Question

A windmill takes a fraction of the wind kinetic energy out as power on a shaft. In what manner does the temperature and wind velocity influence the power? Hint: write the power as mass flow rate times specific work.

Answer 1

The work as a fraction f of the flow of kinetic energy becomes

so the power is proportional to the velocity cubed. The temperature enters through the density, so assuming air as ideal gas ρ = 1/v = P/RT and the power is inversely proportional to temperature