Page 391 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 375

The velocity field given by Eq. (i) obviously satisfies the equation of continuity:

for any v(r).

Fig. 6.8

In the absence of body forces, the Navier-Stokes equations, in cylindrical coordinates for the
velocity field of Eq. (i) are :

From Eqs. (6.13. la) and (6.13.1b), we see that/? depends only on z and from Eq. (6.13.1c), we
have

thus, dp/dz is a constant. Let

then