# Piping Geometry Factor

Piping geometry factor, abbreviated as \(F_p\), a dimensionless number, is the pressure and velocity changes caused by fittings such as bends, expanders, reducers, tees, and Y's if directly conected to the valve.

## Piping Geometry Factor Formula |
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\(\large{ F_p = \frac{1}{ \sqrt{1\;+\;\frac{\Sigma K}{0.00214} \; \left( \frac{C_v}{D_v^2} \right)^2 } } }\) | ||

Symbol |
English |
Metric |

\(\large{ F_p }\) = piping geometry factor | \(\large{ dimensionless }\) | |

\(\large{ D_v }\) = nominal valve size | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ C_v }\) = flow coefficient | \(\large{ dimensionless }\) | |

\(\large{ \Sigma K }\) = algebraic sum | \(\large{ dimensionless }\) |

## Solve for: |
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\(\large{ \Sigma K = K_1 + K_2 + K_{B1} + K_{B2} }\) \(\large{ \Sigma K }\) (the algebraic sum of the velocity head loss coefficient for all the fittings that are attached to the valve) |
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Symbol |
English |
Metric |

\(\large{ K_1 }\) = resistance coefficient of upstream fittings | \(\large{ dimensionless }\) | |

\(\large{ K_2 }\) = resistance coefficient of downstream fittings | \(\large{ dimensionless }\) | |

\(\large{ K_{B1} }\) = inlet Bernoulli coefficient | \(\large{ dimensionless }\) | |

\(\large{ K_{B2} }\) = outlet Bernoulli coefficient | \(\large{ dimensionless }\) | |

\(\large{ D_v }\) = nominal valve size | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ d }\) = pipe inside diameter, upstream and downstream | \(\large{ in }\) | \(\large{ mm }\) |

## Solve for: |
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\(\large{ K_1 = 0.5 \; \left( 1 - \frac{D_v^2}{d^2} \right)^2 }\) (inlet expander / reducer) \(\large{ K_1 = 1.0 \; \left( 1 - \frac{D_v^2}{d^2} \right)^2 }\) (outlet expander / reducer) \(\large{ K_1 + K_1 = 1.5 \; \left( 1 - \frac{D_v^2}{d^2} \right)^2 }\) (for a valve installed between identical expander / reducer) \(\large{ K_{B1} }\) or \(\large{ K_{B2} = 1 - \left( \frac{D_v}{d} \right)^4 }\) \(\large{ K_{B1} }\) or \(\large{ K_{B2} }\)(are only used when the diameter of the piping approaching the valve is different from the diameter of the piping leaving the valve) |

Tags: Pressure Equations Valve Equations Pipe Equations Pipeline Equations