A fluid is considered homogenous from the standpoint of mass if its density is uniform throughout. Such an idealized state is rarely if ever attained except for limited portions of a fluid, since all real fluids are to some extent compressible and consequently their density must vary in the direction of gravity. The sea relative to the atmosphere might be considered as homogeneous. However, it will be shown later that even the slight variations in density which do exist are of prime importance in the computation of ocean currents.
In an idealized homogeneous fluid the isobaric surfaces under quasi-static conditions would all have the same inclination relative to the surfaces of and would have a spacing (for equal units of p) which would be proportional to g alone. Since the latter varies only slightly with elevation, the geometrical spacing would consequently be very nearly constant. The spacing of the surfaces of p with respect to would be exactly constant. This situation is schematically illustrated in Fig. 3.08-1(a).