CONTROL VALVE

PRESSURE DROP AND SIZING

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CONTENT

Chapter Description Page

I Purpose of Control Valve 2

II Type and Main Components of Control Valve 3

III Power 5

IV. Pressure Drop Across Control Valve 7

V. Symbols and Units 10

VI. Unit Conversion 11

Table 1. Typical Flow Factors for single ported C.V. 12

Table 2. Typical flow factor for rotary type C.V. 13

Table 3. Properties of Fluids 14

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PRESSURE DROP AND SIZING

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I. PURPOSE OF CONTROL VALVE

Control valve is required to control capacity or pressure of fluid where is flowing in piping

system. Pressure control is included liquid level such as in level control. Control valve is

also used as an instrument to control temperature where capacity of mixing fluid in an

equipment or piping is handled by control valve. Figure 1 shows typical application of

control valve.

Temperature control Level control

Flow controller

Figure 1. Typical application of control valve

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PRESSURE DROP AND SIZING

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Typical pressure controller

Figure 1. (continue) Typical application of control valve

II. TYPE AND MAIN COMPONENTS OF CONTROL VALVE

Figure 2 shows main components of control valve and figure 3 shows several type of

control valves.

Figure 2. Main component of control valve

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Figure 3. Types of control valve when divided into number of port, plug & seat type,

number of connection and valve types

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PRESSURE DROP AND SIZING

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Figure 3. (continue) Types of control valve

III. POWER

Control valves are powered by manual, pneumatic system or electric motor. Instrument

air is commonly used for pneumatic power. Figure 4 shows typical of control valve

power system.

Figure 4. Types of actuator and power system for control valve

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PRESSURE DROP AND SIZING

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Figure 4. (continue) Types of actuator and power system for control valve

CONTROL VALVE

PRESSURE DROP AND SIZING

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2

2..363.1

Cv

QSG

222

72

..

10....3136.2

PoCvY

QnZToMW

IV. PRESSURE DROP ACROSS CONTROL VALVE

The following figure is schematic illustration to show fluid flow at around port and plug of

control valve.

Figure 5. Illustration of fluid flow inside the control valve

Pressure drop of fluid where flows across control valve can be determined as the

following equations.

For liquid,

PLOSS = kg/cm2 (1)

For gas

P/Po = (2)

Or by other method,

P/Po =

2

5.0

.

333..

483.2sin

64.59

1

ToSGPoCg

Qnarc

C (2A)

Where Cv is flow coefficient of valve or valve sizing coefficient given by manufacturers.

Q is volume flow in m3/hr, Qn is volume flow at normal condition in Nm3/hr, Po and To is

fluid pressure and temperature in kg/cm2A and K, MW is fluid and SG is specific gravity.

Y is expansion coefficient, C1 universal flow coefficient, Cg is gas flow coefficient also

given by manufacturers. Typical Y is,

CONTROL VALVE

PRESSURE DROP AND SIZING

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22

2

.

..364.1

CvmY

QSG

Y =

TXk

PoP

..3

)/(4.11 (3)

k is gas adiabatic exponent, XT is pressure ratio factor when valve is installed without

fitting (elbows or reducers very close to valve). XT is given by manufacturers.

When control valve is installed with fittings, replace XT by XTP,

XTP =

12

24

42

2

2

1147.2071V

VV

T

P

T

d

Cv

Do

d

Do

dX

F

X

(4)

And equation (3) become,

Y =

TPXk

PoP

..3

)/(4.11 (5)

FP is piping construction factor and dV is nominal valve size in mm (it is not port diameter,

d but casing connection size) are given by manufacturers. Do is pipe diameter upstream

fitting in mm. If control valve constructed between identical reducers,

FP =

5.02

2

2

2

2

193.7001V

V

d

Cv

Do

d (6)

If all fittings pressure drop installed in the piping system has been calculated such as in

article “Fluid flow in pipe” in this blog, it will more simple to use equation (3) without XTP

and FP factor.

For liquid-gas mixture

PLOSS = kg/cm2 (7)

Cvm = (Cv+Cg)(1+Fm) (8)

Fm = RQ for RQ < 0.6 and Fm=1.334 RQ – 0.201 for 0.6< RQ <0.9 (9)

RQ = Qg / (QLIQ + Qg)

Qg is gas volume flow, QLIQ is liquid volume flow and RQ is gas-liquid volume ratio.

Limitation and correction

Viscosity correction

For viscous liquid such as oil, Cv in equation (1) shall be corrected become,

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CVR = Cv.Fv (10)

Fv is viscosity correction for Cv. For pressure drop calculation, Fv is given as the following

equations.

