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# Liquid, Steam and Gas - Flow Coefficients Cv

## Calculate flow coefficients for the 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)

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 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)

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)

#### 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)

Critical (Choked) pressure drop in metric units:

kv = m / (12 pi)                                (2b)

where

m = steam flow (kg/hr)

pi = inlet steam absolute pressure (bara)

#### 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)                                        (2c)

where

po = outlet steam absolute 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.

Critical pressure drop is approximately 47% of inlet pi absolute pressure. With critical pressure drop the outlet absolute pressure po is approximately 53% of inlet pi pressure.

#### Pressure Drop Larger than Critical Pressure Drop

For pressure drop larger than the critical pressure drop the flow is choked. The flow coefficient can be calculated 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 Temperature (oF)

#### Pressure Drop Less than Critical Pressure Drop

For pressure drop less than the critical pressure drop the flow is not choked. The flow coefficient can be calculated as:

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

where

dp = (pi - po)

po = outlet gas absolute pressure (psia)

## Related Topics

• ### Control Valve Sizing

Control Valve terminology, bodies, trim, flow characteristics, Cv and Kv sizing, noise, actuators, positioners and more.
• ### Design of Control and Safety Valves

Sizing and dimensions of control valves & equipment in steam and condensate systems.
• ### Process Control Systems

Instrumentation, design and documentation of process control systems.
• ### Steam and Condensate

Design of steam & condensate systems with properties, capacities, sizing of pipe lines, system configuration and more.
• ### Water Systems

Design of hot and cold water service and utility systems with properties, capacities, sizing of pipe lines and more.

## Related Documents

• ### API 6D Valves - Pressure Ratings vs. Temperature

Temperature and pressure ratings for valves according API 6D.
• ### ASTM A216 Valves - Pressure Ratings vs. Temperature

Pressure and temperature ratings for cast carbon steel valves.
• ### Ball Valves - Flow Coefficients Cv

Flow coefficients - Cv - for typical ball valves - reduced and full bore.
• ### Butterfly Valves - Flow Coefficients Cv

Typical flow coefficients - Cv - for butterfly valves.
• ### Control Valves - Adding Flow Coefficients for Valves in Series or Parallel

How to add flow coefficients for control valves in series or parallel.
• ### Flow Coefficient Cv vs. Flow Factor Kv

Comparing flow coefficients Cv to flow factors Kv.
• ### Liquids - Critical Pressure Ratios

Critical pressure ratios for water and other liquids.
• ### Steam & Condensate Equations

Steam consumption and condensate generation when heating liquid or gas flows
• ### Steam Control Valves - Calculate Flow Factor Kv

Designing steam control valves and their Kv values.
• ### Steam Flow - Orifices

Steam flow through orifices - for steam pressures ranging 2 - 300 psi
• ### Steam Pipes - Pressure Drop vs. Steam Flow

Steam pipes and pressure drop diagrams - imperial and metric units.
• ### Straight Through Diaphragm Valves - Flow Coefficients

Flow coefficients - Cv - and flow factors - Kv - for straight through diaphragm valves.
• ### Valve Selection Guide

Applications guide for selecting valves.
• ### Valves - Specific Services

In case of a specific service - the choose of a valve may be simplified by following an established practice.
• ### Valves - Typical Operating Temperatures

Operating temperatures for typical categories of valves - ball valves, butterfly valves and more.
• ### Volume Flow - Online Unit Converter

Convert between volume flow units like gpm, liter/sec, cfm, m3/h.
• ### Water Control Valves - Flow Factor Kv Diagram

Sizing of water control valves - SI units
• ### Water Control Valves - Flow Coefficient Cv Diagram

Sizing of water control valves - Imperial units.
• ### Water Control Valves - Kv Calculation

Designing water process control valves and their Kv values.
• ### Weir Diaphragm Valves - Flow Coefficients and Flow Factors

Typical flow coefficients - Cv - and flow factors - Kv - for weir diaphragm valves.

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## Citation

• The Engineering ToolBox (2003). Liquid, Steam and Gas - Flow Coefficients Cv . [online] Available at: https://www.engineeringtoolbox.com/flow-coefficients-d_277.html [Accessed Day Month Year].

Modify the access date according your visit.

6.3.17

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