## Control Valve Relation between Cv and Kv

### How do we get value 1.156 (Conversion Factor) in formula Cv = 1.156Kv or Cv= 1.156×Q×sqrt (G/delta P). Please explain.

**Answer:**

For measuring the valve capacity of control valves, the coefficient Cv or its metric equivalent Kv is adopted.

The Valve Coefficient (**Cv – in Imperial unit**) – the number of US GALLON PER MINUTE of water at 60 °F that will flow through a valve at specific opening with a pressure drop of 1 psi across the valve.

The flow factor (**Kv – in Metric unit**) – the amount of water that will flow in m3/hr. with a temperature range 5 to 30 °C and pressure drop of 1 bar.

#### The relationship between Cv and Kv is

**Cv** = 1.156 * Kv. **OR**

**Kv** = 0.864 * Cv

The flow rate for a liquid **Q = Cv * Sq. Root of ( Δ****P/SG)**

Q = Flow in US GPM.

Cv = Flow Coefficient of control valve

ΔP = Differential pressure

SG = Specific Gravity of fluid (reference against water at 60 °F)

Now we discuss about how we get the conversion factor of 1.156 in the formula, Cv = 1.156Kv

#### Unit conversions from Imperial to Metric (vice versa)

1 US gpm = 0.227125 m3/hr and 1 m3/hr = 4.4028812454 US GPM

1 psi = 0.06894757 bar and 1 bar = 14.503773773 psi

60 deg F = 15.5 deg C

#### Conversion of units for Cv to Kv

Cv = 1 m3/hr * sqrt (1/1bar)

Cv = 4.4028812454 US GPM * sqrt (1/14.503773773 psi)

Cv = 4.4028812454 US GPM * 0.2625786985 *1/psi

Cv = 1.1561 US GPM /psi

**Cv = 1.156 Kv**

#### Conversion of units for Kv to Cv

Kv = 1Us gpm *sqrt (1/1psi)

Kv = 0.227125 m3/hr * sqrt (1/0.06894757 bar)

Kv = 0.2271 * 3.808 * m3/ hr

Kv = 0.864 m3/ hr

**Kv = 0.864 Cv**

At a particular percentage of opening of valve giving Cv = 1 will pass 1US GPM ( at 60 °F) and a pressure differential of 1 psi upstream and downstream across the valve.

For the same pressure conditions, if we increase the valve opening to create Cv = 10, It will pass 10 US GPM provided 1 psi pressure drop across the valve (remains same).

Q = 1/1.156 Cv * Sq. Root of ( Δ P/SG)

Q = 0.865 Cv * Sq. Root of ( Δ P/SG)

Q = Flow in m3/hr.,

Δ P = 1 bar,

SG = 1 for water at 15°C (Equivalent of 60°C Imperial units)

In metric units, the same valve with Cv = 1 pass 0.864 m3/hr. (at 15 °C) with a delta P of 1 bar across the valve.

#### **Summary **:

For any specific valve opening with an equivalent pressure drop and equivalent temperature, by applying multiplication factor we get equal flows in both Imperial and metric units.

### Example :

Simple Example of conversion factor between two different mass units is:

1 Kg = 2.2 * Pounds

In a simple balance consisting two pans – 1 Kg of Weight in one pan and in second pan need to put 2.2 Times Pound weight, then only two pans stay equal in a simple balance. (Under same environmental conditions)

Kg = Kilogram is a Metric unit

Pound is Imperial unit.

10 Kg = 2.2 * 10 Pounds = 22 Pounds.

100 Kg = 2.2 * 100 Pounds = 220 Pounds

Same is the relation between Cv and Kv.

Author: R. Jagan Mohan Rao

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