Flow Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

flow coefficient 1Flow coefficient, abbreviated as \(C_v\), 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.

 

Flow Coefficient formulas

\(\large{ C_v = Q \; \sqrt{ \frac{ SG }{ \Delta p } }  }\)  (for liquid)
\(\large{ Q = C_v \; \sqrt{ \frac{ \Delta p }{ SG } }  }\)  (for liquid) Solve for Q
\(\large{ \Delta p =  \left( \frac{ Q }{ C_v } \right)^2 \; S  }\)   (for liquid) Solve for \(\Delta p\)
   
\(\large{ C_v = \frac{ Q }{ 1360 }   \;   \sqrt{    \frac{ T_a \; SG }{  \left( p_i \;+\; 15 \right) \; \Delta p }   }    }\) (for air & gas)
\(\large{ Q = 1360 \; C_v \;   \sqrt{    \frac{  \left( p_i \;+\; 15 \right) \; \Delta p }{ T_a \; SG }   }    }\) (for air & gas) Solve for Q
\(\large{ \Delta p =  \left( \frac { T_a \; SG }{ p_i \;+\; 15 } \right)  \; \left( \frac { Q }{ 1360 \; C_v } \right)^2   }\) (for air & gas) Solve for \(\Delta p\)
   
\(\large{ C_v = \frac{ Q }{ 63 } \; \sqrt {\frac{ \upsilon }{ \Delta p } }  }\) (for steam)
\(\large{ Q = 63 \; C_v \; \sqrt {\frac{ \Delta p }{ \upsilon } }  }\) (for steam) Solve for Q
\(\large{ \Delta p =  \upsilon \; \left( \frac { Q }{ 63 \; C_v } \right)^2  }\) (for steam) Solve for \(\Delta p\)

Where:

\(\large{ C_v }\) = flow coefficient

\(\large{ T_a }\) = absolute temperature \(^\circ R\) (\(^\circ R = ^\circ F + 460\))

\(\large{ Q }\) = flow rate (gpm for liquid)

\(\large{ Q }\) = flow rate (SCFH for air & gas)

\(\large{ Q }\) = flow rate (lb/hr for steam)

\(\large{ p_i }\) = inlet pressure

\(\large{ \Delta p }\) = pressure differential (pressure drop across the valve)

\(\large{ SG }\) = specific gravity (water at 60°F = 1.0000)

\(\large{ \upsilon }\)   (Greek symbol upsilon) = specific volume

 

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