How to Use Flow Coefficients (Cv) for Hydraulic Fluids
FLUID POWER  Design Data Sheet 17
In case you have forgotten nowtouse the Cv flow coefficient (flow factor) for selecting valve size, this data sheet will review the use of Cv coefficients for hydraulic fluids. Cv information for compressed air is in Data Sheet 22.
Some manufacturers publish Cv coefficients for describing the volume of flow which can be put through their valves without exceeding a certain maximum pressure loss. Cv flow coefficient ratings have several advantages: they provide a means of comparing the flow capacities of different brands of valves; they simplify the job of selecting an adequately sized valve without wasteful oversizing; and they allow the designer to predict with reasonable accuracy just how a newly designed system will perform.
What is the Cv Flow Coefficient? In the U.S. system of units, the Cv coefficient is the number of U.S. gallons per minute of water that will pass through a given orifice area at a pressure drop of 1 PSI. An orifice or valve passage which has a Cv coefficient of 1.00 will pass 1 GPM of water (specific gravity 1.0) with a pressure drop of 1 PSI. To pass 2 GPM of water at the same pressure drop, the valve orifice would have to have a Cv of 2.0, etc.
The definition of Cv is based on water, which has a G (specific gravity) = 1.0. Fluids with other gravities will flow at different rates. For example, heavier fluids will have a greater pressure loss through the same valve passage. The viscosity of the fluid will also affect its flow rate through a valve. Fluids with higher viscosity will have a higher pressure drop than water which has a viscosity of about 35 SSU.
How is Cv Determined for a Valve? The valve manufacturer must determine the Cv coefficients experimentally, by actual test. These tests are usually conducted with water. The published Cv coefficient should then be corrected by the user for specific gravity and viscosity of his fluid.
Table 1  PSI Pressure Drops for Cv Flow Coefficients for a Flow of 1 GPM (Multiply table values times the square of the actual flow through the valve)
Before using this chart, take the published Cv of your valve and correct it (if necessary) for viscosity of your fluid. See details on back side of this sheet. This table plots Cv factors against pressure drop for a flow of 1 GPM through the valve. Find the pressure drop opposite your corrected Cv factor, then multiply this times the square of the flow of 1 GPM. Find the pressure drop at a flow of 16 GPM at the same Cv = 2.20.
0.250 × √162 = 64 PSI
For values of Cv not listed in the table, use this formula for a flow of 1 GPM.
PSI (for 1 GPM flow) = 1 ÷ Cv²
Information in this data sheet is based on a flow equation published by the Fluid Controls Institute. Certain approximations in the formula may cause the results to vary de to pressure conditions, fluids, or valve configurations. The approximate flow equation is:
Cv = GPM × √G ÷ √PSI
Corrected Cv 
PSI Drop per GPM 

