Engineers in a thriving vertical take-off-landing (VTOL) company want to test their new propeller design in...

 

Transcribed Image Text:

Engineers in a thriving vertical take-off-landing (VTOL) company want to test their new propeller design in a wind tunnel experiment. The thrust T, developed by a propeller of a given shape depends on its diameter D, the fluid density p, dynamic viscosity μ, the angular speed of rotation w, and the advance velocity V. To conduct a meaningful experimental campaign with the least number of tests, they want to understand the relation between these parameters. (a) Identify the dimensionless groups for this problem, choosing the repeating variables as diameter (D), advance ratio (V), and density (p). Explain your answer clearly: Show the dimensions for all variables, indicate how many Pi groups are required and why, and name the obtained dimensionless groups. [15 marks] (b) If the manufactured model for wind tunnel experiments is 1:3 scale, what should be the wind tunnel speed to have a dynamically similar conditions with the prototype flying at 60 m/s. Assume the viscosity and density of air does not change. Engineers in a thriving vertical take-off-landing (VTOL) company want to test their new propeller design in a wind tunnel experiment. The thrust T, developed by a propeller of a given shape depends on its diameter D, the fluid density p, dynamic viscosity μ, the angular speed of rotation w, and the advance velocity V. To conduct a meaningful experimental campaign with the least number of tests, they want to understand the relation between these parameters. (a) Identify the dimensionless groups for this problem, choosing the repeating variables as diameter (D), advance ratio (V), and density (p). Explain your answer clearly: Show the dimensions for all variables, indicate how many Pi groups are required and why, and name the obtained dimensionless groups. [15 marks] (b) If the manufactured model for wind tunnel experiments is 1:3 scale, what should be the wind tunnel speed to have a dynamically similar conditions with the prototype flying at 60 m/s. Assume the viscosity and density of air does not change.

Answer rating: 100% (QA)

Given T 3 M L T D Thrust N MLT Diameter m L Density kgm ML dynamic viscosity Nsm ML T a... View the full answer