## Womack Data Sheet 17: How to Use Flow Coefficients (Cv) for Hydraulic Fluids

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 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**

CorrectedCv |
PSI Dropper GPM |
CorrectedCv |
PSI Dropper GPM |
CorrectedCv |
PSI Dropper 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 |
||

SSUViscosity |
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 |

© 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.