(a) Show that for a wind turbine spacing of 3 rotor diameters crosswind and 10 rotor diameters downwind, the power generated per unit land area for a wind farm is independent of rotor diameter and is equal to $\frac { P } { A _ { \text {land } } } = \frac { \pi \rho \eta } { 240 } v ^ { 3 }$ where ρ is the air density and η is the turbine efficiency.
(b) Show that when the velocity is measured in m/s, the power per unit area is in kg/s³.
(c) Discuss the relevance of hub height on the answer to part (a).

Question

(a) Show that for a wind turbine spacing of 3 rotor diameters crosswind and 10 rotor diameters downwind, the power generated per unit land area for a wind farm is independent of rotor diameter and is equal to

\frac { P } { A _ { \text {land } } } = \frac { \pi \rho \eta } { 240 } v ^ { 3 }

where ρ is the air density and η is the turbine efficiency.
(b) Show that when the velocity is measured in m/s, the power per unit area is in kg/s³.
(c) Discuss the relevance of hub height on the answer to part (a).

Quizplus · Accepted Answer

The Answer of (a) Show that for a wind turbine spacing of 3 rotor diameters crosswind and 10 rotor diameters downwind, the power generated per unit land area for a wind farm is independent of rotor diameter and is equal to $$\frac { P } { A _ { \text {land } } } = \frac { \pi \rho \eta } { 240 } v ^ { 3 }$$ where ρ is the air density and η is the turbine efficiency. (b) Show that when the velocity is measured in m/s, the power per unit area is in kg/s³. (c) Discuss the relevance of hub height on the answer to part (a).

(A) Show That for a Wind Turbine Spacing of 3 PAland =πρη240v3\frac { P } { A _ { \text {land } } } = \frac { \pi \rho \eta } { 240 } v ^ { 3 }Aland ​P​=240πρη​v3

(A) Show That for a Wind Turbine Spacing of 3 $\frac { P } { A _ { \text {land } } } = \frac { \pi \rho \eta } { 240 } v ^ { 3 }$