ENGINEERING DESIGN CALCULATION - DENNIS KIRK

ORIFICE FLOW CALCULATIONS - Refer Crane Flow of Fluids 1983 (pages 2-14 to 2-15) Ver 1.201
Project: Validate Calculation Instructions:
Tag No: Provide the input data in the yellow cells and clear the green cells.
Description: Crane Flow of Fluids Example 3, page 3-14 If Cd is not known use an initial value of 0.6 then.........
- when data entry is complete use Autoslove to recalculate Cd.
Upstream Pipe ID d1 38.1 mm Provide either Dynamic or Kinematic viscosity but not both.
Orifice ID d 25 mm Provide either Density for incompressible or Molecular Weight for compressible flow.
The green cells can be used to overide the values determined by the application if
Orifice Area A =PI()*d^2/4 490.9 mm2
required.
Beta Ratio b =d/d1 0.656 Valid for ratios 0.2 to 0.75
i) Discharge Coefficient Cd (typically 0.6 for near critical flow orifice) Currently #VALUE! of critical press ratio
Flow Coefficient C =Cd/Sqrt(1-B^4) 0.836 (See page A-20)
or ii) if Cd unknown then find C from Table A-20 0.836 then Cd = 0.75 and Korifice = (1-b^2)/(C^2.b^2) = 1.894
or iii) Value of C auto calculated from Table A-20 #VALUE! #VALUE!
Upstream Pressure p1 150 kPa(g) Dynamic Viscosity 450 cP
Downstream Pressure p2 146.5 kPa(g) Kinematic Viscosity cSt
Differential Press. dp 3.5 kPa
Orifice Type - Nozzle or Venturi Meter OR Square Edge Orifice S Square Edge Orifice
Reynolds Number 2 ~Laminar Flow WARNING - Re outside range of calculation

Incompressible Fluids: Warning - Either Density or MW should be blank

Density D 0.9 kg/m3 SG 0.001
Flow Velocity V 31.7265067 m/sec
Flow q =C.A.Sqrt[2.(p1-p2)/D] 0.036171131 m3/sec 2.170267861 m3/min 130.216072 m3/hr
(Eqn. 2-23) 36.17113102 l/sec 2170.267861 l/min 130216.072 l/hr
0.032554018 kg/sec 1.953241075 kg/min 0.11719446 Tonnes/hr
Compressible Fluids: Warning - Either Density or MW should be blank
Molecular Weight MW 19.4231 Specific Gravity 0.671
Upstream Temperature T1 15 deg C
Compressibility Factor Z from tables 0.9967
Density D 2.044 kg/m3 #VALUE! kg/Sm3
Specific Heat Ratio g from tables 1.4 Valid for ratios 1.25 to 1.45
Difference Press Ratio =(p1-p2)/p'1 0.014 Valid for ratio 0 to 0.60
Expansion Factor Y from table A-21 #VALUE!
Flow Velocity V #VALUE! m/sec
Non Critical Flow q =Y.C.A.Sqrt[2.(p1-p2)/D] #VALUE! Am3/sec #VALUE! Am3/min #VALUE! Am3/hr
(Eqn. 2-24) #VALUE! Sm3/sec #VALUE! Sm3/min #VALUE! Sm3/hr #VALUE! MMSCFD
#VALUE! kg/sec #VALUE! kg/min #VALUE! Tonnes/hr
Critical Pressure Ratio rc from table A-21 #VALUE!
Actual Pressure Ratio r =p'2/p'1 0.986 #VALUE!
Critical Pressure p1cr =p'2/rc #VALUE! kPa(g)
p2cr =p'1.rc #VALUE! kPa(g)
Choked Flow q =Y.C.A.Sqrt[2.p1.(1-rc)/D] #VALUE! Am3/sec #VALUE! Am3/min #VALUE! Am3/hr
(See page 2-15) #VALUE! Sm3/sec #VALUE! Sm3/min #VALUE! Sm3/hr #VALUE! MMSCFD
#VALUE! kg/sec #VALUE! kg/min #VALUE! Tonnes/hr
www.ozemail.com.au/~denniskb denniskb@ozemail.com.au

