# Flow Coefficient

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics Flow 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 $$\large{ \frac{ft^3}{lbm} }$$ $$\large{ \frac{m^3}{kg} }$$ 