## 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.