Analysis of flow frictional resistance in U-tubes under ocean conditions

The additional forces in U-tubes under ocean conditions, which include heaving and rolling as well as pitching motion, are investigated, respectively. Based on the Navier-Stokes equations of turbulent flow, the correlations of frictional resistance coefficient of single-phase flow in U-tubes under ocean conditions are derived theoretically. The effects of some important parameters on the frictional resistance coefficient are also analyzed. It is shown that the frictional resistance coefficient will fluctuate with time under ocean conditions, and the more severe the motion is, the bigger the oscillating amplitude of the frictional resistance coefficient is. Further the oscillating amplitude of the frictional resistance coefficient is related to the fluid Reynolds number, the U-tube radius and the fluid density difference between the inlet and outlet of the U-tubes.