A wind turbine with an efficiency of $$42 \% \text { produces } 1 \text {-MW output at a wind }$$ velocity of 13 m/s. What is the turbine rotor diameter?

Name: A wind turbine with an efficiency of \[42 \% \text { produces } 1 \text {-MW output at a wind }\] velocity of 13 m/s. What is the turbine rotor diameter?
Brand: Quizplus
Rating: 4.8 (50 reviews)

Question

Quizplus · Accepted Answer

The Answer is From equation (10.5)

P = \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) \eta A v ^ { 3 }

or

A = \frac { P } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) \eta v ^ { 3 } }

Solving for A gives

A = \frac { 10 ^ { 6 } \mathrm {~W} } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) imes ( 0.42 ) imes ( 13 \mathrm {~m} / \mathrm { s } ) ^ { 3 } } = 1800 \mathrm {~m} ^ { 2 }

Then

A = \pi r ^ { 2 } = \pi d ^ { 2 } / 4

. So

d = \sqrt { \frac { 4 A } { \pi } } = \sqrt { \frac { 4 imes 1800 \mathrm {~m} ^ { 2 } } { 3.14 } } = 48 \mathrm {~m}

A Wind Turbine with an Efficiency Of 42% produces 1-MW output at a wind 42 \% \text { produces } 1 \text {-MW output at a wind }42% produces 1-MW output at a wind

A Wind Turbine with an Efficiency Of $42 \% \text { produces } 1 \text {-MW output at a wind }$