Resistance coefficient   

Resistance coefficient



Resistance coefficient K




Δ p: Pressure loss of the component
K : Dimensionless resistance coefficient (friction factor) of the component. K is assumed to be constant.
ρ: Density
v: Average speed in the characteristic cross section
: Volume flow
A: Characteristic cross section
d: Inner diameter of the characteristic cross section.
For valves as a general rule the characteristic diameter equals the nominal diameter DN.

Equation (1) is derived from the equation of Darcy-Weisbach .

The resistance coefficient K is assumed to be constant. This assumption is correct for completely turbulent flow. In many other cases the inaccuracy is acceptable. With K=const. equation (1) can be written as follows:


The valve manufacturer Mason-Neilan (MA, USA) introduced in the 1940s the flow coefficient cv . In the 1950s cv was introduced as kv -value   (kvs-value for rated travel) in the metric system [Früh 1957]. The flow coefficients cv and kv describe a valve´s reference point of operation . The reference fluid is water (ρo = density of water at 15,6 ºC) [VDI/VDE 2173-2007 page 8].

kv: o = kv [m³/h]  @   Δpo = 1 [bar]  
cv,us: o = cv,us [USgal/min]  @   Δpo = 1 [psi] o[m³/h] = 0.2271 cv,us [USgal/min]  @   Δpo = 0.0689 [bar]
cv,uk: o = cv,uk [UKgal/min]  @   Δpo = 1 [psi] o[m³/h] = 0.2728 cv,uk [UKgal/min]  @   Δpo = 0.0689 [bar]


With equation (4) we can describe the correlation between kv and cv
Putting equation (1) to K and with A = π/4 d2 the correlation between resistance coefficient K and flow coefficient kv becomes equation (5):


By lowering the pressure behind a valve the volume flow can´t rise without limits. Pressures below the vapour pressure lead to cavitation. The noise level rises and at maximum cavitation we face choked flow. According to [VDI/VDE 2173-2007 page 10] we can note for control valves:

  p1: Absolute pressure at the inlet
pv: Vapour pressure
pc: Critical pressure (Water: pc=221,2 bar)
 
Ball valve: FL= 0.5-0.7
Butterfly valve
(aperture angle 60-70º)
: FL= 0.55-0.75
Low-noise control valve: FL= 0.88-0.98

More detailed information (including not turbulent flow) can be found in [DIN EN 60534 2012].

Literature
[DIN EN 60534 2012] DIN EN 60534-2-1: Stellventile für die Prozessregelung, Beuth-Verlag Berlin, Januar 2012
[Früh 1957] K.F.Früh: Berechnung des Durchflusses in Regelventilen mit Hilfe des kv-Koeffizienten, Regelungstechnik Heft 9; 5. Jahrgang 1957
[VDI/VDE 2173-2007] VDI/VDE 2173: Stömungstechnische Kenngrössen von Stellventilen und deren Bestimmung, Beuth-Verlag Berlin, September 2007




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