How to Use Flow Coefficients (Cv) for Hydraulic Fluids

FLUID POWER - Design Data Sheet 17

In case you have forgotten now-to-use 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 time the square of the actual flow through the valve

Before using this chart, take the published Cv of your valve and correct it (if neccessary) 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 pressre 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
 32clear Corrected
Cv
PSI Drop
per GPM
 32clear 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 stokes tor 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 16.

19.2 + 16 = 1.20

Next, go to Table 1 to determine pressure loss on a flow of 1 GPM. Table 1 shows a pressure drop of 0.694 PSI. For a flow of 15 GPM:

PSI drop = 0.694 × 152 = 156.2 PSI

Finally, deduct about 10% because of the lower specific gravity of hydraulic oil:

156.2 - 15.6 = 140.6 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
 32clear
mm

Inches
 32clear
mm

Inches
 32clear
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.

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