Question

4. The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate N, and the number of blades n. Show all steps in answering the following. (a) Write the above relationship in a dimensionless form. (b) A model windmill, of diameter 50 cm, develops 2.7 kW at sea level (air density p =1.225 kg/m³) when the wind speed is 40 m/s and rotating at 4800 rev/min. What power will be developed by a geometrically and dynamically similar prototype of diameter 5 m, in winds of 1200 m/s at 2000m altitude (where air density is1 kg/m³)? ii. What is the appropriate rotation rate of the prototype?

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5