## Valve Sizing Relations

1. Incompressible Fluids

Bernoulli's equation applied across the valve relates the pressure drop and flow rate in terms of the valve loss coefficient. This equation can be rearranged to give the flow rate as follows:

where A is an appropriate flow area, V is the velocity through that area, APv = P1 — P2 is the pressure drop across the valve, and Kf is the loss coefficient referred to the velocity V. However, in a control valve the internal flow geometry is relatively complex and the area (and hence V) varies throughout the valve. Also, the pressure drop is not the maximum value in the valve (which would occur if P2 is at the discharge vena contracta, as for the orifice meter) but is the net unrecovered pressure loss, corresponding to P2 which is far enough downstream that any possible pressure recovery has occurred. The flow area and geometrical factors are thus combined, along with the density of the reference fluid and the friction loss coefficient, into a

Liquid Level Systems

Control Valve Pressura Drop |
Beat Inherent Characteristic |

Constant AP |
Linear |

Decreasing AP with Increasing Load. AP at Maximum Load > 20% of Minimum Load AP |
Linear |

Decreasing AP with Increasing Load, AP at Maximum Load < 20% of Minimum Load AP |
Equal-Percentage |

Increasing AP with Increasing Load, AP at Maximum Load < 200% of Minimum Load AP |
Linear |

Increasing AP with Increasing Load. AP at Maximum Load > 200% of Minimum Load AP |
Quick Opening |

Pressure Control Systems | |

Application |
Best Inherent Characteristic |

Liquid Process |
Equal-Percentage |

Gas Process, Smalt Volume, Less Than 10 ft. of Pipe Between Control Valve and Load Valve |
Equal-Percentage |

Gas Process. Large Volume (Process has a Receiver, Distribution System or Transmission Line Exceeding 100 ft. of Nominal Pipe Volume) Decreasing AP with Increasing Load, AP at Maximum Load > 20% of Minimum Load AP |
Linear |

Gas Process. Large Volume. Decreasing AP with Increasing Load. AP at Maximum Load < 20% of Minimum Load AP |
Equal-Percentage |

Flow Control Processes

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