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1. Cv and Kv definition

2. Calculation of Cv of a valve in
laminar flow

3. Calculation example

3. Calculation example

Please refer to the valve flow coefficient page of Process
Engineer's tools.

The principle behind sizing a control valve for laminar flow is to calculate a correction factor to apply to the Cv calculated for turbulent flow.

**Cv_corrected = Cv_turbulent / F _{R}
**

With

Cv_turbulent = Cv calculated with regular Cv equations for turbulent liquid
flow

F_{R} = correction factor

The correction factor F_{R} can be calculated with the
following step by step guide :

**STEP 1 : calculate Cv_turbulent**

**Calculate the Cv in turbulent flow thanks to the following
equation, explained
in detail in this page.**

**STEP 2 : select a valve and define its rated Cv [Baumann]
**

From the Cv calculated above, select in a catalogue a valve of the type you wish to use with a Cv greater than the one calculated for turbulent flow (some source propose to select a rated Cv 90% higher than the turbulent Cv [Valve World]). Read the rated Cv of this valve (higher than turbulent Cv), and get from the manufacturer brochure the following data :

- F
_{L}= pressure recovery factory (critical flow factor) - F
_{d}= valve style modifier ; if unknow, the following values are given by [Baumann] for valves having a Cv > 0.1 - Single seated, parabolic plug = 0.46
- Double seated, parabolic plug = 0.32
- Butterfly valve = 0.57
- Segmented ball valve = 0.98 (when wide open), larger than 6 inches
- Eccentric rotary plug valves = 0.42

**STEP 3 : calculate the Reynolds of the valve [Baumann] [Valve
Wolrd]
**

The Reynolds number for the valve can be calculated by Re_{v}
= (17000*F_{d}*q)/(ν.[C_{vR}*F_{L}]^{0.5})
:

With

Re_{v} = Reynolds of the valve (-)

F_{d} = valve style modifier (see STEP 2)

q = flow through the valve (gpm)

C_{vR} = rated Cv of the valve considered (see STEP 2)

F_{L} = pressure recovery factory (critical flow factor)
(see STEP 2)

ν = kinematic viscosity (centistokes, 10-6 m/s2) = μ/d

μ = dynamic viscosity (cP)

d = density of the liquid

Or, in metric units, Re_{v} = (76000*F_{d}*q)/(ν.[C_{vR}*F_{L}]^{0.5})
:

With Re_{v} = Reynolds of the valve (-)

F_{d} = valve style modifier (see STEP 2)

q = flow through the valve (m3/h)

C_{VR} = rated Cv of the valve considered (see STEP 2)

F_{L} = pressure recovery factory (critical flow factor)
(see STEP 2)

ν = kinematic viscosity (centistokes, 10-6 m/s2) = μ/d

μ = dynamic viscosity (cP)

d = density of the liquid

**STEP 4 : Calculation of Cv/d ^{2 }[Valve World]
**

The calculation of Cv/d^{2} is required for the next steps
of the valve sizing. **d is the inlet diameter the valve selected
at step 2**. Be careful, it should be expressed in inches.

**STEP 5 : Calculation of F _{R }[Baumann]
**

The factor F_{R} can be determined from Rev and Cd=Cv/d^{2}
thanks to an abacus given by [Baumann].

Blue curve : Cd<10, globe valves

Red curve : 10<Cd<15, globe valves and eccentric rotary plug
valves

Orange curve : 15<Cd<25, butterfly valves

Green curve : Cd>25, ball valves and very small valve with
Cd<1

**STEP 6 : Calculation of Cv_corrected**

Cv_corrected can thus be calculated thanks to Cv_turbulent / F_{R}
with Cv_turbulent calculated at Step 1 and FR calculated at step 2.

**STEP 7 : Compare Cv_corrected to Cv_assumed [Valve Wolrd]
**

The Cv_corrected is compared the Cv assumed at step 2.

If Cv_corrected < Cv_assumed with Cv_corrected ~ 0.5*Cv_assumed, then the valve selected is fine for laminar flow.

If Cv_corrected > 0.8*Cv_assumed or even Cv_corrected > Cv_assumed, then the calculated must be repeated by selecting a valve with a higher Cv_assumed, advised to be 90% higher of the original value.

Considering a liquid of a viscosity of 1000 centistokes, with a density 0.9, what is the valve Cv required to ensure a pressure drop of 25 Psig for a flow of 30 gpm ?

**STEP 1 : calculate the Cv turbulent**

Cv_turbulent = q.(d/DP)0.5 = 30*(0.9/25)^{0.5} = 5.7

**STEP 2 : select a valve**

The Engineer wishes to use a globe valve of inlet diameter 1 inch. He anticipates a higher Cv required 90% higher than Cv turbulent, which means a Cv of 10.8.

Looking in a catalogue for Globe valve, the Engineer finds a model with a Cv of 12. The Engineer selects this valve. FL = 0.95 according to the manufacturer.

The coefficient F_{d} is 0.46 according to paragraph 2.

**STEP 3 : calculate the Reynolds number of the valve**

Re_{v} = (17000*F_{d}*q)/(ν.[C_{vR}*F_{L}]^{0.5})
= (17000*0.46*30)/(1000*(12*1)^{0.5}) = 67.7

**STEP 4 : Calculation of Cv/d ^{2}**

Cv/d2 = 12/1^{2} = 12

**STEP 5 : Calculation of F _{R}**

F_{R} is calculated from the Abacus given in section 2 step
5. In the present case, it is 1st necessary to calculate Cd=Cv/d^{2}
= 12 then check the 2nd curve on the graph for Rev=67.7

F_{R} = 0.52

**STEP 6 : calculate the Cv for laminar flow**

Cv_corrected = Cv_turbulent / F_{R = }5.7/0.52 = 10.96

**STEP 7 : control the value calculated**

The Cv corrected is equal to 10.96 while the valve selected has a Cv of 12. 10.96/12 = 0.91.

The valve would regulate at 91% of its maximum Cv. It is too high,
it could be advised to re-run the calculation by selecting a
slightly bigger valve, for example with a Cv of 20.

Source

[Valve World] The derivation of
the equation for Reynolds Number for use in the sizing of

control valves for non-turbulent flow (laminar and transitional)

control valves for non-turbulent flow (laminar and transitional)

[Baumann]** **Valve sizing
made easy

https://www.isa.org/pdfs/product-pdfs/sample-chapters/Baumann-ControlValvePrimer_Chapter5/