Engineering Homework Help

Engineers at wind turbine company are seeking to perform experiments on a new wind turbine model in a pressurized tunnel. The rationale is that, by using air under pressure, fluid density can be increased to match the Reynolds number and avoid too high velocities in the wind tunnel. They select a facility, where air can be pressurized to 10 MPa and the corresponding air density and viscosity are r = 116 kg/m3 and μ = 1.43 ×10–5 kg/m×s, respectively. They test a turbine model scaled down by a factor of 25. The real wind turbine has a diameter D = 100 m and operates at a wind speed U¥ = 10 m/s. What should be the velocity in the wind tunnel for dynamic similarity? If the power produced by the model in the wind tunnel is 3 kW, what would be the power produced by the real wind turbine?

(Assume standard air property for the real wind turbine).