On Vibration of a Fluid contained in an Annular Region bounded by two Concentric or Excentric Circular Cylinders

Abstract

Here we take up the case of a fluid contained in an annular region bounded by two concentric or excentric circular cylinders (both of infinite length). When the inner cylinder vibrates, the fluid also vibrates and a vibratory hydrodynamic pressure is set up in the fluid. The Author has made a theoretical calculation about the amplitude of this vibratory pressure, for the following two cases : - (A) Two-dimensional motion, for the case of concentric circular cylinders. The fluid may have a whirling or tangential velocity, together with the vibratory motion. The compressibility of the fluid is taken into account but the viscosity is neglected. (B) Two-dimensional motion, for the case of excentric circular cylinders. The fluid may have a whirling velocity, together with the vibratory motion. The fluid is assumed to be incompressible and non-viscous. In conclusion, it is pointed out that the maximum value of the amplitude of vibratory pressure varies with the square of the frequency of vibration, and that in some cases it can become so great that the phenomenon of cavitation may be caused by it.