FORMULAS, CONVERSIONS & GUIDELINES
FORMULAS FOR VALVE SIZING
Control Valve Sizing for Saturated Steam
The following formulas for Valve Sizing are based on ISA Standard 75.01.01-2007 (60534-2-1 Mod). The formulas assume pipe sizes equal to the size of the valve ports, with no attached fittings. Cv = Valve Flow Coefficient g = Heat Capacity Ratio for Steam = 1.3 (0-300 psig) D P = Pressure Drop = P 1 - P 2
F g = Heat Capacity Ratio Factor for Steam = g/ 1.4 = 1.3/1.4=0.93
x = Pressure Drop Ratio = D P/P 1 D P c r = Critical Pressure Drop x T = Critical Pressure Drop Ratio for Air x cr = Critical Pressure Drop Ratio for Steam
P 1 = Absolute Inlet Pressure (psia) P 2 = Absolute Outlet Pressure (psia) W = Saturated Steam Flow (lbs/hr) T 1 = Steam Inlet Temperature (˚R) (see table) Z 1 = Steam Compressibility Factor (see table)
= D P c r / P 1 = F g x T = 0.93 x T
Cv = For Critical Flow W
For Sub-critical Flow
W
Cv =
x cr /(T 1 Z 1 )
82 P 1 (1 – x /3 x cr )
x /(T 1 Z 1 )
54.6 P 1
When D P / P 1 < x cr : x = D P / P 1
When D P / P 1 > x cr
For single-ported globe valve with flow-to-open seating arrangement: x T = 0.72 x cr = 0.93 x T = 0.67
W
W
Cv =
Cv =
82 P 1 (1 – x /2)
54.6 P 1
x /(T 1 Z 1 )
0.67/(T 1 Z 1 )
When D P / P 1 < 0.67
When D P / P 1 > 0.67
Saturated Steam Table
Example: Determine the Cv Value for a Control Valve with 60 psig Inlet Steam Pressure, and 30 psig Outlet Pressure with a Flow Rate of 4,000 lbs/hr. W = 4,000 lbs/hr
P 1 psig
P 1 psia
T 1 ( R)
Z 1
0
14.7 24.7 34.7 44.7 54.7 64.7 74.7 84.7 94.7
672 699 718 734 746 757 767 776 784 791 798 804 810 815 821 826 830 835 839 843 848 851 855 859 862 866 869 872 875 879 882
0.985 0.978 0.973 0.968 0.963 0.959 0.955 0.951 0.947 0.943 0.940 0.936 0.933 0.930 0.927 0.923 0.920 0.917 0.915 0.912 0.909 0.906 0.903 0.901 0.898 0.895 0.893 0.890 0.888 0.885 0.883
10 20 30 40 50 60 70 80 90
P 1 = 60 psig = 74.7 psia P 2 = 30 psig = 44.7 psia D P = 30 psi x = D P / P 1 = 30/74.4 = 0.40 x cr = 0.93 x T = 0.93 x 0.72 = 0.67 Since x < x cr flow is sub-critical T 1 = 767 (from table)
104.7 114.7 124.7 134.7 144.7 154.7 164.7 174.7 184.7 194.7 204.7 214.7 224.7 234.7 244.7 254.7 264.7 274.7 284.7 294.7 304.7 314.7
100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
W
Cv =
82 P 1 (1 – x /2) When D P / P 1 < 0.67
x /( T 1 Z 1 )
4,000
Cv =
82 (74.7)(1 – 0.4/2)
0.4/(767 x 0.955)
= 4,000 = 35 114.6
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