The Simple Viscous Fluid

Since hydrodynamic lubrication depends on the behavior of real fluids with the property of viscosity, we cannot overlook the influence of shear stresses in the lubricant fluid even though they may be small compared to the normal pressures in the fluid. Each orthogonal component of tension, o, will differ from -p by quantities depending on the motion of distortion, which, as we have seen, are functions of a, fa, and c only. Let us postulate that these functions are linear and write out the following relations [4]  

The postulate used in formulating the equations above is not wholly arbitrary the format of these equations has a close analogy with the stress-strain relations for hydrostatic pressure in an elastic solid [5], the linearity of which follows directly from Hooke s law. 

The sum of the stress components o, and in Eqns 3-14a to 3-14c equals -3p, from which it follows that 

On writing out the partial differential equivalents, Eqns 3-14 become 

The quantity n is the absolute or dynamic viscosity of the fluid. As derived here, viscosity is an adjustment to the hydrodynamic equations relating stress and flow in a fluid to make them fit a postulated mode of behavior. But, as shown in Chapter 4, viscosity can also be defined 

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