374776812.xls Orifice-Crane 12/18/2017

1.170

0.20
1.120 0.30
0.40
0.45
0.50
0.55
0.57
1.070 5
0.60
0.62
5
0.65
0.67
1.020 5
0.70
0.72
5
0.75
0.970

0.920
1000 10000 100000 1000000 10000000
1.400

1.200

1.000 0.20
0.30
0.40

0.800
0.50

0.60

0.600 0.65
0.70

0.75
0.400 0.80

0.200

0.000
1 10 100 1000 10000 100000 1000000 10000000
 ENGINEERING DESIGN CALCULATION - DENNIS KIRK

Nozzle or Venturi Meter Expansion Factor (Specific Heat Ratio = 1.3 Approximately)
Pressure Ratio 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60
Beta Ratio 0.2 1.000 0.990 0.979 0.967 0.954 0.942 0.929 0.917 0.904 0.893 0.880 0.867 0.854 0.840 0.827 0.813 0.799 0.785 0.770 0.756 0.742 0.726 0.711 0.698
0.5 1.000 0.988 0.975 0.963 0.950 0.936 0.923 0.911 0.897 0.884 0.871 0.857 0.843 0.828 0.814 0.799 0.784 0.770 0.756 0.741 0.727 0.711 0.698
0.6 1.000 0.987 0.973 0.960 0.944 0.930 0.916 0.902 0.890 0.875 0.861 0.846 0.831 0.817 0.802 0.787 0.771 0.757 0.741 0.726 0.711 0.698 0.685
0.7 1.000 0.986 0.971 0.953 0.936 0.921 0.904 0.890 0.874 0.859 0.842 0.826 0.811 0.794 0.780 0.765 0.750 0.734 0.720 0.705 0.691 0.674
0.75 1.000 0.983 0.966 0.948 0.929 0.910 0.893 0.875 0.858 0.841 0.825 0.807 0.790 0.773 0.758 0.742 0.725 0.710 0.693 0.678 0.661
Square Edge Orifice
Pressure Ratio 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60
Beta Ratio 0.2 1.000 0.995 0.989 0.982 0.976 0.970 0.964 0.958 0.951 0.945 0.938 0.931 0.925 0.919 0.913 0.906 0.900 0.893 0.887 0.881 0.874 0.867 0.861 0.854 0.848 0.841 0.834 0.827 0.821 0.814 0.809
0.5 1.000 0.993 0.986 0.979 0.972 0.965 0.959 0.953 0.947 0.940 0.932 0.926 0.920 0.913 0.907 0.900 0.894 0.887 0.880 0.874 0.867 0.860 0.854 0.847 0.840 0.833 0.826 0.819 0.812 0.805 0.799
0.6 1.000 0.993 0.986 0.978 0.971 0.964 0.958 0.951 0.945 0.937 0.930 0.923 0.916 0.909 0.902 0.894 0.887 0.880 0.873 0.867 0.860 0.852 0.845 0.837 0.830 0.822 0.815 0.808 0.801 0.794 0.788
0.7 1.000 0.992 0.985 0.977 0.970 0.962 0.956 0.949 0.940 0.932 0.924 0.917 0.910 0.901 0.893 0.885 0.878 0.871 0.863 0.856 0.849 0.841 0.832 0.823 0.815 0.809 0.801 0.793 0.785 0.778 0.771
0.75 1.000 0.993 0.983 0.975 0.968 0.960 0.951 0.943 0.934 0.927 0.920 0.912 0.904 0.896 0.888 0.880 0.871 0.863 0.855 0.848 0.840 0.831 0.822 0.813 0.805 0.798 0.789 0.781 0.773 0.766 0.760
Expansion Factor

