# Flow Coefficient

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Flow coefficient, abbreviated as $$C_v$$, 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 Formula

(Eq. 1)  $$\large{ C_v = Q \; \sqrt {\frac{SG}{\Delta p} } }$$

(Eq. 2 by volume)  $$\large{ C_v = Q \; \left( {\frac{SG}{\Delta p} } \right) ^{\frac{1}{2} } }$$

(Eq. 3 by weight)  $$\large{ C_v = \frac {W}{500 \; \left( SG \; \Delta p \right) ^{\frac{1}{2}} } }$$

Where:

$$\large{ C_v }$$ = flow coefficient

$$\large{ Q }$$ = flow rate capacity

$$\large{ W }$$ = flow weight

$$\large{ \Delta p }$$ = pressure differential

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

Solve for:

$$\large{ Q = C_v \; \sqrt {\frac{SG} {\Delta p} } }$$

$$\large{ \Delta p = SG \; \left( {\frac{Q} {C_c} } \right) ^{\frac{1}{2} } }$$

$$\large{ C_v = 1.157 \; K_v }$$     (US units)

$$\large{ K_v = 0.8646 \; C_v }$$     (SI )units