An improved theoretical model for the dynamics and stability of a vertical cantilevered pipe aspirating fluid

In this paper, a new theoretical model for the dynamics and stability of a vertical cantilevered aspirating pipe is developed based on the Newtonian method. The effects of the hydrodynamic forces at the free end on the dynamics and stability of the cantilevered pipe are examined in detail. A new comprehensive governing equation is discretized using the Galerkin method. Numerical results are presented to demonstrate the effects of the axial flow velocity ratio, flow angle ratio, and tangential velocity ratio on the eigenfrequency and critical velocity of the cantilevered pipe system. The theoretical model results are also found to be in good quantitative agreement with experimental results.