# Flow Coefficient

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

Tags: Equations for Coefficient Equations for Flow Equations for Valves