  The global energy budget of the hot gas flows in early-type galaxies is used
to explain the recent observational results that S0 galaxies have lower mean
X-ray luminosity $L_X$ per unit optical luminosity $L_B$ than do ellipticals.
This could be explained with a higher heat input or with a lower gravitational
energy (all per unit gas mass), at fixed $L_B$. The effect of the flattening of
the mass distribution is investigated with galaxy models described by the
Miyamoto-Nagai potential--density pair, to which a dark matter halo of various
shapes is added. For these models the analytical expressions of the
gravitational energy, and the stellar kinetic energy associated with various
relative amounts of random motions and rotational streaming, are derived. It is
found that rotation cannot produce a change in the flow phase of the hot gas,
independently of the galaxy shape and the presence of dark matter. The effect
of flattening instead can be substantial in reducing the binding energy of the
hot gas. Thus S0s and possibly non spherical Es are less able to retain a
significant halo of hot gas than rounder Es of the same $\lb$.
