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Flow Coefficient - *C*_{v} - and Formulas for Liquids, Steam and Gases - Online Calculators

_{v}

## Flow coefficient and proper design of control valves

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With the flow coefficient - *C*_{v} - flow capacities of valves at different sizes, types and manufacturers can be compared. The flow coefficient is in general determined experimentally and express the water flow capacity in imperial units - *GPM (US gallons per minute) *that a valve will pass for a pressure drop of *1 lb/in ^{2} (psi)*.

The flow factor - *Kv* - is also commonly used, but capacities are expressed in SI-units.

The flow coefficient - *C*_{v} - required for a specific application can be estimated by using specific formulas for the different fluids or gases. With the estimated *C _{v}* value - the correct valve can be selected from the manufacturers catalogs.

### Flow Coefficient - *C*_{v} - for Liquids

For liquids the flow coefficient - *C*_{v} -is expressed with water flow capacity in *gallons per minute (GPM) of 60 ^{o}F* with pressure drop

*1 psi (lb/in*.

^{2})#### Flow expressed by volume

C_{v}= q (SG / dp)^{1/2}(1)

where

q = water flow (US gallons per minute)

SG = specific gravity (1 for water)

dp = pressure drop (psi)

or alternatively in SI units:

C_{v}= 11.6 q (SG / dp)^{1/2}(1b)

where

q = water flow (m^{3}/h)

SG = specific gravity (1 for water)

dp = pressure drop (kPa)

#### Flow expressed by weight

C_{v}= w / (500 (dp SG)^{1/2})(1c)

where

w = water flow (lb/h)

SG = specific gravity (1 for water)

dp = pressure drop (psia)

or alternatively in SI units:

C_{v}= 5.8 w / (500 (dp SG)^{1/2})(1d)

where

w = water flow (kg/h)

SG = specific gravity (1 for water)

dp = pressure drop (kPa)

#### Example - Flow Coefficient Liquid

The flow coefficient for a control valve which in full open position passes *25 gallons per minute* of water with a *one pound per square inch* pressure drop can be calculated as:

C_{v}= (25 gpm) (1 / (1 psi))^{1/2}

= 25

### Flow Coefficient - *C*_{v} - for Saturated Steam

Since steam and gases are compressible fluids, the formula must be altered to accommodate changes in density.

#### Critical (Choked) Pressure Drop

With choked flow and critical pressure drop, the outlet pressure - *p _{o}* - after the control valve is aprox. 58% of the inlet pressure -

*p*before the control valve. The flow coefficient at choked - or critical - flow can be expressed as:

_{i }-

C_{v}= m / 1.61 p_{i}(2)

where

m = steam flow (lb/h)

p_{i}= inlet steam absolute pressure (psia)

p_{o}= outlet steam absolute pressure (psia)

#### Non Critical Pressure Drop

For non critical pressure drop the outlet pressure - *p _{o}* - after the control valve is more than

*58%*of the inlet pressure -

*p*before the control valve. The flow coefficient for non critical flow can be expressed as:

_{i }-

C_{v}= m / (2.1 ( (p_{i}+ p_{o}) dp)^{1/2}) (2b)

### Flow Coefficient - *C*_{v} - Super-heated Steam

The flow coefficient for superheated steam should be multiplied with a correction factor:

C_{v}= C_{v_saturated}(1 + 0.00065 dt) (3)

where

dt = steam temperature above saturation temperature at the actual pressure (^{o}F)

#### Example - flow coefficient super-heated steam

The flow coefficient for steam super-heated with *50 ^{o}F* can be calculated as:

C_{v}= C_{v_saturated}(1 + 0.00065 (50^{o}F) =1.0325 C_{v_saturated}

### Flow Coefficient - *C*_{v} - Saturated Wet Steam

Saturated wet steam includes non evaporated water particles reducing the "steam quality" and a flow coefficient for very wet saturated steam should be multiplied with a correction factor:

C_{v}= C_{v_saturated}ζ^{1/2}(4)

where

ζ = dryness fraction

#### Example - Flow Coefficient Wet Saturated Steam

For steam with moisture content *5%* the dryness fraction can be calculated as:

ζ = w_{s}/ (w_{w}+ w_{s})

= 0.95 / (0.95 + 0.05)

= 0.95

where

w_{w}= mass of water

w_{s}= mass of steam

The flow coefficient can be calculated as:

C_{v}= C_{v_}_{saturated}(0.95)^{1/2}

= 0.97 C_{v_saturated}

### Flow Coefficient - *C*_{v} - Air and other Gases

**Note!** - there is a difference between critical and non critical pressure drops.

For critical pressure drop, where the outlet pressure - *p _{o}* - from the control valve is less than

*53%*of the inlet pressure -

*p*the flow coefficient can be expressed as:

_{i},

C_{v}= q [SG (T + 460)]^{1/2}/ 660 p_{i}(5)

where

q = free gas per hour, standard cubic feet per hour (Cu.ft/h)

SG = specific gravity of flowing gas gas relative to air at 14.7 psia and 60^{o}F

T = flowing air or gas temperature (^{o}F)

p_{i}= inlet gas absolute pressure (psia)

For non critical pressure drop, where the outlet pressure - *p _{o}* - from the control valve is greater than

*53%*of the inlet pressure -

*p*he flow coefficient can be expressed as:

_{i}, t

C_{v}= q [SG (T + 460)]^{1/2}/ [1360 (dp p_{o})^{1/2}] (5b)

where

dp = (p_{i}- p_{o})

p_{o}= outlet gas absolute pressure (psia)

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