Answer :
The power produced by the turbine was calculated to be (1/2) × 1.112 × π/4 × (x + 1.25)² × 0.3048² × (6.705)³ × 0.25 watts.
Given that the wind speed, V = 15 mph, T = 10°C, p = 0.9 bar, and the efficiency of the turbine, n = 25%.
The diameter of the wind turbine is D = x + 1.25 ft, where x is the last two digits of your student ID.
To calculate the power that can be produced by the turbine, use the formula for the power of a wind turbine:
Power = (1/2) × density × area × V³ × n
Where density, ρ = p / (R × (T + 273))
where R = 287 J/(kg.K) is the gas constant for air.
Now, the diameter of the wind turbine is D = x + 1.25 ft. Convert it to meters:
Diameter, D = (x + 1.25) ft
= (x + 1.25) × 0.3048 m/ft
= (x + 1.25) × 0.3048 m/ft
= (x + 1.25) × 0.3048 m/ft
= (x + 1.25) × 0.3048 m/ft
= (x + 1.25) × 0.3048 m/ft
= (x + 1.25) × 0.3048 m/ft
where 0.3048 m/ft is the conversion factor from feet to meters.
Now, the area of the turbine, A = π/4 × D².
Area, A = π/4 × D²
= π/4 × (x + 1.25)² × 0.3048² m²
where π = 3.1416 is the value of pi.
Now, the density of the air, ρ = p / (R × (T + 273)).
Density, ρ = p / (R × (T + 273))
= 0.9 bar / (287 J/(kg.K) × (10 + 273) K)
= 1.112 kg/m³
Now, substituting the values of density, area, wind speed, and efficiency in the formula for power, we get:
Power = (1/2) × density × area × V³ × n
= (1/2) × 1.112 kg/m³ × π/4 × (x + 1.25)² × 0.3048² m² × (15 mph × 0.447 m/s/mph)³ × 0.25
= (1/2) × 1.112 × π/4 × (x + 1.25)² × 0.3048² × (6.705)³ × 0.25 watts
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