The air density at the summit of Mons Olympus, the highest mountain on the plane

Question

The air density at the summit of Mons Olympus, the highest mountain on the planet Mars, is 0.1% of the air density at sea level on Earth. What is the speed of wind blowing over the top of Mount Olympus that carries the same power per square meter as a 10 m/s wind blowing at the sea level on Earth? The average current power consumption of the US is approximately 1.2 TW. The efficiency of mass-produced silicon photovoltaic panels is about 15%. The isolation at the Nevada desert areas is 7.2 kWh/m^2/24 h. If we wanted to build a solar power plant in the Nevada desert with an average power of 1.2 TW, we would have to cover with PV panels an area of the size: approximately 41times 41 km^2; approximately 82 times 82 km^2; approximately 164 times 164 km^2; approximately 328 times 328 km^2.

Explanation / Answer

Wind Power is given by

P=(1/2)Apv3

Given

P/A =Constant and

p2=0.1%p1 =0.001p1

=>p1v13 = p2v23

v2 =[(p1/p2)*v13]1/3

v2 = [(p1/0.001p1)*103]1/3

v2=100 m/s

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