2B03-Lab 3 - Darcy's Law

ENVIRSC 2B03 Soils and the Environment S.K. Carey, 2022 LAB #3 DARCY’S LAW Due week of November 28 online before the start of your lab. INTRODUCTION Fundamentals of Water Flow Understanding the movement of water through soils is very important in both agricultural and urbanized areas. The direction and flow rate of water can influence the amount of water that reaches plant roots, the water table, local streams, wells and drainage systems. There are three types of water movement within soil: saturated flow, unsaturated flow and vapor movement. In this lab we will focus on saturated water flow where the pores in the soil are completely filled with water. Water movement depends on the hydraulic conductivity of a soil (see chapter 5 of the text). Hydraulic conductivity is defined as a measure of the “ease” of a soil to allow water movement. Hydraulic conductivity depends on the pore space geometry of a soil because the connection of pores and their size and shape determine water flow pathways. The larger the pore sizes, the more easily water will flow through the soil. Sandy soils usually have larger pores and thus they generally have a higher saturated hydraulic conductivity than finer-textured soils like clay and silt. Worm holes and pores created by dead root channels (biopores) as well as fractures associated with soil structure are all termed macro-pores and can account for a large proportion of the water movement in saturated soils. Soils with a stable sorted granular structure conduct water more rapidly than those with unstable, graded structural units, which can break down upon saturation and lead to clogged pores. Entrapped air can also impede the movement of water, resulting in an apparently lower saturated hydraulic conductivity. By measuring the water flow through columns of saturated sands, Darcy (1856) determined that the volume of water flowing through soil in a given time is proportional to the hydraulic gradient (dh/dx) through the cross-sectional area of the column and the soil’s hydraulic conductivity (K s ) (eq 1.1). Hydraulic gradient (dh/dx in eq 1.1) is defined as the rate of change in hydraulic head over distance and can be expressed as the difference in hydraulic head (h 2 -h 1 ) divided by the distance between the measurement points (x) (eq 1.1). Hydraulic head (h) is equal to the sum of gravitational (z) and pressure (ψ) heads (eq 1.2). It is the driving force in Darcy’s Law (eq. 1.1). For example, a larger hydraulic gradient causes a larger volume of water to flow through the soil in a given time. eq 1.1 (Darcy’s Law) t A V q w × = dx dh K q s - = x h h K q s 1 2 - - =

ENVIRSC 2B03 Soils and the Environment S.K. Carey, 2022 where q = Darcy velocity (cm/sec) K s = saturated hydraulic conductivity (cm/sec) dh/dx = hydraulic gradient (dimensionless) V w = volume of flow in specific time interval (cm 3 ) A = cross sectional area of the soil (cm 2 ) t = time interval (sec) h 2 -h 1 = hydraulic head difference (cm water) x = distance over which the hydraulic head difference is measured (cm) eq 1.2 (Hydraulic Head) where h = hydraulic head (cm) z = gravitational head (cm) Ψ = pressure head (cm of water) Measuring Saturated Hydraulic Conductivity In this lab you will measure the saturated hydraulic conductivity of two soils using the Falling Head Method ; which involves adding water once to the inlet tube and allowing the water to percolate through the soil sample as the hydraulic gradient decreases exponentially over time. This method initially applies a relatively large hydraulic head to the top of the soil sample, then the applied hydraulic head decreases over time as the water flows through the soil sample. This generates an exponentially decreasing flow rate over time. The hydraulic conductivity of the soil can then be determined by measuring the length of time required for the falling water level to pass between two points on the inlet tube (H 2 , H 1 ) (Refer to Figure 1 for experimental set-up) . By integrating Darcy’s formula (eq. 1.1) for saturated water flow, the saturated hydraulic conductivity for the falling head method is: where a = the cross-sectional area of the glass tube (cm) A = the cross-sectional area of the soil sample (cm) L = the length of soil sample in the cylinder (cm) H 1 = the larger height of tube for time measurement (cm) H 2 = the smaller height of tube for time measurement (cm) t = time for water to pass from H 1 to H 2 (sec) Note: Only simplified Hydraulic Head theory was covered in this lab, however in Earth Sc 3W03, the concept of hydraulic head is thoroughly developed and discussed. In addition, an alternative method ( Constant Head Method ) is used for calculating saturated hydraulic conductivity in Earth Sc 3W03 so I recommend y + = z h ÷ ÷ ø ö ç ç è æ ´ ú û ù ê ë é × × = 2 1 ln H H t A L a K s