deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 4bf9fb8..9bf18ae 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]  where V is the volume of fluid expelled along the fault, h is the effective width of the fault, $C_{p}^{w}$ C_{p}^{w}  and $C_{p}^{r}$ C_{p}^{r}  are the specific heat capacities of water and rock respectively, $\rho$_{w} \rho_{w}  and $\rho$_{r} \rho_{r}  the densities of water and rock, and k the thermal diffusivity of rock. Noting that and selecting values of 120$^{\circ}$, 100$^{\circ}$ 120^{\circ}, 100^{\circ}  and 40$^{\circ}$C 40^{\circ}C  respectively for $\Theta$_{i}, $\Theta$_{1} \Theta_{i}, \Theta_{1}  and {\Theta$_{2}, 3000m for \textit{x}_{1}, 1000m for \textit{x}_{2} and an effective fault width of 1m we find that the maximum duration for an individual fluid pulse is a function