Mason equation

Mason equation

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 B. J. Mason.[1] 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).

Equation

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.

Thus if the drop has a size r, the inward mass flow rate is given by[1]

 \frac{dM}{dt} = 4 \pi r_{p} D_{v} (\rho_{0} - \rho_{w} ) \,

and the sensible heat flux by[1]

 \frac{dQ}{dt} = 4 \pi r_{p} K (T_{0} - T_{w}) \,

and the final expression for the growth rate is[1]

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) ]}

where

References

  1. ^ a b c d 1. B. J. Mason The Physics of Clouds (1957) Oxford Univ. Press.



Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Mason's rule — Mason s gain formula (MGF) is a method for finding the transfer function of a linear signal flow graph (SFG). The formula was derived by Samuel Jefferson Mason[1] and is named after its discoverer. MGF is an alternate method to finding the… …   Wikipedia

  • Équation de Mason-Weaver — L équation de Mason Weaver est une équation décrivant la sédimentation et la diffusion de solutés sous l action d une force uniforme, typiquement un champ de pesanteur[1]. Sommaire 1 Expression mathématique …   Wikipédia en Français

  • Mason–Weaver equation — The Mason–Weaver equation (named after Max Mason and Warren Weaver) describes the sedimentation and diffusion of solutes under a uniform force, usually a gravitational field.[1] Assuming that the gravitational field is aligned in the z direction… …   Wikipedia

  • Mason-Weaver equation — The Mason Weaver equation describes the sedimentation and diffusion of solutes under a uniform force, usually a gravitational field.cite journal | last = Mason | first = M | coauthors = Weaver W | year = 1924 | title = The Settling of Small… …   Wikipedia

  • Mason's Invariant — Introduction When trying to solve a seemingly difficult problem, Sam said to concentrate on the easier ones first; the rest, including the hardest ones, will follow, recalled Andrew Viterbi, co founder and former vice president of Qualcomm. He… …   Wikipedia

  • Mason's invariant — In electronics, Mason s invariant, named after Samuel Jefferson Mason, is a measure of the quality of transistors. When trying to solve a seemingly difficult problem, Sam said to concentrate on the easier ones first; the rest, including the… …   Wikipedia

  • Basil John Mason — Sir Basil John Mason, CB, FRS (born 18 August 1923) is an expert on cloud physics and former Director of the UK Meteorological Office. His work includes the Mason Equation, giving the growth or evaporation of small water droplets. He worked at… …   Wikipedia

  • Marsha Mason — Born April 3, 1942 (1942 04 03) (age 69) St. Louis, Missouri, U.S …   Wikipedia

  • Heat transfer — is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase change …   Wikipedia

  • Richard Liboff — Richard L. Liboff is a U.S. physicist who has authored five books and nearly 150 other publications in variety of fields, including plasma physics, planetary physics, cosmology, quantum chaos, and quantum billiards.He earned his Ph.D., 1961 from… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”