Corrected Cv 
PSI Drop per GPM 

Corrected Cv 
PSI Drop per GPM 
0.10 
100 
3.00 
0.111 
7.50 
0.018 
0.15 
44 
3.10 
0.104 
7.75 
0.017 
0.20 
25 
3.20 
0.098 
8.00 
0.016 
0.25 
16 
3.30 
0.092 
8.25 
0.015 
0.30 
11 
3.40 
0.087 
8.50 
0.014 
0.35 
8.16 
3.50 
0.082 
8.75 
0.013 
0.40 
6.25 
3.60 
0.077 
9.00 
0.012 
0.50 
4.00 
3.70 
0.073 
9.50 
0.011 
0.60 
2.78 
3.80 
0.069 
10.0 
0.010 
0.70 
2.04 
3.90 
0.066 
11.0 
0.008 
0.80 
1.56 
4.00 
0.063 
12.0 
0.007 
0.90 
1.24 
4.25 
0.055 
13.0 
0.006 
1.00 
1.00 
4.50 
0.049 
14.0 
0.005 
1.20 
0.694 
4.75 
0.044 
16.0 
0.004 
1.40 
0.510 
5.00 
0.040 
18.0 
0.003 
1.60 
0.391 
5.25 
0.036 
22.0 
0.002 
1.80 
0.309 
5.50 
0.033 
30.0 
0.001 
2.00 
0.250 
5.75 
0.030 
35.0 
0.0008 
2.20 
0.207 
6.00 
0.028 
40.0 
0.0006 
2.40 
0.174 
6.25 
0.026 
45.0 
0.0005 
2.60 
0.148 
6.50 
0.024 
50.0 
0.0004 
2.70 
0.137 
6.75 
0.022 
60.0 
0.0003 
2.80 
0.128 
7.00 
0.020 
70.0 
0.0002 
2.90 
0.119 
7.25 
0.019 
90.0 
0.0001 
HOW TO USE Cv COEFFICIENTS The most common usage of the Cv flow coefficient is to predict the pressure loss to be expected across a valve while fluid is flowing through it. The Cv rating published by the valve manufacturer is used for this determination.
If the Cv is stated in terms of water flow, it must be corrected for viscosity and specific gravity of other fluids. However, if the Cv rating is specifically stated as for a certain fluid and viscosity, this means that adjustments have already been made. The pressure drop in relation to the GPM flow may then be determined directly from Table 1.
If no definite fluid is specified, it can be assumed that the Cv rating is for water flow. Since both the viscosity and specific gravity of a fluid affect the pressure drop through a valve orifice, corrections must be made for all other fluids.
TABLE 2 
SSU Viscosity 
Centistokes 
Factor 
50 
7.5 
6.7 
100 
21 
19 
150 
33 
29 
200 
43 
38 
250 
53 
47 
300 
65 
58 
400 
87 
78 
500 
110 
98 
750 
163 
145 
1,000 
215 
192 
STEP 1. Correction for Viscosity Flow resistance is directly proportional to centistoke viscosity. If valve manufacturer gives the Cv for water flow, fluids with higher viscosity will have higher resistance to flow in proportion to their viscosity, as related to the viscosity of water.
Table 2 was prepared for conversion from water, which has a viscosity of 1.12 centistokes at 60°F, to fluids of higher viscosity. Factors in the third column may be used as dividers to convert a water Cv rating into a corrected Cv at higher viscosities, or may be used as multipliers to find the increase in flow resistance when using a more viscous fluid.
Example: A valve has a published Cv of 5.4 on 60°F water. Find the corrected Cv for a viscosity of 150 SSU. The factor from Table 2 is 29. The flow resistance will be 29 times greater on 150 SSU. The Cv may be adjusted by division: New Cv = 5.4 ÷ 29 = 0.186. Use this in Table 1. To adjust from one SSU to another, from 100 to 150 SSU for example, take the ratio between the two factors:
29 ÷ 19 = 1.53 increase in flow resistance
The viscosity to which you are correcting must be the viscosity at the operating temperature, not the rating at 100°F. No other temperature correction is necessary. No correction is needed for viscosities less than 50 SSU.
STEP 2. Using the Table 1 After correcting the Cv for viscosity in Step 1, go to Table 1 and find the pressure drop for a flow of 1 GPM. Then follow the instructions alongside the table. STEP 3. Correction for Specific Gravity Flow resistance will be approximately in proportion to specific gravity of the fluid. Gravities of hydraulic fluids range from 0.9 for petroleum oil, through 1.00 for water, up to 1.20 for synthetic fluids. If the published Cv is for water, the pressure drop with hydraulic oil will be about 10% less than for water, or with synthetic fluids will be about 20% higher. Example of Pressure Loss Determination by Cv Rating On a certain valve a Cv rating of 19.2 is published for water flow. Find the pressure drop through this valve on a 15 GPM flow of 200 SSU hydraulic oil.
First, convert the Cv from water to 200 SSU viscosity.· Table 2 shows a correction factor of 38.
19.2 ÷ 38 = 0.505
Next, go to Table 1 to determine pressure loss on a flow of 1 GPM. Table 1 shows a pressure drop of 3.92 PSI for a flow of 15 GPM:
PSI drop = 4.0 × 15² = 882 PSI
Finally, deduct about 10% because of the lower specific gravity of hydraulic oil:
882 PSI × 90% = 794 PSI (answer)
SI AND METRIC Cv FLOW COEFFICIENTS SI (international standard) Cv flow coefficients are the number of liters per minute of water which will pass through a given orifice or passage at a pressure drop of 1 bar. If the flow coefficient is given in SI units, it may be converted to U.S. units by dividing it by 54.9. Then the procedure given in this data sheet may be followed to determine pressure drop through a valve, in PSI.
If the metric Cv is given in units of the number of liters per minute of water which will pass through an orifice at a pressure drop of 1 Newton per sq meter (Pascal), it may be converted to U.S. units by dividing it by 5.487 × 10^{4}. CONVERSIONS  MM TO INCHES Conversion factor: 1 mm = 0.03937 inches. For other metric and SI conversions see Design Data Sheets 2, 21, and 25.
mm 
Inches 

mm 
Inches 

mm 
Inches 

mm 
Inches 
1 
0.0394 
26 
1.0236 
51 
2.0079 
76 
2.9921 
2 
0.0787 
27 
1.0630 
52 
2.0472 
77 
3.0315 
3 
0.1181 
28 
1.1024 
53 
2.0866 
78 
3.0709 
4 
0.1575 
29 
1.1417 
54 
2.1260 
79 
3.1102 
5 
0.1969 
30 
1.1811 
55 
2.1654 
80 
3.1496 
6 
0.2362 
31 
1.2205 
56 
2.2047 
81 
3.1890 
7 
0.2756 
32 
1.2598 
57 
2.2441 
82 
3.2283 
8 
0.3150 
33 
1.2992 
58 
2.2835 
83 
3.2677 
9 
0.3543 
34 
1.3386 
59 
2.3228 
84 
3.3071 
10 
0.3937 
35 
1.3780 
60 
2.3622 
85 
3.3465 
11 
0.4331 
36 
1.4173 
61 
2.4016 
86 
3.3858 
12 
0.4724 
37 
1.4567 
62 
2.4410 
87 
3.4252 
13 
0.5118 
38 
1.4961 
63 
2.4803 
88 
3.4646 
14 
0.5512 
39 
1.5354 
64 
2.5197 
89 
3.5039 
15 
0.5906 
40 
1.5748 
65 
2.5591 
90 
3.5433 
16 
0.6299 
41 
1.6142 
66 
2.5984 
91 
3.5827 
17 
0.6693 
42 
1.6535 
67 
2.6378 
92 
3.6220 
18 
0.7087 
43 
1.6929 
68 
2.6772 
93 
3.6614 
19 
0.7480 
44 
1.7323 
69 
2.7165 
94 
3.7008 
20 
0.7874 
45 
1.7717 
70 
2.7559 
95 
3.7402 
21 
0.8268 
46 
1.8110 
71 
2.7953 
96 
3.7795 
22 
0.8661 
47 
1.8504 
72 
2.8347 
97 
3.8189 
23 
0.9055 
48 
1.8898 
73 
2.8740 
98 
3.8583 
24 
0.9449 
49 
1.9291 
74 
2.9134 
99 
3.8976 
25 
0.9843 
50 
1.9685 
75 
2.9528 
100 
3.9370 
Download a PDF of Fluid Power Design Data Sheet 17  How to Use Flow Coefficients (Cv) for Hydraulic Fluids.
© 1989 by Womack Machine Supply Co. This company assumes no liability for errors in data nor in safe and/or satisfactory operation of equipment designed from this information.
