**Chapter 5 Videos: Similarity and Dimensional Analysis (Buckingham Pi Theorem)**

**Part 1: Dimensional Analysis and Similarity (12:24)**

Brief introduction to the concepts of similarity and dimensional analysis in fluid mechanics. Flow over a smooth cylinder and aerodynamic drag are discussed in the context of similarity.

YouTube Video

Chapter 5 Part 1 (pdf) | |

File Size: | 3795 kb |

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**Part 2: Dimensional Analysis and Similarity (42:46)**

Discussion of the Buckingham Pi Theorem with a solved example for drag on a rectangular plate.

YouTube Video

Chapter 5 Part 2 (pdf) | |

File Size: | 1524 kb |

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**Part 3: Dimensional Analysis and Similarity (14:54**

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A dimensional analysis problem is solved to reproduce the form of Stokes' equation for drag over a sphere in creeping flow. This example shows how to deal with a dimensional analysis problem that has only one Pi parameter.

YouTube Video

Chapter 5 Part 3 (pdf) | |

File Size: | 5893 kb |

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**Part 4: Dimensional Analysis and Similarity (33:09)**

A sample problem involving dimensional analysis of forced convective heat transfer is solved in detail. The use of the resulting dimensionless parameters (Nusselt, Reynolds and Prandtl numbers) for correlating experimental data is discussed.

YouTube Video

Chapter 5 Part 4 (pdf) | |

File Size: | 1412 kb |

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**Part 5: Dimensional Analysis and Similarity (16:02)**

A discussion of some of the common dimensionless parameters in fluid mechanics: Reynolds number, Mach Number, Froude number, Weber number and Strouhal number.

YouTube Video

Chapter 5 Part 5 (pdf) | |

File Size: | 3413 kb |

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**Part 6: Dimensional Analysis and Similarity (17:46)**

A discussion of the Theory of Models. A discussion of how the results from model testing (for example in a wind tunnel) can be "scaled up" to predict the performance of the full scale system. The video concludes with a solved problem involving predicting the drag force on a billboard using results from model test in a water tunnel.

YouTube Video

Chapter 5 Part 6 (pdf) | |

File Size: | 666 kb |

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**Part 7: Dimensional Analysis and Similarity (30:03)**

A discussion of some typical model studies in fluid mechanics. An solved example of modelling a dam spill way is presented. An example of the models in the motion picture industry is briefly discussed.

YouTube Video

Chapter 5 Part 7 (pdf) | |

File Size: | 998 kb |

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**Solved Examples: Form Drag (22:41)**

Two solved examples of using dimensionless drag coefficient to calculate form drag. The form drag on a cylinder in a water flow is considered. The drag on a sports car is also calculated.

YouTube Video

Solved Example of Form Drag (pdf) | |

File Size: | 1774 kb |

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**Optional Chapter 5 Video**

**Part 8: Dimensional Analysis and Similarity (27:38)**

The method of Ipsen, an alternate procedure for determining dimensionless (Pi) parameters. Two solved examples are presented.

**Note: The Method of Ipsen will NOT be on the MEC516/BME516 Fall 2023 final exam.**

YouTube Video

Chapter 5 Part 8 (pdf) | |

File Size: | 657 kb |

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**Toronto Metropolitan University**