446_01c_hw3_4 - e i w w w on condensati s s ρ Note To...

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Metr 446 Homework # 3 and 4 Due Friday, October 5 1) Calculate the minimum cloud height necessary for a 5 µ m droplet introduced into the base of the cloud to reach sufficient size to fall back out of the cloud as a precipitation drop. Also calculate the size of the drop as it exits from the base of the cloud. Assume unit collection efficiency, negligible fall speed of the small cloud droplets collected, an updraft velocity within the cloud of 3 m/s, a temperature of 273 K, a supersaturation of 0.15%, and a constant liquid water density ( ρ d ) of 1 g/m 3 . Do not neglect the influence of condensational warming on condensational growth. ) ( ) ( ., . 3 2 2 2 + = T R e DL r e e T DR dt dr use
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Unformatted text preview: e i w w w on condensati s s λ ρ Note: To solve this, you will have to numerically integrate the condensation and collision growth rate expressions, and an iterative solution will be necessary to relate droplet fall velocity to radius using the expressions below. In other words, you will have to use either a spreadsheet or a programming language to solve the problem. [ ] [ ] 5 687 . 2 160 9 16 3 2 ' 10 2 Re 500 44 . 500 Re 2 Re 15 . 1 Re 24 2 Re 1 . Re) 2 ln( Re Re 1 Re 24 1 . Re Re 24 2 Re 3 8 4 × < < = < < + = < < + + = < = = = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ D D D D t a a w D t w d d collision C C C C r w g r C w w dt dr η ε...
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