A research facility on the moon will include a series of canals connected to a central lake, which will simultaneously provide transportation about the facility and utilize the temperature-stabilizing effect of a body of water. Experiments will be done on Earth to determine the optimum canal depth, H, for a boat that will be used to transport people and equipment. The optimum depth depends upon the boat's hull length, l, speed, U, water density, p, viscosity, u, and gravitational acceleration, g.
(a) How many dimensionless groupings are there?
(b) What are the dimensionless groupings? if necessary, manipulate your groupings to show that two of them are the Froude number and the Reynolds number, both based on l.
(c) The experiments will be done in a water channel for which temperature is 60C. While the canal water will be at 20C. Consequently, the kinematic viscosity in the expermiment will be 0.47 times the canal value. Moon's gravitational acceleration is 1/6 times that of Earth. The ratio H/l will be identical for the Earth-based water channel and the moon-based canals. In order to achieve dynamic similitude, what size model will be used for the experiments?