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| The '''Mason equation''' is an approximate analytical expression for the growth (due to [[condensation]]) or [[evaporation]] of a water droplet—it is due to the meteorologist [[Basil John Mason|B. J. Mason]].<ref name=Mason>1. B. J. Mason ''The Physics of Clouds'' (1957) Oxford Univ. Press.</ref> The expression is found by recognising that mass [[diffusion]] towards the water drop in a supersaturated environment transports energy as [[latent heat]], and this has to be balanced by the diffusion of [[sensible heat]] back across the [[boundary layer]], (and the energy of heatup of the drop, but for a cloud-sized drop this last term is usually small).
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| == Equation ==
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| In Mason's formulation the changes in temperature across the boundary layer can be related to the changes in saturated vapour pressure by the [[Clausius-Clapeyron relation]]; the two energy transport terms must be nearly equal but opposite in sign and so this sets the interface temperature of the drop. The resulting expression for the growth rate is significantly lower than that expected if the drop were not warmed by the latent heat.
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| Thus if the drop has a size ''r'', the inward mass flow rate is given by<ref name=Mason/>
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| ::<math> \frac{dM}{dt} = 4 \pi r_{p} D_{v} (\rho_{0} - \rho_{w} ) \,</math>
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| and the sensible [[heat flux]] by<ref name=Mason/>
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| ::<math> \frac{dQ}{dt} = 4 \pi r_{p} K (T_{0} - T_{w}) \,</math>
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| and the final expression for the growth rate is<ref name=Mason/>
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| :: <math>r \frac{dr}{dt} = \frac {(S-1)} { [(L/RT-1) \cdot L \rho_l /K T_0 + (\rho_l R T_0)/ (D \rho_v) ]}</math>
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| where
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| * ''S'' is the [[supersaturation]] far from the drop
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| * ''L'' is the [[latent heat]]
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| * ''K'' is the vapour [[thermal conductivity]]
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| * ''D'' is the binary [[diffusion coefficient]]
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| * ''R'' is the [[gas constant]]
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| ==References==
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| <references/>
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| [[Category:Thermodynamic equations]]
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| [[Category:Atmospheric thermodynamics]]
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| [[Category:Equations]]
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| {{climate-stub}}
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Latest revision as of 16:07, 7 February 2014
Hi there, I am Alyson Pomerleau and I believe it sounds quite great when you say it. To climb is some thing I truly enjoy performing. I am an invoicing officer and I'll be promoted quickly. Alaska is the only location I've been residing in but now I'm contemplating other options.
My web blog - free tarot readings [go to website]