Expansion Factor
Expansion Factor for 1.3 Expansion Factor for 1.4

1.000 1.000
0.2
0.950 0.2
0.950
0.5
0.5
0.900 0.6 0.900 0.6 Nozzle or Venturi Meter Specific Heat Ratio
0.7 1.25 1.3 1.35 1.4 1.45 #VALUE!
0.850 0.850 0.7
0.75 1.000 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
0.75
0.800 0.2 0.800 0.2
0.5
0.750 0.750 0.5 Square Edge Orifice Specific Heat Ratio
0.6 1.25 1.3 1.35 1.4 1.45
0.6
0.700 0.7 0.700 1.000 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
0.7
0.650 0.75
0.650 0.75

0.600 0.600
00 06 12 18 24 30 36 42 48 54 60 0 0 .0 6 .1 2 .1 8 .2 4 .3 0 .3 6 .4 2 .4 8 . 5 4
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 0 0 0 0 0 0 0 0
Pressure Ratio Pressure Ratio

Nozzle or Venturi Meter Expansion Factor (Specific Heat Ratio = 1.4 Approximately)
Pressure Ratio 0.00 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
Beta Ratio 0.2 1.000 0.988 0.980 0.970 0.959 0.947 0.935 0.923 0.911 0.900 0.887 0.874 0.862 0.850 0.838 0.825 0.813 0.800 0.786 0.771 0.757 0.741 0.728 0.714 0.701
0.5 1.000 0.988 0.979 0.967 0.954 0.941 0.928 0.916 0.904 0.892 0.879 0.865 0.853 0.841 0.828 0.814 0.802 0.787 0.772 0.759 0.743 0.728 0.713 0.699
0.6 1.000 0.987 0.977 0.963 0.949 0.936 0.921 0.908 0.896 0.884 0.870 0.854 0.841 0.827 0.813 0.799 0.783 0.770 0.757 0.743 0.730 0.716 0.700 0.687
0.7 1.000 0.987 0.974 0.959 0.942 0.927 0.912 0.898 0.882 0.867 0.851 0.835 0.821 0.807 0.791 0.775 0.761 0.748 0.732 0.716 0.702 0.686 0.670
0.75 1.000 0.982 0.967 0.950 0.932 0.917 0.901 0.883 0.868 0.852 0.837 0.820 0.804 0.790 0.773 0.758 0.742 0.727 0.711 0.697 0.681 0.663
Square Edge Orifice
Pressure Ratio 0.00 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
Beta Ratio 0.2 1.000 0.993 0.987 0.982 0.976 0.971 0.966 0.960 0.953 0.949 0.943 0.936 0.931 0.926 0.920 0.914 0.908 0.902 0.895 0.890 0.883 0.876 0.871 0.865 0.860 0.854 0.848 0.842 0.836 0.830 0.823
0.5 1.000 0.994 0.988 0.982 0.976 0.970 0.964 0.958 0.951 0.945 0.938 0.932 0.926 0.920 0.914 0.908 0.902 0.896 0.889 0.882 0.876 0.870 0.863 0.857 0.851 0.845 0.839 0.832 0.825 0.820 0.812
0.6 1.000 0.994 0.988 0.981 0.975 0.969 0.963 0.957 0.949 0.943 0.936 0.929 0.923 0.916 0.909 0.902 0.896 0.890 0.883 0.876 0.870 0.862 0.856 0.850 0.842 0.836 0.829 0.822 0.816 0.809 0.802
0.7 1.000 0.993 0.986 0.979 0.972 0.965 0.959 0.952 0.944 0.938 0.930 0.924 0.917 0.910 0.903 0.895 0.888 0.881 0.873 0.865 0.859 0.851 0.843 0.837 0.829 0.821 0.815 0.808 0.802 0.797 0.789
0.75 1.000 0.992 0.984 0.978 0.970 0.961 0.954 0.947 0.939 0.932 0.925 0.918 0.911 0.904 0.896 0.889 0.880 0.871 0.864 0.857 0.850 0.841 0.834 0.826 0.819 0.811 0.805 0.798 0.790 0.782 0.773
C ritical Pressu re R atio

