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Hydrodynamics of Ideal Liquids

  • Kolumban HutterEmail author
  • Yongqi Wang
Chapter
  • 1.9k Downloads
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

This chapter starts with kinematic concepts such as ‘motion’, ‘velocity’, ‘Eulerian and Lagrangean descriptions’, and then proceeds to describe ‘streamlines’, ‘trajectories’ and ‘streak lines’, illuminating these with illustrative examples. Next, the balance laws of mass and linear momentum are discussed both in global and local form and specialized to Eulerian fluids. The Bernoulli equation, defined as the path-integration of the scalar product of the momentum equation with the velocity field is given extensive space; it is discussed both when referred to non-inertial and inertial frames and when the integration is conducted along any path or along streamlines. Ample space is devoted to applications of the Bernoulli equation to typical examples, e.g., venturi pipes, Prandtl pipes, Torricelli flow out of a vessel, including clepsydra clocks. Global formulations of the momentum equation are equally touched and applied to the problem of Borda’s exit flows, impact of a jet on a wall, mixing processes of non-uniform velocities in plane conduits, hydraulic jumps and flow of a density preserving fluid through a periodic grid of wings. Aerodynamics is given a first glimpse by studying plane flow around infinitely long wings, specifically by deriving the Kutta-Joukowski condition of smooth flow off the wing’s trailing edge, which fixes the circulation around the wing. The chapter closes with a presentation of the balance of moment of momentum and its application to the Segner water wheel and Euler’s turbine equation.

Keywords

Kinematics Streamlines Trajectories Streaklines Balances of mass and linear momentum Bernoulli equation Plane wing theory Balance of moment of momentum 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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