# Flow Coefficient

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 Index

The flow coefficient is commonly used in fluid flow calculations to determine the pressure drop across a control device and the resulting flow rate.  It is often provided by the manufacturer for specific valves, pumps or orifice plates, and can also be calculated experimentally using flow tests with a specific fluid and testing apparatus.  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 formula

$$C_v \;=\; Q \; \sqrt{ SG \;/\; \Delta p }$$     (Liquid Flow Coefficient)

$$Q \;=\; \sqrt{ C_v^2 \; ( \Delta p \;/\; SG ) }$$

$$SG \;=\; C_v^2 \; ( \Delta p \;/\; Q^2 )$$

$$\Delta p \;=\; SG \; C_v^2 \;/\; Q^2$$

### Solve for Cv

 flow rate, Q specific gravity, SG pressure differential, Δp

### Solve for Q

 flow coefficient for liquid flow, Cv pressure differential, Δp specific gravity, SG

### Solve for SG

 flow coefficient for liquid flow, Cv pressure differential, Δp flow rate , Q

### Solve for Δp

 specific gravity, SG flow coefficient for liquid flow, Cv flow rate, Q

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

### Air and Gas Flow Coefficient formula

$$C_v \;=\; ( Q \;/\; 1360 ) \; \sqrt{ T_a \; SG \;/\; ( p_i + 15 ) \; \Delta p }$$
Symbol English  Metric
$$C_v$$ = flow coefficient $$dimensionless$$
$$Q$$ = flow rate (SCFH for air & gas) $$ft^3 \;/\; hr$$ $$m^3 \;/\; hr$$
$$T_a$$ = absolute temperature $$^\circ R$$ ($$^\circ R = ^\circ F + 460$$) $$F$$ $$R$$
$$SG$$ = specific gravity (water at 60°F = 1.0000) $$dimensionless$$
$$p_i$$ = inlet pressure $$lbf \;/\; in^2$$ $$Pa$$
$$\Delta p$$ = pressure differential (pressure drop across the valve) $$lbf \;/\; in^2$$ $$Pa$$

### Steam Flow Coefficient formula

$$C_v = ( Q \;/\; 63 ) \; \sqrt{ \upsilon \;/\; \Delta p }$$
Symbol English Metric
$$C_v$$ = flow coefficient $$dimensionless$$
$$Q$$ = flow rate (lb/hr for steam) $$lbm \;/\; hr$$ $$L \;/\; hr$$
$$\upsilon$$   (Greek symbol upsilon) = specific volume $$ft^3 \;/\; lbm$$ $$m^3 \;/\; kg$$
$$\Delta p$$ = pressure differential (pressure drop across the valve) $$lbf \;/\; in^2$$ $$Pa$$