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Name QI: 1. Suppose that the power to drive a propeller of an airplane depends on d (diameter of the propeller), U (free-stream velocity), o (angular velocity of propeller), c (velocity of sound), p (density of fluid), and u (viscosity). Find the dimensionless groups. In your opinion, which of these are the most important and should be duplicated in a model testing? (Take p U d as repeating variables). 2. A 1/25 scale model of an airship is tested in water at 20 °C. If the airship travels at 5 m/s in air at atmospheric pressure and 20 °C, find the velocity for the model to achieve similitude. Also, find the ratio of the drag force on the prototype to that on the model. The densiti of water and air at these conditions are 1000 kg/m and 1.2 kg/ The corresponding dynamic viscosities of water and air are 16 N s/m2 and 1.81x10- N s/m². Dimensional analysis for the force yields: F=p V2 L2 f(Re).