5.1 Introduction
In Section 4 we discuss equations in general and introduced the main groundwater flow equation, which is shown here as Equation (37).
| [latex]\frac{{\partial q}_{x}}{\partial x} + \frac{{\partial q}_{y}}{\partial y} + \frac{{\partial q}_{z}}{\partial z} = S_{s}\frac{\partial h}{\partial t}[/latex] | (37) |
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where (parameter dimensions are dark green font with mass as M, length as L, time as T):
| [latex]q[/latex] | = | specific discharge (i.e., groundwater flow) in the x, y, or z direction (LT-1) |
|---|---|---|
| [latex]h[/latex] | = | hydraulic head (L) |
| [latex]t[/latex] | = | time (T) |
| [latex]x[/latex], [latex]y[/latex], [latex]z[/latex] | = | lengths in the principal directions in our coordinate systems |
We also substituted Darcy’s law, shown as Equation (38) for [latex]q[/latex], and to get Equation (39).
| [latex]q = - K\frac{dh}{dl}[/latex] | (38) |
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where (parameter dimensions are dark green font with mass as M, length as L, time as T):
| [latex]K[/latex] | = | hydraulic conductivity (LT-1) | ||
|---|---|---|---|---|
| [latex]\frac{dh}{dl}[/latex] | = | hydraulic gradient, or change in head with length (:) | ||
| [latex]\frac{\partial\left( K_{x}\frac{\partial h}{\partial x} \right)}{\partial x} + \frac{\partial\left( K_{y}\frac{\partial h}{\partial y} \right)}{\partial y} + \frac{\partial\left( K_{z}\frac{\partial h}{\partial z} \right)}{\partial z} = S_{s}\frac{\partial h}{\partial t}[/latex] | (39) | |||
[latex]S_{s}[/latex] is a storage parameter called the specific storage. It is a coefficient that relates changes in head in an aquifer to the change in the amount of water stored in the aquifer at a certain point. In other words, it is a quantity that tells us how much water that a unit volume of aquifer can yield for a unit decline in head. The term to the right of the equal sign in Equation (39) is equivalent to [latex]\mathrm{\Delta}S/\mathrm{\Delta}T[/latex] of Equation (1)—that is, it represents the change in storage with respect to time. As stated in Section 5, Equation (39) is another way of expressing the continuity equation.
In this section, we discuss storage parameters in general and how they relate to confined versus unconfined aquifer conditions. We also discuss transient versus steady-state conditions in dynamic systems like aquifers.