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Basic Concepts of Fluid Flow

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Abstract

This first chapter introduces the basic concepts of fluid flow and its mathematical description. First, conservation principles for mass, momentum, and scalar quantities are introduced. The governing equations are presented in coordinate-free vector form, in differential form using Cartesian coordinates and base vectors, and in integral form. Dimensionless equations in differential form are also given, together with the description of the main parameters (Reynolds number, Mach number etc.). Several simplified forms of governing equations are also described, followed by the mathematical classification of flows. The plan of the book closes this chapter.

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Notes

  1. 1.

    Bold symbols, e.g., \(\mathbf {v}\) or \(\mathbf {f}\) are vectors with three components in the context of this book.

  2. 2.

    This equation is often called the control volume equation or the Reynolds’ transport theorem.

  3. 3.

    For example, blood can be treated as Newtonian at high shear rates (Tokuda et al. 2008), but with a variable viscosity in other cases (Perktold and Rappitsch 1995).

  4. 4.

    Under certain circumstances, e.g., very high pressure or in the deep ocean, the compressibility of liquids needs to be accounted for. Likewise, as noted in Sect. 1.1, in simulating the atmosphere, the compressible version of the flow equations might need to be used even though the Mach number is very small.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Joel H. Ferziger

  2. University of Duisburg-Essen, Duisburg, Germany

    Milovan Perić

  3. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA

    Robert L. Street

Authors
  1. Joel H. Ferziger
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  2. Milovan Perić
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  3. Robert L. Street
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Correspondence to Milovan Perić .

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Ferziger, J.H., Perić, M., Street, R.L. (2020). Basic Concepts of Fluid Flow. In: Computational Methods for Fluid Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-99693-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-99693-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99691-2

  • Online ISBN: 978-3-319-99693-6

  • eBook Packages: EngineeringEngineering (R0)

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