Thermodynamics Question The average wind speed in Morgantown

Thermodynamics Question

The average wind speed in Morgantown is about 2m/s for July. Suppose you wanted to product 2kW of power from a windmill, what must the minimum diameter of your rotors be? What if you had a turbine with a combined efficiency of 30%? Assume the average temperature is 25 degree C.

Solution

Energy produced by wind mill is kinetic energy = 1/2*m*v²

but m= density * volume flow rate = density * area * velocity

volume fow rate = area * velocity

E= 1/2* density * area* velocity²

2000=1/2*1.02*2² * Area

Area=2000*2/1.02/4=980m²

Area= pi /4* d²/4=980

d=35 m in first case

Turbine Efficiency= Desired Power putput/Actual Power output

Actual power output=Desired POwer output/Turbine Efficiency= 2/0.30=6.66 Kw

Put P=6666 w instead of 2000 w

Area=6666*2/1.02/4=3267m²

Area= pi /4* d²/4=3267

d=64m in second case