Question

Assume the density of air = 1.2 kg/m3 and Cp = 0.3. Remember that Area= r2 where r is the blade length.

1)How many Watts can a turbine generate in a 10 m/s wind and 1m blade length?

2)How many Watts can a turbine generate in a 15 m/s wind and 0.50m blade length?

3)How many Watts can a turbine generate in a 20 m/s wind and 0.25m blade length?

HELP ASAP

Answer 1

The number of watts which is the power of the turbine for each case is respectively; 600 W; 506.25 W; 300 W

What is the power of the turbine?

We are given;

Density of air; ρ = 1.2 kg/m³

Area; A = r² with r being the blade length

Formula for power in turbine is;

P = ¹/₂ρAv³

1) v = 10 m/s and r = 1 m.

Thus;

P = ¹/₂ * 1.2 * 1² * 10³

P = 600 W

2) v = 15 m/s and r = 0.5 m.

Thus;

Power = ¹/₂ * 1.2 * 0.5² * 15³

P = 506.25 W

3) v = 20 m/s and r = 0.25 m.

Thus;

Power = ¹/₂ * 1.2 * 0.25² * 20³

P = 300 W

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