Prevailing winds in middle latitudes of the northern hemisphere are westerly, blowing from west to east at typical speed \(v\). The tendency of the Coriolis pseudoforce to deflect the path southward is typically balanced by a horizontal pressure gradient that keeps the air flowing eastward. The pressure gradient is related through the ideal gas law to the north-south temperature gradient, with warmer air in the south. Find an expression for the wind speed in terms of the temperature gradient \(\Delta T / \Delta x\), the latitude \(\lambda\), the earth's angular velocity \(\Omega\), and any necessary gas constants. Estimate the typical temperature gradient and find the typical flow velocity. Are the results reasonable? Would you expect prevailing winds in comparable southern latitudes to be westerly or easterly?