§ 28. The general equation of the steady motion of a fluid given under
Hydrodynamics furnishes immediately three results as to the
distribution of pressure in a stream which may here be assumed.
(a) If the motion is rectilinear and uniform, the variation of
pressure is the same as in a fluid at rest. In a stream flowing in an
open channel, for instance, when the effect of eddies produced by the
roughness of the sides is neglected, the pressure at each point is
simply the hydrostatic pressure due to the depth below the free
surface.
(b) If the velocity of the fluid is very small, the distribution of
pressure is approximately the same as in a fluid at rest.
(c) If the fluid molecules take precisely the accelerations which they
would have if independent and submitted only to the external forces,
the pressure is uniform. Thus in a jet falling freely in the air the
pressure throughout any cross section is uniform and equal to the
atmospheric pressure.
(d) In any bounded plane section traversed normally by streams which
are rectilinear for a certain distance on either side of the section,
the distribution of pressure is the same as in a fluid at rest.