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# Flow Coefficient - Cv - for Liquid, Steam and Gas - Formulas and Online Calculators

## Flow coefficient and proper design of control valves - Imperial Units

With the flow coefficients capacities of valves at different sizes, types and manufacturers can be compared. The flow coefficients are in general determined experimentally and express the

flow capacity in imperial units - GPM (US gallons per minute) that a valve will pass for a pressure drop of 1 lb/in2 (psi)

The flow factor - Kv - is also commonly used with capacity in SI-units.

The flow coefficient - Cv - required for a specific application can be estimated by using specific formulas for the different fluids or gases. With an estimated Cv value - the correct size of control valve can be selected from the manufacturers catalogs.

Note that an oversized control valve may hurt process variability by putting too much gain in the valve leaving less flexibility for the controller. An oversized valve operates more frequently at lower openings with increased dead band as result.

### Flow Coefficient - Cv - for Liquids

For liquids the flow coefficient - Cv -is expressed with water flow capacity in gallons per minute (GPM) of 60oF with pressure drop 1 psi (lb/in2).

#### Flow expressed by volume

Cv = q (SG / dp)1/2                                    (1)

where

q = water flow (US gallons per minute)

SG = specific gravity (1 for water)

dp = pressure drop (psi)

Water flow (US gal per minute)

Pressure drop (psi)

or alternatively in metric units:

Cv = 11.6 q (SG / dp)1/2                                (1b)

where

q = water flow (m3/hr)

SG = specific gravity (1 for water)

dp = pressure drop (kPa)

Water flow (m3/hr)

Pressure drop (kPa) Water Control Valves - flow coefficient Cv diagram

#### Flow expressed by weight

Cv = w / (500 (dp SG)1/2)                             (1c)

where

w = water flow (lb/hr)

SG = specific gravity (1 for water)

dp = pressure drop (psia)

Water flow (lb/hr)

Pressure drop (psi)

or alternatively in SI units:

Cv = 5.8 w / (500 (dp SG)1/2)                                (1d)

where

w = water flow (kg/hr)

SG = specific gravity (1 for water)

dp = pressure drop (kPa)

Water flow (kg/hr)

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:

Cv = (25 gpm) (1 / (1 psi))1/2

= 25

### Flow Coefficient - Cv - 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 - po - after the control valve is aprox. 58% of the inlet pressure - pi -  before the control valve. The flow coefficient at choked - or critical - flow can be expressed as:

Cv = m / 1.61 pi                                (2)

where

m = steam flow (lb/hr)

pi = inlet steam absolute pressure (psia)

Steam flow (lb/hr)

Inlet Steam Pressure (psia)

#### Non Critical Pressure Drop

For non critical pressure drop the outlet pressure - po - after the control valve is more than 58% of the inlet pressure - pi before the control valve. The flow coefficient for non critical flow can be expressed as:

Cv = m / (2.1 ( (pi + po) dp) 1/2)                                        (2b)

where

po = outlet steam absolute pressure (psia)

Steam flow (lb/hr)

Inlet Steam Pressure (psia)

Outlet Steam Pressure (psia)

### Flow Coefficient - Cv - Super-heated Steam

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

Cv = Cv_saturated (1 + 0.00065 dt)                                     (3)

where

dt = steam temperature above saturation temperature at the actual pressure (oF)

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

The flow coefficient for steam super-heated with 50oF can be calculated as:

Cv = Cv_saturated (1 + 0.00065 (50oF) =1.0325 Cv_saturated

### Flow Coefficient - Cv - 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:

Cv = Cv_saturated ζ1/2                                   (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 = ws / (ww + ws)

= 0.95 / (0.95 + 0.05)

= 0.95

where

ww = mass of water

ws = mass of steam

The flow coefficient can be calculated as:

Cv = Cv_saturated (0.95)1/2

= 0.97 Cv_saturated

### Flow Coefficient - Cv - Air and other Gases

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

For sub critical pressure drop - chocked flow, where the outlet pressure - po - from the control valve is less than 53% of the inlet pressure - pi, the flow coefficient can be expressed as:

Cv = q [SG (T + 460)]1/2/ (FL 834) pi                                   (5)

where

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

SG = upstream specific gravity of flowing gas gas relative to air (SG = 1.0) at 14.7 psia and 60oF

T = flowing air or gas temperature (oF)

FL = pressure recovery factor

pi = inlet gas absolute pressure (psia)

Gas flow (Cu.ft./h) (f.a.d)

Inlet Gas Absolute Pressure (psia)

Pressure recovery factor

upstream Specific Gravity Gas

Gas Temperature (oF)

For non critical pressure drop, where the outlet pressure - po - from the control valve is greater than 53% of the inlet pressure - pi, the flow coefficient can be expressed as:

Cv = q [SG (T + 460)]1/2/ [1360 (dp po)1/2]                                    (5b)

where

dp = (pi - po)

po = outlet gas absolute pressure (psia)

Gas flow (Cu. ft./h) (f.a.d)

Inlet Gas Pressure (psia)

Outlet Gas Pressure (psia)

upstream Specific Gravity Gas

Gas Temperature (oF)

## Related Topics

• Steam and Condensate - Steam & condensate systems- properties, capacities, pipe sizing, systems configuration and more
• Control Valves - Control Valve terminology, bodies, trim, flow characteristics, Cv and Kv sizing, noise, actuators and positioners
• Process Control - Instrumentation and process control systems, design and documentation
• Water Systems - Hot and cold water service systems - design properties, capacities, sizing and more
• Control Valves and Equipment - Sizing and dimensions of control valves & equipment in steam and condensate systems

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## Citation

• Engineering ToolBox, (2003). Flow Coefficient - Cv - for Liquid, Steam and Gas - Formulas and Online Calculators. [online] Available at: https://www.engineeringtoolbox.com/flow-coefficients-d_277.html [Accessed Day Mo. Year].

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