Incompressible laminar flow - newtonian and non-newtonian fluids

The problems of incompressible flows dominate a large part of the fluid mechanics scene. For this reason, they are given special attention in this book and we devote two chapters to this subject. In the present chapter we deal with various steadystate and transient situations in which the flow is forced by appropriate pressure gradients and boundary forces. In the next chapter we shall consider free surface flows in which gravity establishes appropriate wave patterns as well as the so-called buoyancy force in which the only driving forces are density changes caused by temperature variations. At this stage we shall also discuss briefly the important subject of turbulence. We have already mentioned in Volume 1 the difficulties that are encountered generally with incompressibility when this is present in the equations of solid mechanics. We shall find that exactly the same problems arise again in fluids especially with very slow flows where the acceleration can be neglected and viscosity is dominant (so-called Stokes flow). Complete identity with solids is found here (namely Chapter 12, Volume I ) . The essential difference in the governing equations for incompressible flows from those of compressible flows is that the coupling between the equations of energy and the other equations is very weak and thus frequently the energy equations can be considered either completely independently or as an iterative step in solving the incompressible flow equations. To proceed further we return to the original equations of fluid dynamics which have been given in Chapters 1 and 3; we repeat these below for problems of small compressibility.