or PART 11: Problems (07%): Solve each problem and show all work, making best at

Question

or PART 11: Problems (07%): Solve each problem and show all work, making best attempt to present an organized solution Partial credit will be awarded wherever possible. PROBLE (1) A model underwater missile of diameter 2.5 m and length 14 m is tested in a fresh water tunnel to determine the forces acting on the real prototype. The geometric scale of the model is 1/20th of the prototype a. Determine the diameter and the length of the prototype? b. If the prototype is to be used in sea water of SG 1.15 and the allowable speed of the prototype missile is 10 m/s, what should be the speed of the water in the tunnel to achieve dynamic similarity? (Assume that the fresh water and sea water have the same viscosity) [20%]

Explanation / Answer

a . Model is the scaled down dimension of the real prototype. So the prototype will always be in higher dimension than the model.

Here the diameter of the model is 2.5m and the length is 14m. The geometry is 1/20 of the prototype. So the diameter of the prototype will be 2.5x20= 50m. The length will be 14x20= 280m.

b. To maintain dynamic similarly, the ratio 1/20 has to be maintained. The speed of the actual prototype is 10m/s, so in the wind tunnel the water has to flow at a velocity of 10/20=0.5m/s.

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