The hydraulic grade line is shown in the diagram in the previous section. The Hydraulic Gradient and Hydraulic Grade Line Most practical applications of groundwater flow have Re < 1, and thus can be modeled with Darcy’s Law. Reynold’s number (Re) for flow through a porous medium is defined as: Re = ρVL/μ, where ρ and μ are the density and viscosity of the liquid, V is the flow velocity (Q/A), and L is a characteristic length, typically taken as the mean grain diameter of the medium. The diagram at the right shows an experimental apparatus illustrating the Darcy’s Law equation and its parameters.ĭarcy’s Law is valid only for laminar flow, which occurs for Reynold’s number less than 1. HL = head loss over a horizontal length, L, in the direction of flow (hL in ft and L in ft) Q = flow rate of liquid through the porous medium, typically in ft3/sec,Ī = cross-sectional area perpendicular to flow, typically in ft2, Putting these two proportionalities together gives the following equation: The equation for Darcy’s Law is based on the observations that the flow rate through a porous medium (such as an aquifer) is proportional to the cross-sectional area perpendicular to flow and is also proportional to the head loss per unit length in the direction of flow. Darcy’s Law gives the relationship among the flow rate of the groundwater, the cross-sectional area of the aquifer perpendicular to the flow, the hydraulic gradient, and the hydraulic conductivity of the aquifer.
A common application is groundwater flow through an aquifer. Darcy’s Law is an empirical relationship for liquid flow through a porous medium.