# Flow Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Flow 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