Research relevance. The article proves the advisability of applying high-speed axial fan systems by aerodynamic configuration with one impeller for gas air-cooling units. 
Objective and methods of research. Equations for the efficiency factor of a fan system and a fan depending on flow kinematics and fan system geometry have been obtained by mathematically analyzing axial flow turbomachine main regularities.
Results. Based on the optimization theory, the formulae for maximum efficiency factor for a fan and a fan system of various specific speeds have been obtained depending on the flow coefficient and the impeller hub ratio. The method of creating the axial fan system aerodynamic configuration has been proposed for the K-type gas air-cooling units with the limiting maximum values of the efficiency factor for the prescribed values of the specific speed, impeller hub ratio, lift-to-drag ratio of the impellor profiles, airflow resistance coefficient of the flow channel, and the flow coefficient. The capability was shown to create the fan system with a speed exceeding 400 and efficiency of not less than 0.86.
Keywords: fan system; flow channel; input elements; output elements; efficiency factor; specific speed; lift-to-drag ratio; air-flow resistance coefficient.

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