Fluid Preliminaries |

By definition, a fluid is a material continuum that is unable to withstand a static shear stress.
Unlike an elastic solid which responds to a shear stress with a recoverable deformation, a fluid responds with
an irrecoverable flow.
Variables needed to define a fluid and its environment are: |

Quantity | Symbol | Object | Units |

pressure | p | scalar | N/m^{2} |

velocity | v | vector | m/s |

density | r | scalar | kg/m^{3} |

viscosity | m | scalar | kg/m-s |

body force | b | vector | N/kg |

time | t | scalar | s |

Examples of fluids include gases and liquids. Typically, liquids are considered to be incompressible, whereas gases are considered to be compressible. However, there are exceptions in everyday engineering applications. |

Types of Flow; Reynolds Number |

Fluid flow can be either laminar or turbulent. The factor that determines which type of flow is present is the ratio of inertia forces to viscous forces within the fluid, expressed by the nondimensional Reynolds Number, |

where V and D are a fluid characteristic velocity and distance.
For example, for fluid flowing in a pipe,
V could be the average fluid velocity, and D would be the pipe diameter.
Typically, viscous stresses within a fluid tend to stabilize and organize the flow, whereas excessive fluid inertia tends to disrupt organized flow leading to chaotic turbulent behavior. Fluid flows are laminar for Reynolds Numbers up to 2000. Beyond a Reynolds Number of 4000, the flow is completely turbulent. Between 2000 and 4000, the flow is in transition between laminar and turbulent, and it is possible to find subregions of both flow types within a given flow field. |

Governing Equations |

Laminar fluid flow is described by the Navier-Stokes equations. For cases of inviscid flow, the Bernoulli equation can be used to describe the flow. When the flow is zero (i.e. statics), the fluid is governed by the laws of fluid statics. |