Chimney height is directly proportional to how strong draft it will create (if there is a temperature difference and if inside and outside pressure is the same). The lower the temperature difference and the longer sideways the smoke will have to travel the taller the chimney has to be to create a sufficient draft to clear out smoke&gasses.
Also, the taller the chimney is the further the smoke will travel before it hits ground level so the more time it will have to disperse (and less likely to get caught in wind effects created by other buildings).
Note that if you want to disperse pollutants the height of the chimney has a double effect, both allowing the smoke to travel further but also sending it up the chimney with greater force so that it’s already more diluted in the chimney (due to pulling in other gases with greater force).
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