smart Instrumentation Sizing Equations

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Smart Instrumentation Version
13.1

Formula for discharge coefficient

Notation

B

b- ratio

C

Discharge coefficient

D

Internal pipe diameter - mm

Di

Internal pipe diameter - inch

Re

Pipe Reynolds number at normal flow rate

Rd

Bore Reynolds number at normal flow rate

Square Edge Orifice

Flange Tappings

  • ISO 5167-1 (1991) and Miller

    If D < 58.62

    C-0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75-0.85598*B^3/D+0.039*B^4/(1-B^4)

    Else

    C-0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75-0.85598*B^3/D+2.286*B^4/(D*(1-B^4))

  • ISO 5167-1 (1998) and ISO 5167 (2003)

    If D<71.12

    C=0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*25.4/D)-0.123*exp(-7*25.4/D))*(1-0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*25.4/D/(1-B)-0.8*(2*25.4/D/(1-B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

    Else

    C=0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*25.4/D)-0.123*exp(-7*25.4/D))*(1-0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*25.4/D/(1-B)-0.8*(2*25.4/D/(1-B))^1.1)*B^1.3

Corner Tappings

  • ISO 5167-1 (1991) and Miller

    C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75

  • ISO 5167-1 (1998) and ISO 5167 (2003)

    If D<71.12

    C=0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080-0.123)*(1-0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0/(1-B)-0.8*(2*0/(1-B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

    Else

    C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080-0.123)*(1- 0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0/(1-B)-0.8*(2*0/(1-B))^1.1)*B^1.3

Radius Tappings

  • ISO 5167-1 (1991) and Miller

    C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75+0.039*B^4/(1-B^4)0.015839*B^3

  • ISO 5167-1 (1998) and ISO 5167 (2003)

    If D<71.12

    C=0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*1)-0.123*exp(-7*1))*(1-0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0.47/(1-B)-0.8*(2*0.47/(1-B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

    Else

    C=0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*1)-0.123*exp(-7*1))*(1-0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0.47/(1-B)-0.8*(2*0.47/(1-B))^1.1)*B^1.3

  • Small-Bore Honed-Orifice Meter Run with Corner Tappings

    C=(0.5991+0.0044/Di+(0.3155+0.0175/Di)*(B^4+2^B^16)+(0.52/Di-0.192+(16.48-1.16/Di)*(B^4+4*B^16))*(Re^(-0.5)))*((1-B^4)^0.5)

  • Small-Bore Honed-Orifice Meter Run with Flange Tappings

    C = (0.5980+0.468*(B^4+10^B^12)+(0.87+8.1*B^4)*(Re^(-0.5)))*((1-B^4)^0.5)

  • Pipe Tappings (2.5D & 8D)

    C = 0.5959+0.461*B^2.1+0.48^B^8+0.039*B^4/(1-B^4)+0.0029*B^2.5*(10^6/Re)^0.75

  • AGA Report 3 (Flange Tappings)

    A0 = 830-5000*B+9000*B^2-4200*B^3+530/Di^0.5

    A1 = 0.5993+0.007/Di+(0.364+0.076/Di^0.5)*B^4

    A2 = 0

    If B<(0.07+0.5/Di) A2 = 0.4*(1.6-1/Di)^5*(0.07+0.5/Di-B)^(5/2)

    A3 = 0

    If B<0.5 A3 = (0.5-B)^(3/2)*(0.009+0.034/Di)

    A4 = 0

    If B>0.7 A4 = (B-0.7)^(5/2)*(65/Di^2+3)

    K0 = (A1+A2-A3+A4)/(1+0.000015*A0)

    EF = A0*Di*B

    C = (1-B^4)^0.5*K0*(1+EF*B/Re)

  • AGA Report 3 (Pipe Tappings)

    A0 = 905-5000*B+9000*B^2-4200*B^3+875/Di

    A1 = 0

    If B<0.25 A1 = (0.25-B)^(5/2)*(1.43/Di^0.5)

    K0 = 0.5925+0.0182/Di+(0.440-0.06/Di)*B^2+(0.935+0.225/Di)*B^5+1.35*B^14+A1

    EP = A0*Di*B

    C = (1-B^4)^0.5*K0*(1+EP*B/Re)

Quarter of Circle (Quadrant Edge) Orifice

C = 0.73823+0.3309*B-1.1615^B^2+1.5084*B^3

Conical Entrance Orifice

If Re<5000*B C = 0.734

Else C = 0.730

Lo-Loss Tube

C = 1.005-0.471*B+0.564^B^2-0.514*B^3

Venturi Tube

  • Classical venturi tube with an “as cast” convergent section C = 0.984

  • Classical venturi tube with a machined convergent section C = 0.995

  • Classical venturi tube with a rough-welded sheet-iron convergent section C = 0.985

  • Universal Venturi Tube C = 0.9797

Nozzle

  • ISO Long Radius Nozzle C = 0.9965-0.00653*(B^0.5)*(10^6/Re)^0.5

  • ASME Long Radius Nozzle C = 0.9975-6.53*B^0.5*Re–0.5

  • ISA 1932 Nozzle C = 0.99-0.2262*B^4.1-( 0.00175*B^2-0.0033*B^4.15)*(10^6/Re)^1.15

