The air density at the summit of Mons Olympus the highest mo

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.

Solution

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