A model study is to be developed to determine the force exerted on bridge piers due to floating chunks of ice in a river. The piers of interest have square cross sections. Assume that the force, R, is a function of the pier width, b, the depth of the ice, d, the velocity of the ice, V, the acceleration of gravity, g, the density of the ice, pi, and a measure of the strength of the ice, Ei, where Ei has the dimension FL-2.

(a) Based on these variables determine a suitable set of dimensionless variables for this problem.
(b) The prototype conditions of interest include an ice thickness of 12 in. and an ice velocity of 6 ft/s. What model ice thickness and velocity would be required if the length scale is to be 1/10?
(c) If the model and prototype ice have the same density, can the model ice have the same strength properties as that of the prototype ice? Explain.