It has been proposed that air pollution in Los Angeles can b

It has been proposed that air pollution in Los Angeles can be abated by drilling large tunnels in the mountains surrounding the basin and pumping the air out into the surrounding deserts. You are to examine the power requirements in displacing the volume of air over the Los Angeles basin. Assume the basin has an area of 4000km ^ 2 and that the polluted air is confined below an elevated inversion with a mean height of 400m. The coefficient of friction for air moving over the basin is assumed to be 0.5 and the minimum energy needed to sustain airflow is equal to the energy dissipated by ground friction. Determine the power required to move the air mass with a velocity of 7 km/h. Compare your result with the power generating capacity of Hoover Dam (1.25 x 10 ^ 6 kW). The power needed to overcome friction is vF, where v the friction coefficient and F is downward force. Recall also that power equals force x velocity.

Solution

density of air = 1 kg/m3
so force downwards = 4000*400*9.81*10^6
So power = .5*4000*400*9.81*(10^6)*7*5/18 = 1526 * 10^10 W = 1.526*10^13 W
Power of Hoover Dam = 1.25 * 10^9 W

The power required is 10^4 times more than what is produced by actual operating dams.