446_01c_test2_practice_soln

446_01c_test2_practice_soln - Test # 2 sample problem...

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Test # 2 sample problem solutions 1) Considering the expressions relating settling velocity to droplet radius, what is the range in the value of the exponent, a, in w t α r a ? 2 1 3 8 ) 44 . 0 ( 500 Re 3 8 2 24 1 . 0 Re 4 & 3 exp 2 2 2 r w g r w for r w g r r w w for HW in ressions the From t a w t t a w t a t α ρ η = > = < 2) Approximately what is the ratio of the concentration of cloud condensation nuclei to ice nuclei in a typical volume of air? Although this ratio varies quite a bit, and also depends on the temperature considered, a value of about 10 7 is a reasonable estimate. 3) Will ice crystals grow or shrink if the relative humidity (with respect to liquid water) is 92% and the temperature is –20 o C? growth e e Pa K K Pa T T R L e e e Pa K K Pa T T R L e RH e RH e equation Clapeyron Clausius s K kg J kg J ref w sub s s s K kg J kg J ref w vap s s ref ice ref liquidl > = × = = = = × = = = 3 . 103 253 1 273 1 461 10 83 . 2 exp ) 611 ( 1 1 exp 9 . 116 253 1 273 1 461 10 5 . 2 exp ) 611 )( 92 . 0 ( 1 1 exp : 6 6 4) How can the addition of high concentrations of small hygroscopic aerosols to a warm cloud increase the likelihood of precipitation? The aerosols are too small to form cloud droplets, but they still take up water and grow. By depleting some of the water vapor present in the cloud, these aerosols will decrease the supersaturation. Because of the decreased supersaturation, there will be fewer aerosol particles (already in the cloud) that are capable of activating. In general, the
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446_01c_test2_practice_soln - Test # 2 sample problem...

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