Awind turbine is rotating at 15 rpm under steady winds flowing through the turbine at a rate of 42,000 kg/s. the tip velocity of the turbine blade is measured to be 250 km/h. if 180 kw power is produced by the turbine, determine (a) the average velocity of the air and (b) the conversion efficiency of the turbine. take the density of air to be 1.31kg/m3.

a) 5.22 m/s

b) 31.4 %

Explanation:

f = rotating speed = 15 rpm = 15/60 =0.25 rps

m = Mass flow rate of air = 42000 kg/s

v = Tip velocity = 250 km/h = 250/3.6 = 69.44 m/s

W = Work output = 180 kW

A = Swept area of wind turbine

r = Radius of wind turbine

η = Efficiency

∴ The average velocity of the air is 5.22 m/s

∴ Conversion efficiency of the turbine is 0.314 or 31.4 %

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