1 - Equations of Motion
Published online by Cambridge University Press: 06 July 2010
Summary
The fluid state
Consider a fluid that can be regarded as continuous and locally homogeneous at all levels of subdivision. At any time t and position x = (x1, x2, x3) the state of the fluid is defined when the velocity v and any two thermodynamic variables are specified. A fluid in unsteady motion, in which temperature and pressure vary with position and time, cannot strictly be in thermodynamic equilibrium, and it will be necessary to discuss how to define the thermodynamic properties of the small individual fluid particles of which the fluid may be supposed to consist.
The distinctive fluid property possessed by both liquids and gases is that these fluid particles can move freely relative to one another under the influence of applied forces or other externally imposed changes at the boundaries of the fluid. Five scalar partial differential equations are required for determining these motions. They are statements of conservation of mass, momentum, and energy, and they are to be solved subject to appropriate boundary and initial conditions, dependent on the problem at hand. This book is concerned with the use of these equations to formulate and analyse a wide range of model problems whose solutions will help the reader to understand the intricacies of fluid motion.
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- Hydrodynamics and Sound , pp. 1 - 13Publisher: Cambridge University PressPrint publication year: 2006