Explanation Given information: The diameter of the circle is d = 82.5 m . The output power is P 1 = 1.5 MW . The wind speed of the generator is v = 12 m / s . The output power is P 2 = 10 MW . The density of air is ρ = 1.21 kg / m 3 . The efficiency for the designs η = η 1 = η 2 . Calculation: Calculate the length of the slipstream ( Δ l ) as shown below. Δ l = v Δ t . Here, v is the velocity of the air and Δ t is the time. Calculate the area of the turbine ( A ) as shown below. A = π d 2 4 Calculate the mass rate of flow ( d m d t ) as shown below. mass = density × volume = density × area × length Δ m = ρ A Δ l Substitute v Δ t for Δ l . Δ m = ρ A v Δ t Calculate the input power of the turbine ( Δ T ) as shown below. Δ T = 1 2 ( Δ m ) v 2 Substitute ρ A v Δ t for Δ m . Δ T = 1 2 ρ A v Δ t × v 2 = 1 2 ρ A v 3 Δ t Δ T Δ t = 1 2 ρ A v 3 d T d t = 1 2 ρ A v 3 Calculate the output power ( P ) using the relation as shown below

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ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 14.3, Problem 14.79P

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Chapter 14.3, Problem 14.78P

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