# Stack/Chimney Effect: a physical explanation on how height of chimney affects $\Delta P$

A fellow engineer told me that there are greenhouses which exploit the stack effect, in order to cover some or all of their electrical energy needs. This is achieved by installing small electrical generators with fans mounted on the rotor, on or near a chimney, which has to be large. Due to pressure difference between the greenhouse and the environment, there is a flow of cold air, from outside, which is capable of rotating the fans and therefore producing electrical energy.

By reading the wiki article on the effect, I understood why the chimney has to be large, since $$\Delta P$$ is proportional to the height h:

$$\Delta P = C\alpha h(\frac{1}{T_0}-\frac{1}{T_i})$$

where

• ΔP = available pressure difference [Pa]
• C = 0.0342, the temperature gradient [K/m]
• a = atmospheric pressure [Pa]
• h = height or distance [m]
• To = absolute outside temperature [K]
• Ti = absolute inside temperature [K]

But can someone explain to me why the height is proportional to ΔP in a physical/mechanical way? or recommend an article/book/paper that explains it?

EDIT:

Something similar (if not exactly the same) is the solar updraft tower. Again, tower has to be as tall as possible, in order to maximize the power generation. But how is this mechanically explained? Is it because of greater pressure, the speed of the air increased, so fans rotate faster? • Pressure difference being proportional to height is just the hydrostatic formula. – Deep Dec 16 '18 at 5:51
• @Deep ok... so which other formulas matter in this case? – thece Dec 16 '18 at 11:18