The Wide World of Fluids article titled "Ice Engineering,". 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 thickness of the ice, \(d\), the velocity of the ice, \(V\), the acceleration of gravity, \(g\), the density of the ice, \(ho_{i}\), and a measure of the strength of the ice, \(E_{i}\), where \(E_{i}\) has the dimensions \(F L^{-2}\).

(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 \(12 \mathrm{in}\). and an ice velocity of \(6 \mathrm{ft} / \mathrm{s}\). 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.