Fractional Calculus of Hydraulic Drag in the Free Falling Process
A new approach to describe the hydraulic drag received by a falling body has been developed through fractional calculus, and the analytical solution has been given. This new method treats the measurement of the hydraulic drag as the fractional derivative of the falling body’s displacement. The existing methods could be classified into two categories. The first ones assume the drag could be described by a quadratic equitation of the body’s velocity and use the classical Newton law to describe the falling process. The second ones do introduce the fractional calculus to describe the dynamic process but still treat the drag as the quadratic of velocity, which make the physics meaning of parameters are obscure. Compared to existing methods, the new approach introduced in this paper is original from the perspectives of basic hypothesis and modeling. To evaluate the performance of this method, series experiments have been conducted with the help of high speed camera. The data fit the new method successfully, and compared to the existing approaches, the new one has the overall better performance on the accuracy to describe the dynamic process of the falling body and owns intuitive physical explanation of its parameters.
Keywordsfractional calculus hydraulic drag falling process
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