Fundamentals of Modern Unsteady Aerodynamics by Ülgen Gülçat

Author:Ülgen Gülçat
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

7.1 Newton’s Impact Theory

The amount of pressure exerted on a surface with impinging flow is equal to the normal component of the momentum exerted by the impinging fluid particles. The theory proposed by Newton and based on this impact idea was interpreted, until the beginning of 20th century, as the cause of the aerodynamic force acting on flying objects! The impact theory on the other hand was not able to produce sufficient lifting force to balance the weight of flying creatures in nature. Naturally, during the years of the emergence of the impact theory and for the following couple of centuries to come the relation between the air speed and the compressibility of air was not known. Therefore, by shear coincidence the evaluation of surface pressure coefficient with the impact theory, independently from the Mach number itself, at very high Mach numbers was given in the first half of the 20th century (Hayes and Probstein 1966). Now, let us evaluate the pressure exerted by the impact theory on a wall inclined with angle θw in a freestream speed of U. The amount of mass per unit time per unit area of the air particles striking the wall, shown in Fig. 7.1, is ρUn. The momentum exerted on the wall by this air mass is ρ(Un)2 which is also equal to the pressure exerted.

Fig. 7.1Velocity components of the fluid particles impinging on a wall at a free stream speed of U

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