## What is the Valve Coefficient?

**The Valve Coefficient or Flow Coefficient of a valve is a convenient method to relate flow rates to the pressure drop. It provides a relative measure of the efficiency of a valve. The valve coefficient is usually denoted by C _{v}. **

In a general sense, the valve flow coefficient, or C_{v} is a number that represents a valve’s ability to pass the flow through it. The bigger the value of Cv, the more will be the flow through the valve with a given pressure drop. Also, the valve C_{v} is directly related to the valve opening. The larger the valve opening, the larger is the C_{v}. The highest possible Valve Coefficient for a valve is found when the valve is fully open.

## What is the unit of C_{v}?

**The unit of Valve coefficient C _{v} is US gal/min, lbf/in^{2}.** However, there are some other notations like

**K**or

_{v}**f**depending on units. K

_{v}is measured in units of l/min, bar, and f is measured in units of Imp gal/min, lbf/in

^{2}. Note that, all three can easily be converted to one another using the factors given in Table 1.

K_{v} | C_{v} | f | |

K_{v} | – | 14.28 | 17.09 |

C_{v} | 0.07 | – | 1.1966 |

f | 0.0589 | 0.8357 | – |

**Table 1: C**

_{v}, K_{v}, and f conversion factors## How do you find the Coefficient of a Valve?

The equations for valve coefficient are different for liquids and gases. The mathematical equation of the Valve coefficient is given below.

## Valve Coefficient C_{v} for Liquids

The Valve coefficient for liquids are given by

### C_{v}=Q*√(SG/ΔP)

Here,

- Q denotes the rate of flow (US gallons per minute).
- SG denotes the specific gravity of the fluid (for water = 1).
- ΔP is the pressure drop across the valve (in psi).
- C
_{v}is the valve flow coefficient.

So following the above equation the Valve coefficient, Cv for liquids can be defined as the volume of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi across the valve.

A C_{v} value of a valve is 1 means a valve will pass 1 gallon per minute (GPM) of 60^{o}F water with a pressure drop (Dp) of 1 (PSI) across the valve. Similarly, a valve with a C_{v} of 280 will pass 280 GPM of 60^{o}F water with a pressure drop of 1 PSI.

## Valve Co-efficient C_{v} for Gases

For gases (non-critical flow) the valve coefficient is given by

### C_{v}=0.06223Q*√[(T**SG)/{Z*(P_{1}^{2}-P_{2}^{2})}

Here,

- Q is the rate of flow (Standard cubic feet per minute).
- P
_{1}is the upstream Pressure (in psia) - P
_{2}is the downstream Pressure (in psia) - Z is the compressibility factor
- T is the absolute temperature (in
^{0}K) - SG is the specific gravity (for air =1)

For the critical flow of gases, Cv is determined using the following formula:

### C_{v}=0.06223(Q/P_{1}J)√{(T*SG)/Z}

Here, J is a function of specific heat ratio (r) and (R=P_{2}/P_{1}) which can be taken from Table 2

Sr No | r | R | J | Sr No | r | R | J | |

1 | 1.2 | 0.564 | 0.825 | 9 | 1.36 | 0.535 | 0.845 | |

2 | 1.22 | 0.561 | 0.828 | 10 | 1.38 | 0.532 | 0.847 | |

3 | 1.24 | 0.557 | 0.832 | 11 | 1.4 | 0.528 | 0.849 | |

4 | 1.26 | 0.553 | 0.833 | 12 | 1.42 | 0.524 | 0.851 | |

5 | 1.28 | 0.549 | 0.836 | 13 | 1.44 | 0.521 | 0.853 | |

6 | 1.3 | 0.546 | 0.838 | 14 | 1.46 | 0.518 | 0.855 | |

7 | 1.32 | 0.542 | 0.84 | 15 | 1.48 | 0.515 | 0.857 | |

8 | 1.34 | 0.539 | 0.843 | 16 | 1.5 | 0.512 | 0.859 |

**Table 2: Values of J for finding Cv of Gases in critical flow.**

The valve coefficient is very important in valve selection as it helps in deciding the proper valve size for a particular application. The valve size, degree of valve opening, detail design, and construction of the valve affect the valve coefficient. Usually, the valve coefficient is quoted for individual valves with a full opening.

## What is the Significance of Valve Coefficient (C_{v})?

Improper C_{v} for a valve may diminish its performance in any one of the following ways:

When the calculated C_{v} is small as compared to the C_{v} required for a specific application:

- The valve or the inside trim will be undersized, which will create starvation for the process fluid.
- Restriction in the valve can increase the upstream pressure which may cause the failure of upstream equipment.
- There could be a higher pressure drop than expected leading to cavitation or flashing.

On the other hand, if the estimated C_{v} is high for a required process,

- Higher C
_{v}will lead to the selection of larger, oversized valves which in turn will increase the cost, space requirement, and weight. - Higher C
_{v}will create a significant control problem if the valve is used in the throttling service. Also, there will be higher pressure drops and faster velocities leading to cavitation, flashing, or erosion of the trim parts.

## Why should I care about Valve Coefficients?

Having a preliminary understanding of C_{v} can help in a number of ways:

- The knowledge of C
_{v}will help in the right size valve selection for a specific application. - It is possible to compare valves from different companies and their flow capacities.
- The value of C
_{v}will give an understanding of the effect of pressure on the system.

Each valve has its own valve coefficient. According to the piping configuration or trim design, valve manufacturers usually publish these C_{v} data for various valve styles. Sometimes they provide a C_{v} curve that provides the relationship of valve flow coefficient with respect to valve opening.

## How to Combine Valve Flow Coefficients?

Valve flow coefficients can easily be combined depending on the flow types in parallel or series.

- For flow in parallel, the flow coefficients are combined as
**C**_{v}=C_{v1}+C_{v2}+C_{v2}+C_{v4}+… - For flow in series, the flow coefficients are combined as follows:
**(1/C**_{v})^{2}=(1/C_{v1})^{2}+(1/C_{v2})^{2}+(1/C_{v3})^{2}+(1/C_{v4})^{2}+….

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