### Head Loss at Pipe Entrance Equations and Calculator

**Fluids Flow Engineering**

**Hydraulic & Pneumatic Design Engineering**

Head Loss at Pipe Entrance Equations and Calculator using the head loss coefficient and head loss of a fluid at a smooth bellmouth pipe entrance.

The head loss h_{L}can be calculated as:

h_{L}= k_{loss} x (u_{m}^{2} / (2 x g) )

Where *k *_{loss} is the head loss coefficient, (u_{m}* *is the mean flow velocity in the pipe, and *g *is the gravitational acceleration. k_{loss}* *is calculated from:

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 = * radius in Meters (m)

*D _{h} *= Inside diameter in Meters (m)

u

_{m}= Flow Velocity m/s

h

_{L}= Head Loss (m)

k

_{loss}= Head Loss - dimension less

D

_{h}= Diameter Ratio - dimension less

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.

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