deletions | additions       diff --git a/Convective Velocities.tex b/Convective Velocities.tex  index eebc8e2..9e78e64 100644  --- a/Convective Velocities.tex  +++ b/Convective Velocities.tex 
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\end{equation}  An average of $W(\Delta r)$ over all possible values of $\Delta r$ and a choice of a numerical factor (1/4) in exchanging $\Delta r$ with $\lambda$ leads to the following expression ($W$ depends quadratically on $\Delta r$):  \begin{equation}  \bar{W} \overline{W}  (\lambda) = \frac{1}{4} W(\lambda) = - \frac{1}{8} g \Delta \rho (\lambda) \lambda. \end{equation}  Under the assumption of no dissipative forces, no transfer of kinetic energy to surrounding matter and no heat loss, then one would conclude $\bar{W}(\lambda) = \bar{1/2\rho v^2}$. However in the MLT one assumes that only half of this work is transformed into kinetic energy. This leads to  \begin{equation}  \overline{\frac{1}{2}\rho v^2} \simeq \frac{1}{2}\rho \bar{v}^2 = \frac{1}{2}\bar{W} \frac{1}{2}\overline{W}  (\lambda) = - \frac{1}{16} g \Delta \rho (\lambda) \lambda, \end{equation}  so that the velocity of convective elements at the level where the mixing length is $\lambda$ can be expressed as  \begin{equation}