Page 379 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 363

Now, Eq. (v) can be written

Let rbe the position vector for a particle at x, then

and

Thus, Eq. (vi) can be written

Using Eqs(ii) and (viii), we obtain

or,

Similar derivation will give

Thus, for all points on the same plane which is perpendicular to the direction of flow (e.g.,
plane A-A in Fig. 6.4)

Example 6.7.3

For the uni-directional flow shown in Fig. 6.5, find the pressure at the point A.
Solution, According to the result of the previous example, the piezometric head of the point
A and the point B are the same. Thus,