## Report DOE/ER/82329-2 Gathered Equations

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*Note: This is the entire set of equations from Report DOE/ER/82329-2,
presented here without explanation. If the user does not have
the TrueType font "SYMBOL" installed on the user's computer,
not all the variables may show properly. It may be useful to print
out the set before reading the other pages.*

[1] , where

rq = relative flow, Q/Ks, (dimensionless), Q = flow (m/s),
Ks = saturated conductivity (m/s), H = total head (m), and x =
vertical displacement (m).

[2]

[3] , where

Dx = x_{2}-x_{1},
the vertical separation between grid cells centered at x_{2}
> x_{1} (m), with the vertical axis positive upwards,
and *Y*_{1} and
*Y*_{2} are the
matric suctions at x_{1} and x_{2}, respectively.

[4] , where

Kv = the Darcian relative conductivity mean for vertical flow
(dimensionless).

[5]

[6]

[7]

[8]

[9]

[10] ,

where Dx = (x_{i+1}-x_{i-1})/2

[11] ,

where kr(x1) = kr1, kr(x2) = kr2, *Y
*(x1) = *Y*1, and *Y *(x2) = *Y*2,
given the relationship kr(*Y *).

[12]

[13]

[14] , where

(m/s) , the saturated conductivity of the
composite relation.

[15]

[16]

[17]

[18]

[19]

[20]

[21] ,

[22] , where

kr = unsaturated relative conductivity (dimensionless), l = fitting
parameter (1/m), y = matric
suction (m), and y_{d}
= displacement pressure (m).

[23] , where
a = kr1, b = , u = l
Dx , Dx = x2 – x1

[24]

[25]

[26]

[27]

[28]

[29]

[30] , NOTE: I believe this equation is in error;
click here for a more accurate form.

[31]

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[64]

[65] , NOTE: I believe this equation is in error;
click here for a more accurate form.

[66]

[67]

[68]

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[70]

[71]

[72]

[73]

[74]

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