4. (10 pts) An axial-flow airturbine to start a turbofan engine has an output torque M that is directly proportional to the volume flow rate Q through the turbine, i.e.,

its performance is determined by the ratio M/Q. This flow comes from an air compressor driven by an APU.This torque ratio M/Q depends upon the density of the air p, the rotor diameter D, and its angular rate of rotation 2. Using the Buckingham Pi method, find the non-dimensional grouping that governs the relationship between the ratio M/Q and the other parameters. How will the torque output from the airturbine be changed by a doubling of: (i) D and (ii) 2?