The capillary rise h, to which a liquid will rise in a small-bore cube depends on the tube radius, r, the acceleration of gravity g, and the fluid properties including fluid viscosity µ, density p,...

The capillary rise h, to which a liquid will rise in a small-bore cube depends on the tube radius, r, the acceleration of gravity g, and the fluid properties including fluid viscosity µ, density p, and surface tension u. Develop an equation encompassing dimensionless groups to relate h/ r to the other variables.

A model for a ship is built to a scale ratio of 1/12 to test its performance in a seawater of density 1030 kg/m3 . Calculate the velocity ratio, the force ratio, and the power ratios between the model and the prototype.