Lecture 20 Ground Water (3) Ground water movement Darcy’s law Hydraulic head Flow nets Dimensions of water flow

Ground Water Movement Ground water moves more or less continuously from areas of recharge to areas of discharge, i.e., forced by hydraulic gradients It also moves by chemical gradients causing spatial variation in osmotic water potential

Ground Water Movement Darcy’s Law: Where ν is the macroscopic velocity of water; K is the saturated hydraulic conductivity; h/l is the hydraulic gradient comprising the change in hydraulic head ( h) with a distance along the direction of flow ( l ).

Hydraulic Head h = ψ + z h = hydraulic head ψ = pressure head z = elevation head

Porosity vs. soil/rock type Table 5.8, WR Ground Water

Terms to Remember Pressure head: water pressure at a given point, which can be measured by a piezometer Elevation head: height above a selected reference height Total head: the sum of pressure and elevation head Potential energy: product of the total head and the gravitational constant Hydraulic gradient: change in the total head per unit distance Hydraulic conductivity: water flux density per unit volume of water and per unit hydraulic gradient Macroscopic velocity: the speed of water flow through the cross-sectional area of solid matrix and interstices  

Ground water movement A simple case: a horizontally uniform and extensive surface 1 Quantity of water flow per unit time: 2 3 w L 4 5 6 7 2 - 1 = 3 - 2 = = 4 - 3 = ……. Ground Water Movement

Ground water movement: flow nets Figure 5.9, WR Ground Water Movement

Mathematical dimension of ground water flow One-dimensional flow: water potential changes in only one direction, e.g. vertical, applicable to homogeneous, extensive horizontal surfaces Two-dimensional flow: water potential changes in two directions, e.g., vertical and one of the horizontal directions, applicable to systems like mountain ridges and valleys of infinite length where the variation along the length can be ignored Three-dimensional flow: water potential changes in all three directions, e.g., vertical and two horizontal directions, applicable to systems like mountain crests Ground Water

Self reading Unconfined groundwater flow (WR, Chapter 5.5.5)