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The Caribbean often has temperatures over $30 \sideset{^{\circ}}{}{\mathrm{C}}$ with 100% humidity.

If I were to build a chimney there, how tall would it have to be before rain formed inside it? Assuming pressure inside = pressure outside.

This table has data for pressure vs. altitude up to 2,400 meters.

The diameter of the chimney seemed relevant for the rate of flow as the volume of air increases with altitude as well as temperature exchange with surrounding air. For these purposes assume the chimney increases in diameter as the pressure decreases to keep a constant velocity of air flowing upward.

At what altitude would precipitation occur?

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  • $\begingroup$ In the warm tropics it is responsible for intense rainfall from clouds lower than 5 km. mpimet.mpg.de/en/communication/climate-faq/… $\endgroup$ – Dale Jan 25 '17 at 4:08
  • $\begingroup$ Rain can form without clouds if the air is supersaturated. But wouldn't water precipitate on the inside surface of a chimney? engineeringtoolbox.com/maximum-moisture-content-air-d_1403.html $\endgroup$ – Dale Jan 25 '17 at 17:20
  • $\begingroup$ It'd help if you could clarify the thought experiment's premises a bit. I mean, I think you're basically asking how tall a chimney would have to be before something like rain would start to form. I think you're providing that the chimney's width varies such that there's a constant mass/mole flowrate throughout it. And the internal gas can be assumed to start out at $30 \sideset{^\circ}{}{\mathrm{C}}$ and 100% relative humidity... at the base, I guess? Then you specify equal pressure inside and out -- but, if it's a pressure-driven flow, presumably there's some departure from that? $\endgroup$ – Nat Sep 3 at 7:17
  • $\begingroup$ In short, it'd seem helpful to have a clear, full specification of the physical situation. $\endgroup$ – Nat Sep 3 at 7:22
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Formation of cloud and precipitation are two different things. A cloud will form inside the chimney if it is tall enough. How tall it has to be depends on many conditions, but cloud bases usually begin at a distance of few kilometers (no definite figure can be stated because this depends on current atmospheric conditions). However just because a cloud has formed does not mean you will eventually get precipitation. It is possible that cloud formed inside the chimney remains as a fog cloud until it dissipates away. Formation of rain requires growth of droplets to substantial sizes (few hundred microns, beginning from an initial size of about a micron or less), and collision and coalescence among droplets, due to its interaction with turbulence in the cloud, is supposed to be the primary mechanism that causes growth of such a magnitude (until collision and coalescence due to gravitational settling takes over). Large range of scales prevalent in the high Reynolds number turbulent flow in clouds ($Re\sim 10^7$ based on large eddy size) seems necessary for this growth. Presence of solid boundaries like that of chimney walls will most likely inhibit turbulence inside the chimney, in particular limit the range of scales of turbulence inside the chimney. Also it would prevent lateral entrainment, which is supposed to be a key factor in cloud growth, although opinion is divided on this issue. Therefore even though I cannot conclusively say that rain wouldn't form inside the chimney (if it were tall enough), I wouldn't bet on it.

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