Flow Coefficients and Computations

Flow Coefficients and Computations

The pipe size in the system ordinarily will determine the valve size. However, to assure accurate throttling or positioning, it is advisable to calculate the valve size. Formulas for liquid and gas are as follows:

Liquid Flow Formula*

Cv = Qa sg/P Qa = Cv P/sg P = sg(Qa/Cv)?

Gas Flow Formula*

Cv = Q/1360 sg(T)/P 2/(P1+P2) Q = 1360 Cv P/sg(T) (P1+P2)/2 P = P1?P1??(sg?T)(Q/[963?Cv])?

* Fluid Controls Institute Inc Standard FCI 62-1 ** SCFH (standard cubic foot per hour) of gas is measured

at 60? F (519.7R) and 14.696 psia. CFH (cubic foot per hour) is measured at any temperature and pressure.

Conversion of CFH to SCFH

SCFH = (Pactual /14.696) ? (519.7?R / Tactual) ? CFHactual

Note: The design of the Straightway Valves are not conducive to good throttling characteristics. Important In general, any reduction in outlet pressure below half the absolute inlet pressure will give no further increase in flow. The value of the ratio of pressure at which maximum flow is obtained varies somewhat depending on the actual fluid.

Where: Cv = Flow Coefficient (gpm/P) sg = Specific Gravity Qa = Actual Flow (gpm) P = Actual Pressure Drop P1?P2 (psi)

Where: Q = Volumetric flow (SCFH)** sg = Specific gravity T = Absolute Flowing Temperature (?F+460) P1 = Inlet Pressure (psia) P2 = Outlet pressure (psia) P = Pressure drop (P1?P2) Cv = Valve Coefficient from Tables

Where: SCFH = Standard cubic feet per hour Pactual = Pressure of gas in psia Tactual = Temperature of gas (?F+460)

5 71 0 09/15 Dia-Flo? Diaphragm Valves

Sec 5: Tech Data

Flow Coefficients and Computations

Example Flow Computations

(flow at pressure drop of 1 psi)

Weir Valves

Problem: Find the rate of flow of water through a 1?" unlined cast iron flanged valve, half open, with a pressure drop of one psi.

Solution: From the `Flanged End ? Unlined' Weir Cv Table, the corresponding rate of flow is 42 gpm.

Problem: Find the valve position of 2?" `Glass Lined valve table', with a water flow of 170 gpm and a pressure drop of 1 psi.

Solution: From the `Glass Lined' valve table the corresponding valve position is 70% open.

Problem: Determine the flow in cubic feet per hour of air through a wide open 2 inch unlined valve. Inlet pressure at 60 psig, outlet pressure at 40 psig, and temperature at 60? F.

Q = (1360) (70) 20/520 (74.7+54.7)/2 Q = 150,400 SCFH

Problem: Find the rate of flow of water through a 2?" soft rubber lined valve, half open with a pressure drop of 3 psi.

Solution: From `Flanged End ? Unlined' Weir Cv Table

Cv = 85 gpm Qa = 85 3 Qa = 147 gpm

Straightway Valves

Problem: Find the rate of flow of water through a 1?" unlined flanged valve, half open, with a pressure drop of 1 psi.

Solution: From Cv Table, the corresponding rate of flow is 72 gpm.

Problem: Find the valve position of a 2?" rubber lined valve, with a water flow of 285 gpm and a pressure drop of 1 psi.

Solution: From Cv Table, the corresponding valve position is 70% open.

Problem: Find valve size and valve position of an unlined valve, with flow at 200 gpm and an actual pressure drop of 5 psi for a liquid with a specific gravity of 1.8.

Solution: Cv =200 1.8/5 = 200 .36 = (200)(0.6) = 120 From Cv Table: A 2" valve has a Cv of 120 at 40% open.

Problem Determine the flow in cubic feet per hour of air through a wide open 2" unlined valve. Inlet pressure at 60 psig, outlet pressure at 40 psig, and temperature at 60? F.

Solution: From Cv Table: Cv = 275 Q = 1360 (275) 20/([1][520]) (74.7+54.7)/2

= 374,000 .04 64.7 = 374,000 ? 1.61 Q = 602,140 Standard Cubic Feet per Hour

Problem: Find the rate of flow of water through a 2?" #5 rubber lined valve, full open, with a pressure drop of 3 psi.

