Repeat Prob. 7–72 for the case in which the propeller operates in a compressible gas instead of a liquid.

Data from Problem 72

A propeller of diameter D rotates at angular velocity ω in a liquid of density ρ and viscosity μ. The required torque T is determined to be a function of D, ω, ρ, and μ. Using dimensional analysis, generate a dimensionless relationship. Identify any established nondimensional parameters that appear in your result.