The major types of water motion inside the moonpool are piston and sloshing motions. Fukuda's formula of the piston motion resonant period (Vijith, 2014) is

(4–111)

where A is the cross-sectional area of the moonpool, h is the draft and =0.479 for a circular area, 0.460 for a rectangular area (b/l=0.5) and 0.473 for a square area. The coefficient of could be related to the added mass at the lower surface of the moonpool.

A simple approximation for the natural frequencies of the sloshing modes inside the rectangular moonpool is given by

(4–112)

where n = (1, 2, 3, ...), l is the moonpool length and (Newman, 2018).