Abstract
In this chapter, we convert the basic equations to a secondary partial differential equation, which only contains one pressure variable, which is the famous Reynolds equation. Reynolds equation is mainly used to solve hydrodynamic lubrication problems of Newtonian fluids. Although some equations similar to Reynolds equation can be obtained to solve some non-Newtonian problems, there are many difficulties to obtain a Reynolds-like equation. We show three main difficulties during derivation and point out that it is very difficult or even impossible to obtain Reynolds-like equations for most non-Newtonian fluids. In order to obtain the solution of a non-Newtonian hydrodynamic lubrication problem it is necessary to solve these difficulties.
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