Amodel propeller 1 m in diameter is tested in a wind tunnel. air approaches the propeller at 50 m=s when it rotates at 1800 rpm. the thrust and torque measured under these conditions are 100 n and 10 nm, respectively. a prototype eight times as large as the model is to be built. at a dynamically similar operating point, the approach air speed is to be 130 m=s. calculate the speed, thrust, and torque of the prototype propeller under these conditions, neglecting the effect of viscosity but including density

7.45 a student is interested in the aerodynamic drag on spheres. she conducts a series of wind tunnel tests on a 10-cm-diameter sphere. the air in the wind tunnel is at 50 â°c and 101.3 kpa. she presents the results of her tests in the form of a correlation, đť’ź = 0.0015v1.92, where đť’ź is the drag force in newtons and v is the velocity in m/s. another student realizes that the results would have been more effectively presented in terms of dimensionless parameters, say, î  1 = f (î  2) = c î  a2 , where î  1 and î  2 are dimensionless parameters and c and a are constants. what are the most appropriate dimensionless parameters (î  1 and î  2) and the corresponding values of c and a? what would be the drag on a 2-cm-diameter sphere placed in a 1-m/s, 20 â°c water stream?