Critical Pressure Ratio Chart

0.6500

0.6300 0.00
0.20
0.6100 0.40
0.50
0.5900 0.60
Critical Pressure Ratio 0.65
Specific Heat Ratio 1.250 1.275 1.300 1.325 1.350 1.375 1.400 1.425 1.450 0.5700
0.70
Beta Ratio 0.00 0.5550 0.5505 0.5455 0.5410 0.5361 0.5320 0.5280 0.5240 0.5200
0.20 0.5550 0.5505 0.5455 0.5412 0.5368 0.5331 0.5294 0.5256 0.5220 0.5500 0.75
0.40 0.5580 0.5540 0.5495 0.5450 0.5405 0.5365 0.5325 0.5284 0.5245 0.80
0.50 0.5630 0.5585 0.5540 0.5495 0.5450 0.5407 0.5364 0.5320 0.5280 0.5300 0.85
0.60 0.5719 0.5677 0.5634 0.5587 0.5545 0.5500 0.5460 0.5421 0.5380
0.65 0.5782 0.5740 0.5696 0.5650 0.5608 0.5561 0.5518 0.5479 0.5440 0.5100
1.250

1.275

1.300

1.325

1.350

1.375

1.400

1.425

1.450

0.70 0.5870 0.5831 0.5790 0.5750 0.5704 0.5660 0.5620 0.5580 0.5540
0.75 0.6010 0.5961 0.5920 0.5879 0.5837 0.5791 0.5750 0.5710 0.5670
0.80 0.6170 0.6132 0.6090 0.6050 0.6010 0.5970 0.5932 0.5890 0.5850
Specific Heat Ratio
0.85 0.6410 0.6370 0.6329 0.6290 0.6254 0.6218 0.6180 0.6140 0.6100

374776812.xls Crane Data Tables 12/18/2017

Square Edge Orifice
Reynolds Number 3 4 6 8 10 14 20 28 40 60 80 101 141 200 286 400 483 600 800 1000 1414 1682 2000 2378 2828 3364 4000 4828 6000 8000 10000 14142 20000 22071 30000 40000 60000 80000 100000
0.20 0.536 0.568 0.608 0.632 0.651 0.673 0.689 0.696 0.698 0.696 0.689 0.682 0.670 0.655 0.642 0.631 0.623 0.617 0.607 0.602 0.599 0.598 0.597 0.596 0.595 0.594 0.593 0.593 0.594 0.595 0.596 0.598 0.598 0.598 0.598 0.598 0.598 0.598 0.598
0.30 0.479 0.521 0.570 0.600 0.625 0.652 0.674 0.697 0.703 0.705 0.703 0.700 0.690 0.679 0.664 0.652 0.643 0.635 0.626 0.619 0.610 0.608 0.607 0.606 0.605 0.605 0.605 0.605 0.605 0.603 0.602 0.601 0.600 0.600 0.600 0.600 0.599 0.599 0.599
0.40 0.439 0.482 0.539 0.576 0.606 0.636 0.658 0.684 0.701 0.709 0.711 0.712 0.710 0.702 0.690 0.676 0.666 0.656 0.646 0.638 0.628 0.624 0.619 0.617 0.616 0.615 0.614 0.614 0.615 0.613 0.612 0.611 0.610 0.609 0.609 0.608 0.608 0.607 0.607
Beta Ratio 0.50 0.392 0.438 0.498 0.546 0.579 0.618 0.652 0.690 0.718 0.735 0.744 0.749 0.752 0.752 0.748 0.738 0.730 0.721 0.709 0.701 0.690 0.685 0.678 0.673 0.667 0.660 0.654 0.648 0.642 0.637 0.633 0.630 0.629 0.628 0.627 0.626 0.625 0.624 0.623
0.60 0.362 0.409 0.472 0.518 0.552 0.598 0.650 0.705 0.747 0.776 0.793 0.800 0.808 0.813 0.815 0.812 0.807 0.799 0.788 0.778 0.760 0.750 0.738 0.728 0.719 0.711 0.702 0.695 0.687 0.678 0.670 0.664 0.660 0.659 0.658 0.657 0.655 0.654 0.654
0.65 0.342 0.396 0.458 0.498 0.534 0.600 0.655 0.720 0.766 0.807 0.836 0.851 0.865 0.872 0.873 0.872 0.868 0.863 0.855 0.844 0.825 0.813 0.798 0.785 0.771 0.756 0.743 0.733 0.720 0.708 0.700 0.690 0.683 0.683 0.682 0.680 0.678 0.676 0.675
0.70 0.312 0.372 0.438 0.492 0.538 0.600 0.658 0.728 0.786 0.843 0.876 0.906 0.927 0.941 0.948 0.951 0.952 0.951 0.948 0.936 0.911 0.892 0.865 0.844 0.821 0.800 0.787 0.771 0.756 0.741 0.731 0.721 0.716 0.715 0.713 0.711 0.707 0.705 0.703
0.75 0.275 0.342 0.424 0.489 0.540 0.602 0.668 0.750 0.817 0.889 0.937 0.972 1.004 1.026 1.041 1.050 1.054 1.055 1.055 1.052 1.034 1.009 0.980 0.948 0.907 0.869 0.842 0.821 0.800 0.783 0.773 0.764 0.760 0.759 0.757 0.754 0.750 0.748 0.746
0.80 0.275 0.342 0.425 0.489 0.548 0.622 0.700 0.783 0.875 0.964 1.033 1.089 1.137 1.173 1.204 1.226 1.234 1.240 1.240 1.240 1.232 1.226 1.216 1.185 1.069 0.986 0.940 0.905 0.878 0.856 0.844

