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Convection
Storyboard
The difference in atmospheric pressure leads to displacement of air masses both at surface level and at heights.
The vertical flow is called convection and is key to cloud formation, rain generation and effective energy flow between surface and atmosphere.
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Número de Rayleigh
Equation
El inicio de convecci?n t?rmica esta descrito por el n?mero de Rayleigh
| $Ra=\displaystyle\frac{\rho^2 g c_p}{\eta\lambda}\displaystyle\frac{(T_e-T_t)}{T_e}h^3$ |
Para un sistema entre dos placas con las temperaturas inferior
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Velocidad de Ascenso
Equation
$v_c=\sqrt{\displaystyle\frac{2hg(\rho_m-\rho}{C_W\rho_m}}$
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Velocidad de Ascenso en función de la Temperatura
Equation
Como la velocidad de acenso es igual a
| $v(z)^2=2g\displaystyle\int_0^zds\displaystyle\frac{(\rho_m(s)-\rho(s))}{\rho(s)}$ |
y en condiciones isobaricas se cumple
| $ \rho_i T_i = \rho_f T_f $ |
la ecuación para la velocidad se puede también escribir en función de la temperatura
| $ v =\sqrt{2 CAPE }$ |
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Mixing ratio of water vapor with air
Equation
The mixing ratio of water vapor with air is defined as the ratio of the masses of each component present in a volume:
$\displaystyle\frac{M_v}{M_a}=\displaystyle\frac{n_vM_{mol,v}}{n_aM_{mol,a}}=\displaystyle\frac{p_v}{p_a}\displaystyle\frac{M_{mol,v}}{M_{mol,a}}\sim 0.01$
Where $M_v$ and $M_a$ are the masses of water vapor and air respectively, $n_v$ and $n_a$ are the moles of water vapor and air, $M_{mol,v}$ and $M_{mol,a}$ are the molar masses of water vapor and air, $p_v$ and $p_a$ are the relative pressures of water vapor and air, and $r$ is the mixing ratio. Therefore, we have
 $ r =\displaystyle\frac{ M_v }{ M_a }$ |
In the specific case of water vapor in air, the mixing ratio is proportional to the relative pressures, which can be quantified using the vapor pressure of water $p_v\sim 1500 Pa$ and the air pressure $p_a\sim 10^5 Pa$. By applying the ideal gas equation and the definition of molar mass, it can be determined that the mixing ratio is approximately $0.01$. This means that the amount of water vapor compared to air is low under normal conditions.
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