Similarity and dimensional considerations and some thermodynamic arguments are applied to planetary atmospheres to estimate such characteristics of their general circulations as the total kinetic energy of the circulation, the rate of generation (or dissipation) of the kinetic energy, the efficiency of an atmosphere in transformation of the supplied energy into energy of atmospheric motions, and the characteristic temperature difference which drives the circulation. As known external parameters there are the energy supply to an atmosphere, the mass of the atmosphere, its heat capacity, the radius of the planet, the angular velocity of rotation, and the gravitational acceleration, g. The energy balance in an atmosphere is maintained by longwave radiation into space which requires one universal constant, Stefan's constant. From these seven dimensional parameters only four have independent dimensions; therefore one may construct three nondimensional complexes which are the criteria of similarity. The first of these is the ratio of the atmospheric scale height to the planetary radius. It is always small; therefore one may propose the first self-similarity hypothesis of the circulation with respect to g; i.e., the exact value of g is not important for the theory. The second criterion of similarity may be interpreted in various ways; it is also small for all the planets, with the possible exception of Mercury (if it has an atmosphere). The self-similarity with respect to this parameter turns out to be the independence on the mass of the atmosphere, if only the mass is large enough. The third criterion of similarity is the ratio of the linear velocity of an atmosphere at the equator to the sound velocity (rotational Mach number). This criterion is small for Venus(and Mercury), of order unity for the Earth and Mars, and large (about 15) for Jupiter and Saturn. If one neglects rotation, then it is possible to derive an expression for the total kinetic energy of an atmosphere where a nondimensional constant enters, which even for the Earth and Mars is of order unity. The lifetime of the circulation τ u is introduced using radius, mean velocity, and a multiplier β which is a measure of the degree of organization of atmospheric motions. The value of β is of the order of unity for slowly rotating planets, but it is very large for the giant rapidly rotating planets. Knowledge of π u allows us to estimate the mean rate of dissipation of the kinetic energy and the efficiency of the atmospheric heat engine. Considering the last quantity to be proportional to δT, the circulation driving temperature difference, one may estimate δT as well. Possible modifications of the theory are proposed for rarified atmospheres, and for rapidly rotating planets. This approach gives estimates which agree well with the observational data for the Earth's atmosphere and with the results of numerical experiments for the Martian atmosphere. For Venus, averaged throughout the atmosphere, the velocities of circulation are estimated to be of the order of 1m/sec and δT ⋍ 2° K . From the kinetic energy of visual motions of Jupiter and Saturn, which can be estimated from observations, it is found that β should be very large. This should lead to a very large lifetime of the overall circulation and of major atmospheric hydrodynamic formations. In this connection a suggestion is proposed that the Great Red Spot might be a long-lived eddy. Attention is paid to the fact that the energy of the visual motions on Saturn is greater by an order of magnitude than on Jupiter, while the similarity criteria are almost equal.