Flow Coefficient for Square Edge Orifices Flow Coefficient for Nozzles

1.300

Flow Coefficient
0.20 0.20
Flow Coefficient

1.200 1.170
0.30 0.30
1.100 0.40
0.40
1.120 0.45
1.000
0.50
0.50
0.900 0.55
1.070 0.575
0.800
0.60 0.60

0.700 0.65 0.625

1.020
0.65
0.70
0.600
0.675

0.500 0.970 0.70

0.75
0.725
0.400 0.80 0.75

0.300 0.920

100000
1000

10000

1000000

10000000
10

100

10000

10000000
1

1000

100000

1000000

Reynolds Number Reynold's Number

Nozzles
Reynolds Number 2000 3000 4000 5000 6000 7047 8000 9000 10233 14142 20000 30000 40000 50000 60000 70000 80000 91622 100000 141421 200000 300000 400000 500000 595662 676083 800000 900000 1000000 1414214 2000000
0.20 0.930 0.943 0.951 0.956 0.960 0.963 0.966 0.968 0.970 0.975 0.978 0.982 0.984 0.987 0.989 0.990 0.990 0.991 0.991 0.992 0.994 0.996 0.997 0.997 0.997 0.997 0.997 0.998 0.998 0.998 0.998
0.30 0.934 0.943 0.949 0.954 0.958 0.961 0.963 0.966 0.971 0.976 0.981 0.984 0.987 0.989 0.990 0.991 0.991 0.991 0.993 0.995 0.996 0.997 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.998
0.40 0.942 0.949 0.955 0.959 0.963 0.967 0.970 0.977 0.981 0.987 0.991 0.993 0.995 0.996 0.997 0.998 0.998 1.000 1.002 1.004 1.006 1.006 1.007 1.008 1.008 1.008 1.008 1.008 1.008
0.45 0.946 0.955 0.962 0.967 0.971 0.974 0.978 0.984 0.989 0.995 0.999 1.001 1.002 1.003 1.004 1.005 1.006 1.009 1.011 1.013 1.014 1.015 1.016 1.017 1.017 1.017 1.017 1.017 1.017
0.50 0.960 0.967 0.973 0.977 0.980 0.984 0.991 0.997 1.003 1.007 1.010 1.012 1.014 1.015 1.016 1.017 1.019 1.020 1.023 1.024 1.025 1.025 1.026 1.026 1.026 1.026 1.026 1.026
Beta Ratio 0.55 0.973 0.980 0.985 0.989 0.993 0.996 1.003 1.010 1.017 1.021 1.025 1.028 1.030 1.031 1.032 1.033 1.035 1.037 1.040 1.041 1.042 1.042 1.043 1.043 1.043 1.044 1.044 1.044
0.575 0.992 0.997 1.001 1.006 1.013 1.020 1.027 1.032 1.035 1.038 1.039 1.040 1.041 1.042 1.044 1.046 1.048 1.050 1.050 1.050 1.051 1.051 1.051 1.051 1.051 1.051
0.60 1.002 1.007 1.011 1.016 1.024 1.030 1.038 1.043 1.046 1.048 1.050 1.051 1.053 1.053 1.056 1.059 1.060 1.061 1.062 1.063 1.063 1.064 1.064 1.064 1.064 1.064
0.625 1.020 1.024 1.028 1.037 1.044 1.051 1.056 1.059 1.061 1.063 1.064 1.065 1.066 1.069 1.071 1.074 1.076 1.077 1.078 1.079 1.079 1.079 1.080 1.080 1.080
0.65 1.037 1.042 1.052 1.061 1.068 1.073 1.076 1.078 1.080 1.081 1.082 1.083 1.086 1.089 1.092 1.093 1.094 1.095 1.096 1.096 1.097 1.097 1.097 1.097
0.675 1.059 1.070 1.080 1.088 1.092 1.095 1.098 1.100 1.101 1.102 1.103 1.106 1.109 1.111 1.113 1.114 1.114 1.115 1.115 1.116 1.116 1.116 1.116
0.70 1.080 1.091 1.101 1.110 1.115 1.119 1.121 1.123 1.124 1.125 1.126 1.129 1.132 1.134 1.136 1.137 1.138 1.139 1.140 1.140 1.140 1.140 1.140
0.725 1.107 1.119 1.127 1.135 1.140 1.144 1.146 1.148 1.150 1.151 1.152 1.155 1.158 1.161 1.163 1.164 1.165 1.166 1.166 1.167 1.167 1.167 1.167
0.75 1.138 1.150 1.159 1.169 1.174 1.177 1.180 1.182 1.184 1.185 1.186 1.190 1.193 1.195 1.197 1.198 1.199 1.199 1.200 1.200 1.200 1.200 1.200

