Finite Element Techniques for Fluid Flow

BASIC PRINCIPLES AND GOVERNING EQUATIONS 161

Taking σ = -pis known as the 'Stokes' condition and leads to

λ = -\μ (4.70)

The volumetric deformation for many fluids

is

small in comparison

to the shearing deformations, and it is generally quite reasonable to

assume the fluid is incompressible. For this case,

4.6 NAVIER-STOKES EQUATIONS—INCOMPRESSIBLE

NEWTONIAN FLUID

It is necessary, at this point, to summarise the equations. We restrict

this summary to incompressible flow, no mechanical-thermal

coupling, and a Newtonian fluid. In Section 4.8 we discuss how the

equations are modified to account for turbulence.

Figure 4.8 shows the classificatio ...