We have a natural gas power plant that produces 238TJ of ele

We have a natural gas power plant that produces 2.38TJ of electricity in one day. As an innovative engineering student you want to propose a change from this fossil fuel plant to wind energy. Officials want to know how much space (in relationship to the total area of 1250 acres) you would need for a wind-energy power plant that could substitute the natural gas power plant (provide your answer as a percentage of the area that the wind plant would occupy). Is it reasonable to substitute this plant for a wind farm? Why or why not? After some careful research, you find these information: common wind turbines are generally 300ft in rotor diameter and average 40% efficiency. Wind turbines need to be spaced at least 7 rotor diameters apart. The average wind velocity is 6.59m/s and it is close enough to sea level that the air density at sea level can be used. The wind turbines would generate electricity 16 hrs per day.

Solution

We will try to solve it!

Energy produced by planet / second = 2.38* E+12/ 60/60/24 ( assuming 24 hour operation).

= 27.55 MW (Joules/sec).

Energy Produced by wind turbine / second, Power = 0.5 x Swept Area x Air Density x Velocity3 = 1.15MW

Where, Sweft area = area covered by turbine rotor = PI * Rotor radius ^2 = 6567 m2

Air density 1.225 kg/m3 @ sea level with Wind velocity 6.59 m/s.

   so at 40% efficiency, Power = 0.46MW for 1 turbine.

There should be minimum 60 wind turbine to match gas power plant.

here wind turbine gives power only for 16 hours, for 24 hours power supply 90 turbines will be required.

Mimimum distance between 2 turbines = 300ft * 7 = 2100 feet.

assuming squre. 396900000 (2100*2100*90) square feet required to place 90 turbines .

1250 acre is 54450000 squre feet. so % of wind plant = (396900000/5445000)% = 728% of total area.

so its NOT worth to go for wind turbine!