  • Venturi Nozzle C = 0.9558-0.196*B^4.5

Eccentric Orifice

  • Diametrically Opposite Flange Tappings

    If D < 100 C = 0.5875+0.3813*B^2.1+0.6898^B^8-0.1963*B^4/(1-B^4)-0.3366*B^3+(7.3-15.7*B+170.8^B^2-399.7*B^3+332.2*B^4)/(Re)^0.75

    Else C = 0.5949+0.4078*B^2.1+0.0547^B^8+0.0955*B^4/(1-B^4)-0.5608*B^3+(-139.7+1328.8*B-4228.2^B^2+5691.9*B^3-2710.4*B^4)/(Re)^0.75

  • Side (90) Flange Tappings

    If D < 100 C = 0.6284+0.1462*B^2.1-0.8464^B^8+0.2603*B^4/(1-B^4)-0.2886*B^3+(69.1-469.4*B+1245.6^B^2-1287.5*B^3+486.2*B^4)/(Re)^0.75

    Else C = 0.6276+0.0828*B^2.1+0.2739^B^8-0.0934*B^4/(1-B^4)-0.1132*B^3+(-103.2+898.3*B-2557.3^B^2+2977*B^3-1131.3*B^4)/(Re)^0.75

  • Diametrically Opposite Vena Contracta Tappings

    If D < 100 Dp1 < 100

    DC = 0.6261+0.1851*Bet0^2.1-0.2879*Bet0^8+0.1170*Bet0^4/(1-Bet0^4)- 0.2845*Bet0^3+(23.3 - 207*Bet0+821.5*Bet0^2-1388.6*Bet0^3+900.3*Bet0^4)/(Re1)^0.75

    Else DC = 0.6276+0.0828*Bet0^2.1+0.2739*Bet0^8-0.0934*Bet0^4/(1-Bet0^4)-0.1132*Bet0^3+( 55.7-471.4*Bet0+1721.8*Bet0^2-2722.6*Bet0^3+1569.4*Bet0^4)/(Re1)^0.75

  • Side (90)° Vena Contracta Tappings

    If D < 100 DC = 0.5917+0.3061*Bet0^2.1+0.3406*Bet0^8-0.1019*Bet0^4/(1-Bet0^4)-0.2715*Bet0^3+(-69.3+556.9*Bet0-1332.2*Bet0^2+1303.7*Bet0^3-394.8*Bet0^4)/(Re1)^0.75

    Else DC = 0.6016+0.3312*Bet0^2.1-1.5581*Bet0^8+0.6510*Bet0^4/(1-Bet0^4)-0.7308*Bet0^3+( 52.8-434.2*Bet0+1571.2*Bet0^2-2460.9*Bet0^3+1420.2*Bet0^4)/(Re1)^0.75

Segmental Orifice

  • Flange Tappings

If D < 100 C = 0.5866+0.3917*B^2.1+0.7586^B^8-0.2273*B^4/(1-B^4)-0.3343*B^3

Else C = 0.6037+0.1598*B^2.1-0.2918^B^8+0.0244*B^4/(1-B^4)-0.0790*B^3

  • Vena Contracta Tappings

If If D < 100 C = 0.5925+0.3380*B^2.1+0.4016^B^8-0.1046*B^4/(1-B^4)-0.3212*B^3

Else C = 0.5922+0.3932*B^2.1+0.3412^B^8-0.0569*B^4/(1-B^4)-0.4628*B^3

Restriction Device

  • Critical Flow

    • Square Edge Orifice (Liquid/Water) C = 0.6

    • Thick Plate Square Edge Orifice (Liquid/Water) C = 0.899

    • Classical Venturi Tube C = 0.985

    • Square Edge Orifice (Gas/Steam) C = 0.83932

    • Toroidal Throat Venturi Nozzle C = 0.99354 - 1.525/Rd^0.5

    • Cylindrical Throat Venturi Nozzle If Rd<3.5*10^5 C = 1 - 7.21/Rd^0.5

      If 3.5*10^5<=Rd<2.5*10^6 C = 0.9887

      If 2.5*10^6<Rd C = 1 - 0.222/Rd^0.2

    • ASME Long Radius Nozzle If Rd<3.5*10^5 C = 1 - 7.21/Rd^0.5

      If 3.5*10^5<=Rd<2.5*10^6 C = 0.9887

      If 2.5*10^6<Rd C = 1 - 0.222/Rd^0.2

  • Sub-Critical Flow

    • Square Edge Orifice (Liquid/Water), Thick Plate Square Edge Orifice (Liquid/Water), and Square Edge Orifice (Gas/Steam)

      L1 = 25.4/D

      L2 = 25.4/D

      A = (19000 * B/Re)^0.8

      M = 2 * L2 / (1 - B)

      C = 0.5961 + 0.0261*B^2 - 0.216 *B^8 + 0.000521*(1000000*B/Re)^0.7 + (0.0188+0.0063*A) * B^3.5 * (1000000/Re)^0.3 + (0.043+0.080*exp(-10*L1) - 0.123*exp(-7*L1)) * (1 - 0.11*A)*(B^4/(1 - B^4)) - 0.031*(M - *M^1.1)*B^1.3.

      IF D < 71.12 THEN C = C +0.011*(0.75 - B) * (2.8 - Di)

    • Classical Venturi Tube C = 0.984

    • Toroidal Throat Venturi Nozzle C = 0.9558-0.196*B^4.5

    • Cylindrical Throat Venturi Nozzle C = 0.9558-0.196*B^4.5

    • ASME Long Radius Nozzle C = 0.9975-6.53*(B^0.5)*(1/Re)^0.5