TABLE OF CONTENTS The motion of a fluid is studied on the basis of the fundamental principle of mechanics, namely the conservation laws of mass, momentum and energy. For a state of matter to which the continuum hypothesis (Sec. 1.2) can be applied, macroscopic motions of the matter (a fluid) are less sensitive to whether the structure of matter is discrete or continuous. In the continuum representation of fluids, the effect of actual discrete molecular motion is taken into account as transport phenomena such as diffusion, viscosity and thermal conductivity in equations of motion. In fluid mechanics, all variables, such as mass density, momentum, energy and thermodynamic variables (pressure, temperature, entropy, enthalpy, or internal energy, etc.), are regarded as continuous and differentiable functions of position and time.
Equilibrium in a material is represented by the property that the thermodynamic state-variables take uniform values at all points of the material. In this situation, each part of the material is assumed to be in equilibrium mechanically and thermodynamically with the surrounding medium. However, in most circumstances where real fluids are exposed, the fluids are hardly in equilibrium, but state variables vary from point to point. When the state variables are not uniform, there occurs exchange of physical quantities dynamically and thermodynamically. Usually when external forcing is absent, the matter is brought to an equilibrium in most circumstances by the exchange. This is considered to be due to the molecular structure or due to random interacting motion of uncountably...
