Page 381 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 365

The equation of continuity takes the form

(B)Spherical Coordinates. With v r>v0,v0 denoting the velocity components in (r, &, <p) the
Navier-Stokes equations for incompressible Newtonian fluid are [see Prob. 6.15]

The equation of continuity takes the form

6.9 Boundary Conditions

On a rigid boundary, we shall impose the non- slip condition (also known as the adherence
condition), i.e., the fluid layer next to a rigid surface moves with that surface, in particular if
the surface is at rest, the velocity of the fluid at the surface is zero. The nonslip condition is
well supported by experiments for practically all fluids, including those that do not wet the
surface (e.g. mercury) and Non-Newtonian fluids (e.g., most polymeric fluids).