Flow Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

flow coefficient 1Flow coefficient, abbreviated as \(C_v\), a dimensionless number, also called valve coefficient or valve flow coefficient, can be described as the volume (in US gallons) of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi across the valve.  This gives us a method to compare flow capabilities of different valves.  The flow coefficient allows us to determine what size valve is required for a given application.

Flow coefficient is primarily used when sizing control valves.  However, it can be used to characterize other types of valves such as ball valves and butterfly valves.

 

Liquid Flow Coefficient formulas

\(\large{ C_v = Q \; \sqrt{ \frac{ SG }{ \Delta p } }  }\) 
\(\large{ Q = C_v \; \sqrt{ \frac{ \Delta p }{ SG } }  }\) 
\(\large{ \Delta p =  \left( \frac{ Q }{ C_v } \right)^2 \; SG  }\)  

Where:

 Units English Metric
\(\large{ C_v }\) = flow coefficient \(\large{ dimensionless }\)
\(\large{ Q }\) = flow rate (gpm for liquid) \(\large{ \frac{gal}{min} }\) \(\large{ \frac{L}{min} }\)
\(\large{ \Delta p }\) = pressure differential (pressure drop across the valve) \(\large{ \frac{lbf}{in^2} }\) \(\large{ Pa }\)
\(\large{ SG }\) = specific gravity (water at 60°F = 1.0000) \(\large{ dimensionless }\)

 

Air and Gas Flow Coefficient formulas

\(\large{ C_v = \frac{ Q }{ 1360 }   \;   \sqrt{    \frac{ T_a \; SG }{  \left( p_i \;+\; 15 \right) \; \Delta p }   }    }\)
\(\large{ Q = 1360 \; C_v \;   \sqrt{    \frac{  \left( p_i \;+\; 15 \right) \; \Delta p }{ T_a \; SG }   }    }\)
\(\large{ \Delta p =  \left( \frac { T_a \; SG }{ p_i \;+\; 15 } \right)  \; \left( \frac { Q }{ 1360 \; C_v } \right)^2   }\)

Where:

 Units English Metric
\(\large{ C_v }\) = flow coefficient \(\large{ dimensionless }\)
\(\large{ T_a }\) = absolute temperature \(^\circ R\) (\(^\circ R = ^\circ F + 460\)) \(\large{ F }\) \(\large{ R }\)
\(\large{ Q }\) = flow rate (SCFH for air & gas) \(\large{ \frac{ft^3}{hr} }\) \(\large{ \frac{m^3}{hr} }\)
\(\large{ p_i }\) = inlet pressure \(\large{ \frac{lbf}{in^2} }\) \(\large{ Pa }\)
\(\large{ \Delta p }\) = pressure differential (pressure drop across the valve) \(\large{ \frac{lbf}{in^2} }\) \(\large{ Pa }\)
\(\large{ SG }\) = specific gravity (water at 60°F = 1.0000) \(\large{ dimensionless }\)

 

Steam Flow Coefficient formulas

\(\large{ C_v = \frac{ Q }{ 63 } \; \sqrt {\frac{ \upsilon }{ \Delta p } }  }\)
\(\large{ Q = 63 \; C_v \; \sqrt {\frac{ \Delta p }{ \upsilon } }  }\)
\(\large{ \Delta p =  \upsilon \; \left( \frac { Q }{ 63 \; C_v } \right)^2  }\)

Where:

 Units English Metric
\(\large{ C_v }\) = flow coefficient \(\large{ dimensionless }\)
\(\large{ Q }\) = flow rate (lb/hr for steam) \(\large{ \frac{lbm}{hr} }\) \(\large{ \frac{L}{hr} }\)
\(\large{ \Delta p }\) = pressure differential (pressure drop across the valve) \(\large{ \frac{lbf}{in^2} }\) \(\large{ Pa }\)
\(\large{ \upsilon }\)   (Greek symbol upsilon) = specific volume \(\large{ \frac{ft^3}{lbm} }\) \(\large{ \frac{m^3}{kg} }\)

 

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Tags: Equations for Coefficient Equations for Pipe Sizing Equations for Flow Equations for Valve Sizing