# Flow Coefficient

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 formula |
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\(\large{ C_v = Q \; \sqrt{ \frac{ SG }{ \Delta p } } }\) | ||

Symbol |
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 formula |
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\(\large{ C_v = \frac{Q}{1360} \; \sqrt{ \frac{ T_a \; SG }{ \left( p_i \;+\; 15 \right) \; \Delta p } } }\) | ||

Symbol |
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 formula |
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\(\large{ C_v = \frac{ Q }{ 63 } \; \sqrt {\frac{ \upsilon }{ \Delta p } } }\) | ||

Symbol |
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 | \(\large{ \frac{ft^3}{lbm} }\) | \(\large{ \frac{m^3}{kg} }\) |

Tags: Coefficient Equations Pipe Sizing Equations Flow Equations Valve Sizing Equations