Question by : Wind turbine question?
A standard 3-blade horizontal axis wind turbine is installed in an area where the average wind speed is 10 meters/second.The Length of each blade is 10 meters and the installation site is at sea level. The Energy conversion efficiency of this turbine is 40% (Betz Limit is 59.3%)
a) How many households can this wind turbine provide enough energy to? (Assume each household uses 4500 kW of energy annually)
b) The Cost of electricity is 0.15 cents per kWh. How much money can this wind turbine generate annually?
Best answer:
Answer by Jacy
Wind Turbine Power:
P = ½ η ρA (COP)V³ N
where:
P = power in watts
ρ = air density (about 1.225 kg/m³ at sea level, less higher up)
A = rotor swept area, exposed to the wind (m²) = π L² = π 10² = 100π
COP = Coefficient of performance (.59 {Betz limit} is the maximum thoretically possible, .35 for a good design)
V = wind speed in meters/sec (10 m/s)
η = generator efficiency (50% for car alternator, 80% or possibly more for a permanent magnet generator or grid-connected induction generator)
Nb = gearbox/bearings efficiency (depends, could be as high as 95% if good)
P = 0.5*0.4*1.225*100π(0.59)10³(0.95) = 43 kW
The energy supplied by the wind turbine operating continuously for 1 yr. is:
E(1 yr) = 43×10³ N m/s (365*24*3600) = 1.356×10^9 J
The annual energy required per household is:
E(annual per household) = 4500×10³ = 4.5×10^6 J
The # of households that can be provided for by the wind turbine is:
#households: n = 1.356×10^9 / 4.5×10^6 = 301
b)
$ = 301*4500*0.15 = $ 203,407.00
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