## The Kv equation

Formulas behind the calculator

The Kv-calculator uses the definitions quoted in ISA-S75.01-1985 "Flow equations for sizing control valves": #### Approximations:

Y=1: as long as X<<Xt where Xt is the critical pressure drop ratio. [Y = 1 - X / 3*Ft*Xt]

Fp=1: this value is the ratio between the Kv of the valve with fittings and the Kv without fittings. It is determined experimentally.

Z=1: true for ideal gasses.

 Q : Volume flow Gg: Specific gravity N : Units constant T1: Upstream temperature Fp: Pipe geometry factor Z: Compressibility factor P1: Upstream pressure X: Pressure drop ratio DP/P1 Y : Expansion factor Ft: Specific Heat ratio

#### Kv measurement test procedure

ISA-S75.02-1988 "Control Valve Capacity Test Procedure" describes two test methods for determining the valve flow coefficient Kv. This section is a extract of the most practical method.

Theory:

At a fixed stem travel the expansion factor Y is a linear function of the pressure drop ratio X (Y=1-X/3FtXt). As X tends to zero Y tends to 1, by plotting YKv as a function of X the value of Kv is determined by the intersection of the straight line fit with the YKv axis: Experimental:

The pressure drop ratio and the flow can be measured with the test setup shown below. Valves V1 and V2 are used to set values of pressure drop ratio X (X=DP/P1), for constant P1 and fixed valve stem travel. P1 and P2 measure absolute pressure. #### Specifying a Kv value for an order

When calculating the Kv of a valve usually the user specifies the values of flow rate and a pressure drop across the valve achieved at the expected stable process conditions. For an adequate regulation these characteristics should be matched by the valve's Kv at 50% stem travel. It is common practice among valve manufacturers to deliver the valve quoting the value of the Kv at 100% travel (valve fully open). Therefore it is recommended to specify that the calculated Kv must be achieved by the valve at a well defined travel position within a given uncertainty.