374776812.xls Crane Data Tables 12/18/2017

200000 400000 600000 800000 1000000
0.598 0.598 0.598 0.598 0.598
0.599 0.599 0.599 0.599 0.599
0.606 0.606 0.606 0.606 0.606
0.621 0.620 0.620 0.620 0.620
0.652 0.651 0.651 0.651 0.651
0.673 0.671 0.671 0.670 0.670
0.703 0.701 0.700 0.700 0.700
0.742 0.740 0.739 0.738 0.738

374776812.xls Crane Data Tables 12/18/2017

 374776812.xls

ORIFICE FLOW CALCULATIONS - NATURAL GAS - AGA Report No 3, Part 1 - Sept 1990

1.6 Orifice Flow Equation

qm=Cd*Ev*Y*(pi()/4)*d^2*sqrt(2*gc*D*dP) qm=mass flow rate

gc=dimensional conversion constant
or qm=N1*Cd*Ev*Y*d^2*sqrt(D*dP) N1=unit conversion factor see 1.11
Cd=orifice plate coefficient of discharge empirical
CALCULATION INCOMPLETE - DENNIS KIRK
(for incompressible fluids at STP - Y=1.00000)
Ev=velocity of approach factor
Y=expansion factor empirical
(STP=15.56 degC, 1 atmosphere[101.3 kPa]) d=orifice plate bore (at Tf)
D=density of fluid (at Pf,Tf)
dP=orifice differential pressure
qv=qm/D qv=volumetric flow rate at flowing conditions actual
Qv=qm/Db Qv=volumetric flowrate at base conditions at STP
Db=density of fliud at base conditions (STP)

1.6.1 Velocity of Approach Factor (Ev)

Ev=1/(sqrt(1-B^4)) B=orifice plate beta ratio

B=d/D1 D1=meter tube I.D. (at Tf)

1.6.2 Orifice Plate Bore (d)

d=dr*[1+a1*(Tf-Tr)] dr=reference orifice plate bore diameter at Tr

a1=coefficient of thermal expansion of orifice
Tf=flowing temperature of fluid
use 20 deg C Tr=reference temp of orifice plate bore diameter

