Background

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DescriptionThis problem involves incompressible liquid flow of oil in a long pipeline. The required flow rate of oil and the total pressure drop are given. The pipeline is long enough and straight enough for the individual fittings to be ignored and the sizing is done based on the overall equivalent length only. The pipe inside surface is defined as "smooth". There is no net change in elevation.

Problem Reference

Coulson and Richardson's Chemical Engineering, Vol 1, 6th Ed, (1999), Page 830, problem 3.23 and Solution Manual, Page 37

Fluid Details

Fluid : | Oil |

Flow rate : | 50 tonne/h |

Phase : | Liquid |

Density : | 950 kg/m³ |

Viscosity : | 1.0e-2 N.s/m² (= 10 cP) |

Roughness : | "smooth" |

Length : | 10 km |

Pressure drop : | 200 kPa |

Elevation change : | nil |

Fittings : | incl. as equiv. length |

Calculate the minimum pipe diameter that would meet the pressure drop limitation

Download LinkYou can run this example in AioFlo by downloading and opening the data file.

Comparison of Results

Calculated Item | Reference | AioFlo | AioFlo |
---|---|---|---|

Roughness | "smooth" | 0.01 mm | 0.1 mm |

Reynolds Number | (not given) | 9214 | 9173 |

Friction Factor (Moody) | (not given) | 0.03164 | 0.03236 |

Pipe ID (mm) | 193 | 191.9 | 192.8 |

In this example Coulson & Richardson have defined the pipe as "smooth" and used the Blasius Equation to model the friction factor. A typical pipe roughness for commercial steel pipe is 0.05 mm. This value has been bracketed in AioFlo by performing the calculation with roughnesses of 0.01 mm and 0.1 mm. It is instructive to note that under these circumstances a 10 fold change in pipe roughness has resulted in a 2.5% change in friction factor and a 0.5% change in required pipe diameter. The insignificant effect of the roughness is because the problem has been formulated such that the Reynolds Number and relative roughness (i.e. e/d) are low and the flow falls into the "smooth flow" regime. Using a roughness value of less than 0.01 mm for this problem would make virtually no difference in the calculated diameter.

The parameters of this problem have been selected by the authors to illustrate the "smooth flow" aspects, and result in a lower velocity (0.5 m/s) than would be usual for an oil pipeline. A low velocity is not able to keep the line clean if there are solids that can settle, and also would not be able to flush air out of any slightly higher points at start-up.