The thrust F of a free aircraft propeller depends upon the density p, the rotation rate...

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The thrust F of a free aircraft propeller depends upon the density p, the rotation rate n (in radian/s), the diameter D, and the forward velocity V and viscosity . Tests of a 25 cm diameter model aircraft propeller, in a sea-level wind-tunnel, yield the following thrust data at a wind velocity of 20 m/s (the air viscosity is kept constant for these tests): Rotation rate radian/min 4800 6000 8000 Thrust N 6.1 19 47 (a) Use this data to make an effective dimensionless plot (you can use Matlab for the plot). To do this, you will first have to find 'proper' non-dimensional II groups and then plot the data for the II groups keeping the II group based on viscosity constant. (b) Use this dimensionless plot (data) to predict the thrust (in N) of a similar 1.6 m diameter prototype when rotating at 3800 rad/min and flying at a speed of 225 mi/hr at 4000 m standard altitude (use density, p = 0.8191 kg/m). Assume that the viscous effects are small and negligible. The thrust F of a free aircraft propeller depends upon the density p, the rotation rate n (in radian/s), the diameter D, and the forward velocity V and viscosity . Tests of a 25 cm diameter model aircraft propeller, in a sea-level wind-tunnel, yield the following thrust data at a wind velocity of 20 m/s (the air viscosity is kept constant for these tests): Rotation rate radian/min 4800 6000 8000 Thrust N 6.1 19 47 (a) Use this data to make an effective dimensionless plot (you can use Matlab for the plot). To do this, you will first have to find 'proper' non-dimensional II groups and then plot the data for the II groups keeping the II group based on viscosity constant. (b) Use this dimensionless plot (data) to predict the thrust (in N) of a similar 1.6 m diameter prototype when rotating at 3800 rad/min and flying at a speed of 225 mi/hr at 4000 m standard altitude (use density, p = 0.8191 kg/m). Assume that the viscous effects are small and negligible.