Pt 2, 2.4.3 dr=dm*[1+a1*(Tr-Tm)] dm=orifice plate bore measured diameter at Tm

Tm=orifice plate bore measurement temperature

1.6.3 Meter Tube Internal Diameter D1)

D1=Dr*[1+a2*(Tf-Tr)] Dr=reference meter tube internal diameter at Tr

a2=coefficient of thermal expansion of meter tube
Pt 2, 2.5.1.2.5 Dr=Dm*[1+a2*(Tr-Tm)] Dm=meter tube measured I.D. at Tm
Tm=meter tube I.D. measurement temperature

Coefficients of Thermal Expansion limitations deg C deg F

Carbon Steel 0.0000112 mm/mm.degC -21.7 67.8 -7 154
Stainless Steel 304, 316 0.0000167 mm/mm.degC -73.3 148.9 -100 300
Monel 0.0000143 mm/mm.degC -73.3 148.9 -100 300

1.7.2 Empirical Coefficient of Discharge for Flange Tapped Orifice Meters (Cd(FT))

Cd(FT)=Ci(FT)+0.000511*[1e6*B/Re]+(0.0210+0.0049*A)*B^4*C Cd(FT)=coeff of discharge at specified pipe Re for flange tapped orifice

Ci(FT)=coeff of discharge at infinite pipe Re for flange tapped orifice
Ci(FT)=Ci(CT)+Tap Term Ci(CT)=coeff of discharge at infinite pipe Re for corner tapped orifice
e=2.71828 Naperian constant
Ci(CT)=0.5961+0.0291*B^2-0.2290*B^8+0.003*(1-B)*M1 L1=correction for tapping location=L2=N4/D1 for flange taps
N4=1.0 for D1 in inches,=25.4 when D1 in millimeters
Tap Term=Upstrm+Dnstrm Re=pipe Reynolds number

Upstrm=[0.043+0.0712*e^(-8.5*L1)-0.1145*e^(-6.0*L1)](1-0.23*A)*B1

Dnstrm=-0.0116*[M2-0.52*M2^1.3]*B^1.1*(1-0.14*A)

B1=B^4/(1-B^4)

M1=max(2.8-D1/N4,0)

M2=2*L2/(1-B)

A=[19000*B/Re]^0.8

C=[1e6*B/Re]^0.35

1.7.3 Reynolds Number (Re)

Re=4*qm/(pi()*u*D1) u=absolute viscosity

N2=unit conversion factor see 1.11
or Re=N2*qm/(u*D1) pi()=3.14159, universal constant

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1.7.4.1 Flow shall be subsonic through the orifice and meter tube

1.8 Empirical Expansion Factor (Y)

Y=Cd1/Cd2 Cd1=coeff of discharge from compressible fluids tests

Cd2=coeff of discharge from incompressible fluids tests

Validity criteria 0<dP/N3/Pf1<0.20 Pf=absolute static pressure at the pressure tap

0.8<Pf1/Pf2<1.0 Pf1=absolute static press at upstream tap
Pf2=absolute static press at downstream tap
N3=unit conversion factor

1.8.1 Upstream Expansion Factor (Y1)

Y1=1-(0.41+0.35*B^4)*x1/k x1=ratio of differential press to abs static press at upstream tap

k=isentropic exponent
x1=dP/N3/Pf1 from upstream static press x1/k=upstream acoustic ratio
Y1=expansion factor based on absolute static upstream press
or x1=dP/(N3*Pf2+dP) from downstream static press

1.8.2 Downstream Expansion Factor (Y2)

Y2=Y1*sqrt((Pf1*Zf2)/(Pf2/Zf1)) Y2=expansion factor based on absolute static downstream press

Zf1=fluid compressibility at upstream tap
or Y2=[1-(0.41+0.35*B^4)*x1/k]*sqrt((Pf1*Zf2)/(Pf2*Zf1)) Zf2=fluid compressibility at downstream tap

x1=dP/(N3*Pf1) upstream press measured

or x1=dP/(N3*Pf2+dP) downstream press measured

1.9.2 Meter Correction Factor (MF)

MF=qmp/qmi qmp=mass flow from master meter

qmi=mass flow indicated by orifice being calibrated
qmi=qvi*D qvi=volumetric flowrate indicated by meter being calibrated

