The effect of internal pipes on the fundamental frequency of liquid sloshing in a circular tank

The article describes a theoretical investigation into the shift in fundamental frequency which arises when an array of pipes is placed in a circular tank. A tank of constant section is specified to enable the problem to be reduced to two dimensions. The associated velocity potential then satisfies the Helmholtz equation. A boundary element method is used to investigate the case of a tank with an arbitrary array of pipes and is verified by the analytical solutions for circular and annular tanks. Results are presented for several cases involving arrays of internal pipes and compared with predictions obtained using an approximate method.