This page calculates the head loss coefficient and head loss at a smooth bellmouth pipe entrance.

The head loss *h _{L}* can be
calculated as:

h* _{L}* = k

Where *k*_{loss}
is the head loss coefficient, *u _{m}* is the mean flow velocity in the pipe, and

k_{loss} = 235.03x^{4}
- 194.09x^{3} + 56.739x^{2} - 7.8163x + 0.50

Where *x* is the defined as:

x = r / D_{h}

Where *r* is the radius of the pipe and *D _{h}* is the
hydraulic diameter.

The *k*_{loss} equation was derived from a
curve fit from points when plotted from
the following data and are accurate plus/minus 10%:

r/D_{h} |
k_{loss} |

0.00 | 0.5 |

0.01 | 0.44 |

0.02 | 0.37 |

0.03 | 0.31 |

0.04 | 0.26 |

0.05 | 0.22 |

0.06 | 0.2 |

0.08 | 0.15 |

0.10 | 0.12 |

0.12 | 0.09 |

0.16 | 0.06 |

0.20 | 0.03 |

**References**

Roberson, John A. and Crowe, Clayton T., *Engineering
Fluid Mechanics*, 2nd Ed., Rudolf Steiner Press, London.1976. p 360 - 384.

Idel'chik, I E. and Fried, Erwin., *Flow Resistance, a
Design Guide for Engineers*, Taylor & Francis, Washington D.C. 1989. p
52.

ASHRAE. *ASHRAE Handbook, 1977 Fundamentals*, American
Society of Heating, Refrigerating And Air Conditioning Engineers, Inc., New
York, 1997. p 32.31.