Y

Figure 2.6: Well-ordered parallel flow important materials, that are not described by the Newtonian law of viscosity are referred to non-newtonian fluids. In this case p may be described as a function of ^ or Tx xy-

In more general flows, there are more general relations between the stress field and the velocity field( namely constitutive law). Here, we consider Stoke's viscosity law. This is based on assumption that each stress is linearly related through a set of constants to each of the six strains rates (.ij,i,j = x,y,z \.ij=.ji). In addition each normal stress is directly related to pressure p. The constants are called viscosity coefficients and fluids behaving accordingly to this relation are called Newtonian fluid. The Stoke's viscosity law degenerates to Newton's viscosity law for the special case of parallel flow. Knowing that most Newtonian fluids have flow properties which are independent of direction of coordinates and also considering that for most fluid p = — a= — 1 (Txx + Tyy + Tzz), we reach the following relationships:

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