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, p,, and a measure of the strength of the ice, Zi, where Z; has the dimensions ML"'T*. Hints: R= (), d, V, 2, p., i). (a) Based on these variables, conduct dimensional analysis based on Buckingham Pi theorem in M-L-T system and write out a relationship between dimensionless Pi terms for this problem. (10 marks) (b) The prototype conditions of interest include an ice thickness of 30 cm, and an ice velocity of 2 m/s. What model ice thickness and velocity would be required if the length scale is to be 1/10? (5 marks) (c) Ifthe model and prototype ice have the same density, can the model ice have the same strength properties as that of the prototype ice? Explain