Sloshing of a Liquid in Connected Cylindrical Tanks Owing to U-Tube Free Oscillations

Abstract

When two parallel cylindrical tanks are connected by a pipe joining the tank bottoms, the liquid can oscillate back and forth between tanks, just as in a U shaped tube. This paper deals with the axisymmetric sloshing oscillations excited in each tank because of the flow back and forth between the tanks. By applying the results from a recent paper [P. G. Bhuta and G. C. K. Yeh, “Liquid Sloshing Due to a Time Dependent Discontinuous Boundary,” Intern. J. Mech. Sci. 7, 475–488 (1965)], the expressions of velocity, pressure, and waveheight are obtained in terms of the liquid density, tank dimensions, pipe radius, and U-tube natural frequency, which, in turn, is a function of the tank dimensions, pipe dimensions, and the magnitude of acceleration vector. Resonance will occur whenever the U-tube natural frequency is equal to any one value of the natural frequencies for the axisymmetric sloshing modes of the liquid in each cylindrical tank. Pertinent dimensions to be avoided are pointed out. Extension of the results to asymmetric sloshing based on a paper by Yeh [“Liquid Sloshing in a Moving Tank with a Time Dependent Discontinuous Boundary,” TRW Space Technol. Labs. Rept. EM 14-12 (6438-6002 RU-000) (June 1964)] is also indicated.