Teaching Darcy ’ s Law Through Hands - on Experimentation

Darcy's Law is one of the most essential concepts in hydrogeology. Before moving on to more complex problems, students must first thoroughly understand the basic principles of one-dimensional fluid flow through saturated porous media that are embodied in Darcy’s Law. We believe that the best way for students to learn these principles is through experimentation. In this paper, we introduce an experimental apparatus and laboratory exercises designed to facilitate student exploration of Darcy’s Law. Our permeameter design is simple and inexpensive to construct from readily available materials; it is also nearly indestructible and easy to use. The exercises we present are flexible, and suitable for high school or university students. Students performing the exercises will gain an understanding of the relationships between hydraulic gradient, pore size, porosity, fluid viscosity, particle size (mean and distribution), and volumetric flow rate. Introduction Darcy’s Law, which describes one-dimensional laminar flow through saturated porous media (i.e., rocks, soil) is perhaps the most essential concept in the study of hydrogeology. Providing students with hands on laboratory experience helps them to develop an intuitive understanding of the relationship between hydraulic head and fluid flow in porous media that is embodied in Darcy’s Law. Once the basic concepts are thoroughly understood, students have a firm foundation from which to move on to more complex and realistic problems. Here we begin by providing an introduction to Darcy’s Law. We then identify a set of fundamental principles regarding flow in porous media that we believe are best learned through laboratory experimentation. After introducing a simple experimental apparatus capable of performing the relevant tests, we conclude by suggesting a series of student exercises with sample results. Darcy’s Law and Groundwater Motion Darcy (1856) performed his original experiments in the context of municipal water filtration for the city of Dijon, France. Unable to find an existing relation between flow rate and filter size, Darcy performed a series of experiments to aid in his design calculations (Hubbert, 1957). Pressurized water entered the top of a sealed vertical column filled with filtration sand and exited through a tap at the base of the column. Potential energy within the fluid was measured at the inlet and outlet using manometers, and reported in meters of water above datum (base of the sand column). Darcy found that for a given sand, volumetric flow rate (Q) was proportional to the cross-sectional area of the column (A), the difference between fluid levels in the inlet and outlet manometers, and the inverse of column length (1/L). The coefficient of proportionality was found to vary with the type of sand used; coarse filtration sand was found to produce a larger coefficient of proportionality than finer sand. In light of subsequent work by others, notably Hubbert (1940), Darcy's Law for steady, onedimensional flow may be written in differential form as