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.
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 ( ΔP/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.
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.
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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