Hydrodynamics of Ordinary Isotropic Fluids

In later chapters where we study laser-induced acoustic (sound, density) waves in liquid crystals, or generally when one deals with acoustic waves, it is necessary to assume that the density p(f, t) is a spatially and temporally varying function. In this chapter, however, we decouple such density wave excitation fi om all the processes under consideration and basically limit our attention to the flow and orientational effects of an incompressible fluid. In that case we have 

For all liquids, in fact for all gas particles or charges in motion, the equation of continuity also holds 

This equation states that the total variation of pv over the snrfaee of an enclosing volume is equal to the rate of decrease of the density. Sinee 3p / 31 = 0, we thus have, from Equation (3.51), 

The equation of motion describing the acceleration dvidt of the flnid elements is simply Newton s law  

Studies of the hydrodynamics of liquids may be said to be eentered around this equation of motion, as we identify all the various origins and mechanisms of forces acting on the fluid elements and attempt to solve for their motion in time and space. 

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