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The values for pipe fittings friction is based on the information provided by the Crane Valve Co. www.cranevalve.com and I have included excerpts from the Crane Technical Paper No.410.

The fittings friction loss is given by:

[1-1] |

where g is the acceleration due to gravity (=32.17 ft/s^{2}) and v is the average fluid velocity at the inlet of the fitting, K is the factor that varies for each type and size of fitting and H_{FF} is the friction value in feet of fluid for the fitting.

The Crane technical paper gives the K value for a fitting in terms of the term f_{T} as in this example for a regular 90 degree elbow (equation [1-2]):

[1-2] |

The friction loss for fittings is based on the assumption that the flow is highly turbulent, in fact that it is so turbulent that the Reynolds number is no longer a factor and pipe roughness is the main parameter affecting friction. This can be seen in the Moody diagram. There is a line in the diagram that locates the position where full turbulence starts.

The term f_{T} is called the friction parameter and is given by the Colebrook or the Swamee-Jain equation, for this purpose I am using the Swamee-Jain formula (equation [1-3]) which is very accurate.

[1-3] |

When the Reynolds number becomes large the value of f_{T} becomes:

[1-4] |

furthermore the Crane technical paper assumes that the roughness of the material will correspond to new steel whose value is 0.00015 ft. Therefore the previous equation for f_{T} becomes:

[1-5] |

Therefore the value of the K factor is easily calculated based on the diameter of the fitting, the friction parameter fT and the multiplication factor for each type of fitting (for example the number 30 in equation [1-2]). The following four charts give the multiplication factor for different fittings.

You can purchase the Crane Technical Paper No. 410 at this location: http://www.cranevalve.com/tech.htm

and the Cameron Hydraulic data book here: http://www.cameronbook.com/Merchant2/Merchant.mv?