The closed physical constraint equations of sand-dust atmosphere are established based on both the interaction of wind-blown-sand two-phase flows and the mass change. Ideal analysis of the equations shows the following findings: (1) the density of the sand-dust atmosphere is bigger than that of the pure atmosphere, which will reduce the velocities of air parcels of the former to some extent; (2) velocity difference between sand-dust particles and air can make the fine particles located in a high-speed region and the coarse particles located in a low-speed region; (3) temperature difference between sand-dust particles and air can make the particles tend to enhance convection through acting as a heat source in updraft and a cold source in downdraft; (4) the constant-volume mass-specific heat capacity of the sand-dust atmosphere can give rise to the generation of new temperature gradient on an isobaric surface and then enhance the entrainment at the boundary of a sand-dust cloud; (5) the gas constant of the sand-dust atmosphere can lead to the generation of new pressure gradient on an isothermal surface and also enhance the entrainment at the boundary of a sand-dust cloud; (6) mass change can largely affect density, velocity and temperature of the sand-dust atmosphere. In brief, compared with the sand-dust cloud given by equations based on passive scalar, the real sand-dust cloud is high and great. Besides this, its inner convection and its entrainment at the boundary are active, and its horizontal motion is slow.