If Re < 35, Fv = 18.12 Re-0.517235 . If 35<Re< 3000, Fv = 2.5422 – 0.001843 Re + 4.5572 Re2.10-5

If 3000<Re<60,000, Fv = 1.4683 Re-0.0349125 . If Re > 60,000, Fv = 1 (11)

Choked Flow and Cavitation

High velocity of liquid at vena contracta will reduce static pressure. If static pressure at

the vena contracta is lower than vapor pressure of liquid, vaporation will accour

(flashing) and than cavitation will also accour at downstream of vena contracta or

surrounding valve plug and other parts nearby where vapor bubbles are become liquid

again when static pressure is back to higher than vapor pressure. If bubbles due to

flashing occurrence are so much, these bubbles will crowd space at downstream of

valve port and limit liquid to flow. This occurrence is called choked flow.

To prevent from above condition, design of pressure drop of liquid across control valve

shall be limited at the following equations.

For globe type valve,

PLOSS-MAX-GLOBE =FL2 (Po – rC.Pv ) kg/cm2 (12)

Km (Po – rC.Pv)

FL is valve recovery coefficient given by manufacturers. Po is upstream pressure and Pv

vapor pressure of liquid in kg/cm2A. rC is critical pressure ratio

rC = 0.96 – 0.28 (Pv/Pc)0.5 (13)

where Pc is thermodynamic critical pressure of liquid.

If valve installed with fittings (reducers or elbows), equation (12) become,

PLOSS-MAX-GLOBE = FL 2(Po – rC.Pv )/Fp2 kg/cm2 (14)

For ball and butterfly (ROTARY) type valve,

PLOSS-MAX-ROTARY = FL 2(Po – rC.Pv ) or = FL 2(Po – rC.Pv )/Fp2 kg/cm2 (15)

FL2 can also be replaced by Km. Ball and butterfly valve is more tend to cavitation. Use

following equation to prevent cavitation.

PLOSS-MAX-ROTARY = Kc(Po – Pv ) (16)

Fc is approximately = 0.67 FL2 or see table.

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Choked condition will also accour for gas, steam and vapor if velocity at vena

contracta reach the sound velocity. Port pressure drop of gas or steam at 0.8 x sound

velocity is,

P sonic = 0.4 Po.k kg/cm2 (17)

Cg MIN = 0.16585.Qn.(SG To)0.5/Po (18)

V. SYMBOLS AND UNITS

Unless otherwise noted, the following symbols and units are used in this manual.

Symbol Description Unit

Cv Flow coefficient

Cvm Flow coefficient for liquid-gas mixture

Cg Gas sizing coefficient

Cs Steam sizing coefficient

D or Do Inside pipe diameter mm

dV, d Nominal control valve size, port dia. mm

Fm Liquid-gas mixture factor

Fp Installation factor

Fv Viscosity correction factor

g Gravity 9.81 m/s2

FL Valve recovery coefficient

L Pipe length m

Viscosity cP (centipoise)

Po Upstream pipe pressure kg/cm2A

Pv Vapor pressure kg/cm2A

Pc Thermodynamic critical pressure kg/cm2A

P or PLOSS Differential pressure/pressure drop kg/cm2

Q Volume flow (see note) m3/hr

Qg & QLIQ Gas and liquid volume flow m3/hr

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RQ Gas-liquid volume ratio

Fluid density kg/m3

Re Reynold Number

rC Critical pressure ratio

SG Specific gravity

T Absolute temperature 0 K

V Fluid velocity m/s

Y Gas net expansion factor

VI. UNIT CONVERSION

Designation Unit to be converted Factor Unit to be used

Length ft 304.8 mm

inch 25.4 mm

Pressure psi 0.07031 kg/cm2

bar 1.0194 kg/cm2

atm. 1.0326 kg/cm2

Pa (Pascal) 1.0194 x 10-5 kg/cm2

Temperature F (Fahrenheit) (tF -32) x (5/9) C

R (Rankin) (5/9) K

C (Celcius) tC + 273 K

Velocity ft/s 0.3048 m/s

ft/min (fpm) 0.00508 m/s

Volume flow GPM (US) 0.227 m3/hr

CFM 1.699 m3/hr

Mass lb 0.4536 kg

Power HP 0.7457 kW

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Head ft 0.3048 m

Enthalpy kcal/kg 4.1868 kJ/kg

BTU/lb 2.326 kJ/kg

Gas constant kcal/kg.K 4.1868 kJ/kg.K

Specific heat BTU/lb.R 4.1868 kJ/kg.K

Density lb/ft3 16.0185 kg/m3

Specific volume ft3 /lb 0.06243 m3/kg

Viscosity N.s/m2 1000 cP

lbf.s/ft2 47880.3 cP

Kinematic to absolute viscosity, = SG . in cSt (centistokes), in cP

Note : American Standard State condition is condition where pressure at 1.013 bar A and

temperature at 15.5 C. In volume, is common written as SCF. Normal condition is at 1.0132

bar A and 0 C. In volume, is common written as Nm3 (Symbol for flow in this article is Qn)

Table 1. Typical Cv, FL and XT for Single Ported Globe Style Valve bodies

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Table 2. Typical Cv, FL and XT for rotary shaft valve

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Table 3. Properties of some fluids

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