Solution: From Cv Table, Cv = 365 Qa = 365 3 or 632 gpm

Problem: Find the pressure drop across a 1?" plastic lined valve 100% open with water flow of 63 gpm

Solution From Cv Table, Cv = 80 P = (63/80)? = 0.62 psi

Dia-Flo? Diaphragm Valves 5 72 0 09/15

Sec 5: Tech Data

Flow Coefficients and Computations

Fluid velocity is a very important design consideration when selecting diaphragm valves. As mentioned previously velocity should be limited to 15?20 fps for clean fluids and 8?10 fps for slurries. Velocity through a Dia-Flo? weir type diaphragm valve can be determined by using the following equation:

V = .321 (Q/A)

Where: V = Velocity in feet per second Q = Flow in gallons per minute A = Area in square inches at the point of greatest restriction (from table below)

Valve Size

/1 2 /3 4 1* 11/4,11/2 2 21/2 3 4 6 8 10 12

10 .03 .06 .09 .23 .38 .55 .84 1.37 3.0 5.8 8.4 11.8

20 .06 .11 .18 .43 .73 1.05 1.60 2.62 5.7 11.2 16.1 22.6

Area Over the Weir for Standard Weir Valves (Square Inches)

30 .08 .16 .26 .62 1.05 1.51 2.30 3.76 8.1 16.1 23.1 32.4

40 .10 .20 .33 .79 1.33 1.93 2.93 4.81 10.4 20.5 29.5 41.4

% OPEN

50

60

.12

.14

.24

.28

.40

.46

.95

1.11

1.61

1.87

2.33

2.71

3.53

4.11

5.78

6.73

12.5

14.5

24.7

28.7

35.5

41.3

49.8

58.0

70 .16 .31 .52 1.24 2.10 3.05 4.62 7.57 16.3 32.3 46.5 65.2

80 .18 .34 .57 1.37 2.31 3.35 5.08 8.33 18.0 35.5 51.1 71.7

90 .19 .37 .62 1.48 2.50 3.62 5.50 9.01 19.5 38.4 55.3 77.5

100 .20 .39 .65 1.56 2.64 3.83 5.81 9.51 20.5 40.6 58.4 81.9

Sec 5: Tech Data

Valve Size 1"* 11/2" 2" 21/2" 3" 4" 6"

10 .06 .10 .14 .14 .30 .60 1.54

20 .11 .21 .22 .39 .65 1.14 2.30

Area Over the Weir for DualRange? Valves (Square Inches)

30 .14 .28 .37 .63 .98 1.62 4.01

40 .18 .34 .63 .88 1.29 2.63 6.63

% OPEN

50

60

.25

.31

.44

.59

.98

1.26

1.31

1.86

1.94

2.51

4.01

4.92

9.43

11.68

70 .38 .80 1.57 2.27 3.35 5.95 13.79

* Includes all 3/4" flanged valves except solid plastic

80 .49 1.00 1.91 2.67 3.99 6.81 15.84

90 .62 1.22 2.11 3.25 4.65 7.85 17.90

100 .65

1.56 2.64 3.83 5.81 9.51 20.50

5 73 0 09/15 Dia-Flo? Diaphragm Valves

Flow Coefficients and Computations

Weir Valve Cv Ratings

%%

FlangFeldanEgnedd?EUndnli?nUednlined

open op1e/2n 3/14/?2 1 31/41/?41& 111//42 & 121/2 221/2 213/2 34 46 68 810 1012 12

10 100.5 03.5 3 11 1112 1127 1370 3309 13095 120050 203020 325050 550

20 200.7 07.7 7 21 2126 2461 4515 5952 29120 24100 406055 659550 950

30 310.0 11.10 1129 2939 3698 6885 18455 134155 351755 5170500 10102075 1275

40 410.5 11.45 1436 3649 4990 19105 121050 240105 47150 7153000 13106000 1600

50 520.0 21.80 1842 4256 15165 111355 123655 246850 49800 9104050 14158075 1875

60 630.0 32.0 2046 4662 16420 114505 125855 258250 592705 9176525 16221500 2100

70 730.5 32.15 2150 5066 16560 115605 126950 259500 1505500 10157025 17222550 2250

80 840.0 42.20 2252 5269 16595 115755 137050 350700 1517205 11127575 17273575 2375

