Question

What allows air to move side ways? Which air moves(hot or cold)?

Answer 1

You ask why a column of hot air (as in a chimney) rises, given that denser cold air is above it, pushing down. It rises, because denser cold air around the BOTTOM of the chimney is under higher pressure than the cold air at the top of the chimney. The extra pressure due to a chimney-height of cold air is pushing it down. The lesser density of hot air means that the chimney-height of hot air causes less pressure than the surrounding cold air.

In formulae, the situation is: outside the chimney,

P(chimney-top)+ρ(cold-air)⋅g⋅hchimney=P(cold-chimney-bottom)P(chimney-top)+ρ(cold-air)⋅g⋅hchimney=P(cold-chimney-bottom)

for the cold air, and inside the chimney

P(chimney-top)+ρ(hot-air)⋅g⋅hchimney=P(hot-chimney-bottom)P(chimney-top)+ρ(hot-air)⋅g⋅hchimney=P(hot-chimney-bottom)

where 'ρρ' is the density of the air.

ρ(cold-air)>ρ(hot-air)ρ(cold-air)>ρ(hot-air)

Thus, the cold air at the chimney bottom is higher pressure than the hot, it pushes its way in, and the hot air is displaced (it rises)