Page 366 - Introduction to Continuum Mechanics

350 Equations Of Hydrostatics

that

or.

All incompressible fluids need not have a spatially uniform density (e.g. salt water with
nonuniform salt concentration with depth may be modeled as a nonhomogeneous fluid). If
the density is also uniform, it is referred to as a " homogeneous fluid," for which p is constant
everywhere.
Substances such as air and vapors which change their density appreciably with pressure are
often treated as compressible fluids. Of course, it is not hard to see that there are situations
where water has to be regarded as compressible and air may be regarded as incompressible.
However, for theoretical studies, it is convenient to regard the incompressible and compres-
sible fluid as two distinct kinds of fluids.

6.3 Equations Of Hydrostatics

The equations of equilibrium are [see Eqs. (4.7.3)]

where /?/ are components of body forces per unit mass.
With

Eq. (6.3.1) becomes

or,

In the case where Bj are components of the weight per unit mass, if we let the positive x$
axis be pointing vertically downward, we have,

so that