90 950.0 52.20 2254 5470 17600 116805 138055 350950 1519705 11178500 18204075 2475

100 1050.5 52.25 2256 5670 17600 116900 139100 361000 162000 12108000 18205050 2550

% % FlangFeldanEgnedd?EPnldas?tiPclaLisntiecdL(inexecdep(etxPceFAp)t PFA) open o3/p4?e1n 31/41?/41& 1111//24 & 121/2 21/2 231/2 34 46 68 8

10 130 3 5 5 10 1107 1470 4600 16005 103590 390 20 250 5 15 15 23 2430 4700 17200 122605 26500 600 30 370 7 25 25 37 3671 16010 110700 147000 407040 740 40 480 8 31 31 50 5802 18220 122100 251005 508530 830 50 590 9 36 36 65 6954 19440 124405 254855 589500 900 60 610 1038 38 68 6988 19580 125605 266350 639060 960 70 7101 1139 39 69 699 19690 126800 268700 617000 1000 80 8101 1140 40 69 16090 110700 127805 268850 6180040 1040 90 910 1039 39 69 16090 110705 127950 269805 6180560 1060 100 1010 1038 38 67 16070 110705 127855 268950 6190070 1070

%% open ope1/n2

10 100.2 20 200.4 30 300.7 40 410.2 50 510.5 60 620.0 70 720.4 80 820.8 90 930.4 100 1040.0

FlangFeldanEgnedd?EHndar?d HRaurbdbRerubLibneerdLined 3/41?/21 3/141?/14 & 111//42 &211/2 221/2 21/2 3 3 4 4 6 6 8 810 1012 12 02.2.9 2.912 1125 1250 2031 3146 41650 150225 223520 324000 400 05.4.4 5.422 2320 3305 3557 51705 102575 275450 456055 657550 750 08.7.2 8.226 2460 4500 5075 71560 163075 375650 6150000 10101025 1125 1.121 1128 2485 4655 6593 92310 214075 475800 8103000 13104025 1425 1.153 1329 2590 5800 81010 112020 225050 550900 9104025 14127500 1700 2.103 1329 2594 5940 91030 132030 236000 600975 9175550 15159000 1900 2.143 1330 3600 1600 101045 142545 246510 6110050 10156050 16250075 2075 2.182 1230 3600 16100 111055 152550 256020 6210075 10177500 17202000 2200 3.141 1131 3519 15195 111560 162060 266025 6215125 11127550 17253000 2300 4.100 1031 3515 15155 111560 162060 266025 6215150 11157050 17253050 2350

Cv rating

Rate of flow depends upon the pressure drop. Cv is the amount of flow in gallons per minute through a valve which results in a 1 psi pressure drop. Throttling characteristics are shown in the same manner with Cv's at various openings. Use formula shown below to compute actual flow at various pressure drops.

Actual Flow (gpm) = Cv P/sg

%% open op1e/2n

10 100.5 20 200.5 30 300.7 40 410.0 50 510.0 60 610.5 70 720.0 80 820.0 90 920.0 100 1020.0

FlangFeldanEgnedd?ESnodft? RSuobftbRerubLibneerdLined 3/1/42?1 13/1/44?1& 111//42 & 211/2 21/2 21/32 3 4 4 6 6 8 8 10 1012 12 02.5.0 2.012 1126 1620 2027 2755 51510 110225 223520 324000 400 03.5.1 3.119 1296 2640 4048 41805 102525 225450 456055 657550 750 04.7.5 4.523 235 355 5566 61655 153530 330650 6150000 10101025 1125 15.0.5 5.525 2456 4670 7083 81395 194530 430800 8103000 13104025 1425 16.0.2 6.226 2561 5185 81500 102020 224065 465900 9104025 14127500 1700 16.5.9 6.926 2563 5395 91517 112730 234080 480975 9175550 15159000 1900 27.0.1 7.126 2564 51405 101533 132335 234595 4915050 10156050 16250075 2075 27.0.2 7.226 2564 51410 111044 142440 24505 5015075 10177500 17202000 2200 27.0.1 7.125 252 51210 111050 152045 245510 5110125 11127550 17253000 2300 27.0.0 7.025 250 51010 111055 152550 25015 5115150 11157050 17253050 2350

%% open open 1" 1"

