A more general discussion Before moving forward, let's give a slightly more general discussion, emphasizing tensor analysis. In fact, this formula reduces to the above Newtonian formula in the special case that , where only if all the indices are the same. Since our derivation of the viscous force is phenomonological, it is both important and useful to make sure all of the assumptions are clearly stated. Stated another way, the viscous effects in fluid capture the macroscopic consequences of dissipative collisions between fluid particles.
Life is simplified by making assumptions.
First, the tensor must be isotropic . Under this assumption, the fourth rank tensor can be decomposed into where A , B and C are numbers and is just the identity matrix. The assumption of isotropy has reduced the complexity of fluid interactions to just three constants. Traditionally, the constant A is called the bulk viscosity , and the constant is called the shear viscosity. For an incompressible fluid where the density remains constant the bulk viscosity is irrelevant because .