# Flow Coefficients K_{v} for Liquid, Steam or Gas

## Flow coefficient K_{v} for liquids, steam and gases - metric units

By using a flow coefficient the capacities of valves with different sizes, different types and from different manufacturers - can be compared.

The flow coefficient K_{v} is in general determined experimentally and express the

- flow capacity in metric units -
*m*that a valve will pass for a pressure drop of^{3}/h -*1 bar*

### K_{v} Liquids

Volumetric flow:

*K _{v} = q (ρ / (1000 (p_{u} - p_{d})))^{1/2} (1)*

*where *

*K _{v} = flow coefficient*

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

*ρ = density (kg/m ^{3})*

*p _{u} = upstream pressure pressure (bar abs)*

*p _{d} = downstream pressure pressure (bar abs)*

Mass flow:

*K _{v} = m / (1000 ρ (p_{u} - p_{d}))^{1/2} (1b)*

*where *

*m = mass flow (kg/h)*

#### Example - Control Valve for Water and Kv Value

The K_{v} value for a valve with water flow *3000 kg/h* and upstream pressure *10 bar* and downstream pressure *7 bar* can be calculated with *(1b)* as

*K _{v} = (3000 kg/h) / (1000 (1000 kg/m^{3}) ((10 bar)_{} - (7 bar)))^{1/2} *

* = 1.7 *

### K_{v} Saturated Steam

*p _{d} > p_{u }/ 2*:

*K _{v} = 0.032 m (v_{d} / (p_{u} - p_{d}))^{1/2} (2)*

*where *

*m = mass flow (kg/h)*

*p _{u} = upstream pressure (bar abs)*

*p _{d} = downstream pressure (bar abs) *

*v _{d} = specific weight of downstream steam and actual temperature (m^{3}/kg) *

*p _{d} < p_{u }/ 2*:

*K _{v} = 0.032 m (2 v_{d2} / p_{u} )^{1/2 } (2b)*

*where *

*v _{d2 }*= specific volume for steam with pressure

*p*and actual temperature

_{u}/ 2*(m*

^{3}/kg)### K_{v} Gases

*p _{d} > p_{u} / 2*:

*K _{v} = 0.0019 q (ρ_{g }T_{u} / (p_{d} (p_{u} - p_{d}))_{})^{1/2} (3)*

*where *

*q = volume flow of gas at 0^{o}C and 1013 mbar (m^{3}/h)*

* ρ_{g }*= density of gas at 0

^{o}C and 1013 mbar (kg/m

^{3})

*T _{u} = upstream temperature (K)*

*p _{u} = upstream pressure (bar abs)*

*p _{d} = downstream pressure (bar abs) *

*p _{d} < p_{u} / 2*:

*K _{v} = 0.0039 q (ρ_{g }T_{u})^{1/2} / p_{u} (3b)*

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