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This paper presents a theoretical model of Coanda attachment mechanisms and laws of the Coanda effect. In this paper, it has been considered a very conventional setup in order to define by a theoretical analysis a mathematical model of the Coanda adhesion. It has been produced a complete mathematical model which could allow simple engineering calculations through an effective solutions of the differential equations of the system. A parametric model has defined as a function of main cinematic and geometric parameters. The final model relates to three fundamental parameters: outlet section, Coanda surfaces radius and inlet velocities. Turbulent and laminar models have defined. Validation through a large CDF campaign has produced in a regime of stream velocities from 5 to 40 m/s with good results.