10 10 1.0 1.0 20 20 1.4 1.4 30 30 2.7 2.7 40 40 4.7 4.7 50 50 7.3 7.3 60 60 10 10 70 70 11 11 80 80 11 11 90 90 11 11 100 100 12 12

FlangFeldanEgnedd?EPnFdA?LPinFeAdLined

1.5" 1.5" 2" 2" 3 " 3 "

3.1 3.1

9 9 19 19

11 11 25 25 53 53

20 20 47 47 91 91

28 28 47 47 125 125

27 27 52 52 113 113

29 29 56 56 124 124

30 30 60 60 134 134

32 32 60 60 141 141

33 33 60 60 147 147

34 34 61 61 150 150

4" 4" 6" 6" 32 32 68 68 77 77 193 193 125 125 318 318 178 178 479 479 231 231 571 571 288 288 644 644 315 315 684 684 330 330 698 698 356 356 728 728 365 365 738 738

Dia-Flo? Diaphragm Valves 5 74 0 09/15

Sec 5: Tech Data

Flow Coefficients and Computations

Weir Valve Cv Ratings

%

Glass Lined

open /1 2 /3 4?1 11/4 & 11/2 2 21/2

3

46

8

10 0.5 1.4 10 11 17 24 32 160 280

20 0.7 4.4 19 25 41 60 63 315 560

30 1.0 8.0 27 42 72 100 130 455 840

40 1.5 12 36 56 96 140 200 590 1125

50 2.0 15 45 72 120 180 265 685 1350

60 3.0 19 51 80 150 215 320 760 1525

70 3.0 22 54 83 170 235 365 805 1625

80 3.5 22 55 83 175 240 400 835 1675

90 4.5 22 54 82 180 245 415 845 1700

100 5.5 22 53 78 180 250 420 850 1700

% open

10 20 30 40 50 60 70 80 90 100

/1 2 0.20 0.50 0.90 1.80 2.50 2.90 3.20 3.40 3.60 3.60

/3 4 0.60 2.20 4.00 5.60 7.00 7.70 8.20 8.40 8.70 8.70

1 0.80 3.40 6.20 8.20 10.50 12.80 14.30 15.20 15.80 15.80

Solid Plastic

11/4

11/2

1.20 1.80

4.00 9.20

9.80 16.00

16.00 21.80

20.90 27.20

25.30 31.50

26.40 31.50

27.10 31.50

27.70 31.50

28.40 31.50

2

3" 4"

6.0 19 34

12.20 43 60

24.50 68 82

38.50 92 103

49.50 106 124

57.00 118 144

60.00 122 160

62.60 124 172

64.00 125 179

65.50 125 185

%

open

1/2"

10 0.2

20 0.4

30 0.7

40 1.2

50 1.5

60 2.0

70 2.4

80 2.8

90 3.0

100 3.5

3/4"

1"

11/2"

2.0 3.0 9

3.1 6.0 16

4.5 8.0 24

5.5 10.0 30

6.0 13.0 36

6.4 14.0 40

6.8 16.0 44

7.0 17.0 47

7.2 18.0 48

7.5 18.6 48

Butt Weld 2" 21/2" 3" 12 20 30 26 37 55 39 52 85 49 65 115 56 75 135 62 83 155 66 89 165 69 94 170 70 95 175 70 95 180

4" 6* 8* 32 105 200 70 210 400 130 315 575 200 415 750 265 480 900 290 520 975 320 550 1050 360 570 1125 385 590 1175 400 600 1200

% open

10 20 30 40 50 60 70 80 90 100

Screwed End Metal

/1 2

/3 4

1 11/4 & 11/2

2

0.4 2 3

9

12

0.6 3 6

16

26

1.0 5 8

24

39

1.4 6 10

30

49

1.6 7 12

36

56

2.0 8 14

40

62

2.6 8 16

44

66

3.0 10 17

47

69

3.8 10 18

48

70

4.4 10 19

48

70

21/2

3

20

78

37 110

52 128

65 140

75 146

83 150

89 156

94 161

96 166

95 172

Cv ratings applying to screwed end metal and flanged unlined valves are based on use of cast iron bodies. For socket weld metal bodies, use Buttweld Cv Table.

Sec 5: Tech Data

5 75 0 09/15 Dia-Flo? Diaphragm Valves

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