# 7.1 Basis for Flow Equation Development

General groundwater flow equations are often referred to as governing equations because they describe the factors that control (i.e., govern) groundwater flow. The equations are based only on Darcy’s Law and the continuity equation for the conservation of mass (of water).

Development of the governing equations is typically accomplished by conceptualizing groundwater flow through a small volume of fully saturated porous material (REV) that reflects overall hydrogeologic properties of a larger deposit. It can be visualized as a cube of porous material of sufficient size (Δ*x*, Δ*y*, Δ*z*) to encompass macroscopic properties governing groundwater flow (Figure 4 and Figure 51). The mass of water within the REV (*M*) depends on the density of the water, the porosity of the element (assuming all pores spaces are fully connected), and the volume of the block as shown in Equation 51. Under steady-state flow conditions, the mass of water in the REV is constant, inflow equals outflow, and heads, gradients and flow rates do not vary with time (Figure 51a). When flow is transient, the mass of water in the REV varies with time, inflow does not equal outflow, and heads, gradients, and flow rates vary with time (Figure 51b).

M = ρ n Δx Δy Δz |
(51) |

where:

M |
= | mass of water in the REV (M) |

ρ |
= | density of water in the REV (M/L^{3}) |

n |
= | fully connected porosity (n_{e}) of the REV (dimensionless) |

Δx, Δy, Δz |
= | length of each side of the REV (L) |