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1.1 Fluid Physical Properties

Viscosity (u) absolute viscosity of fluid at flowing conditions

for flow at high Re viscosity variations may be ignored

for flow at low Re viscosity variations with Pf, Tf need to be evaluated

Density (Dtp, Db)

from composition data determine Db

use equations of state to calculate Dtp
temperature changes from upstream tap, downstream tap and thermowell may be ignored

Isentropic Exponent (k)

Pf/Dtp^k=Constant isentropic expansion of an ideal gas

k at base conditions may normally be used for all Tf, Pf

1.11 Unit Conversion Factors

1.11.1 Orifice Flow Equation (N1)

IP Units SI Units US Units US Units US Units Metr Units Metr Units

pi() 3.141593 3.141593 3.14159 3.14159 3.14159 3.14159 3.14159
gc 32.174 NA 32.174 32.174 32.174 NA NA lbm-ft/(lbf-sec2)
gc NA 1 NA NA NA 1 1 kg*m/(N*sec2)
d Feet Meters Inches Inches Inches mm mm
dP lbf/ft2 Pa lbf/ft2 in H2O# in H2O## mbar kPa
Dtp lbm/ft3 kg/m3 lbm/ft3 lbm/ft3 lbm/ft3 kg/m3 kg/m3
Db lbm/ft3 kg/m3 lbm/ft3 lbm/ft3 lbm/ft3 kg/m3 kg/m3
qm lbm/sec kg/sec lbm/sec lbm/sec lbm/sec kg/sec kg/sec
qv ft3/sec m3/sec ft3/sec ft3/sec ft3/sec m3/sec m3/sec
Qv Sft3/sec Nm3/sec Sft3/sec Sft3/sec Sft3/sec Nm3/sec Nm3/sec
N1 6.30025 1.11072 0.525021 0.0997424 0.0997019 3.51241E-4 3.51241E-5

#-H2O 60 ##-H2O 68

1.11.2 Reynolds Number Equation (N2)

IP Units SI Units US Units US Units Metr Units Metr Units

qm lbm/sec kg/sec lbm/sec lbm/sec kg/sec kg/sec
pi() 3.14159 3.14159 3.14159 3.14159 3.14159 3.14159
u lbm/ft-sec kg/m*sec Centipoise Poise Centipoise Poise
D Feet Meters Inches Inches mm mm
N2 1.27324 1.27324 22737.5 227.375 127324 12732.4

1.11.3 Expansion Factor Equation (N3)

IP Units SI Units US Units US Units US Units Metr Units Metr Units Metr Units
dP lbf/ft2 Pa lb/in2 in H2O# in H2O## kPa mbar mbar
P lbf/ft2 Pa lb/in2 lb/in2 lb/in2 MPa Bar MPa
N3 1 1 1 27.707 27.73 1000 1000 0.01

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flange tapped orifice

nge tapped orifice
ner tapped orifice

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nstream press

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ORIFICE PLATE FLOW CALCULATION:

Crane Flow of Fluids (p 2-14, 3-26, 4-15, A-20)

q=Y.C.A.Sqrt((2.dP/p) q = Rate of Flow m3/sec 0.054314 195.5293

Y = Nett Expansion Factor 0.93
CALCULATION INCOMPLETE - DENNIS KIRK
C = Orifice Flow Coefficient 1.02
A = Orifice Open Area m2 0.000491
dP = Orifice Pressure Drop Pa 80000
p = Upstream Fluid Density kg/m3 11.76

R = Specific Gas Constant 1.89

Sg = Specific Gravity 1.529
Specific Heat Ratio 1.3
Pipe Diameter 52.5 mm
Orifice Diameter 25 mm
Diameter Ratio 0.4762
Upstream Pressure 700 kPag
Downstream Pressure 620 kPag
Pressure Ratio 0.0998
Temperature 90 deg C
363 deg K

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RK

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