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 MovementDarcy’s Law:

12

12

ll

hhK

l

hKv

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 headψ = pressure headz = elevation head

Porosity vs. soil/rock type

Table 5.8, WR Ground Water

Terms to RememberPressure head: water pressure at a given point, which can be measured by a piezometerElevation head: height above a selected reference heightTotal head: the sum of pressure and elevation headPotential energy: product of the total head and the gravitational constantHydraulic gradient: change in the total head per unit distanceHydraulic conductivity: water flux density per unit volume of water and per unit hydraulic gradientMacroscopic 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

Ground Water Movement

L

WKq

1

2

3

4

5

6

7

w L

Quantity of water flow per unit time:

= - 12 = - 23 = - 34 = …….

Ground water movement: flow nets

Figure 5.9, WR Ground Water Movement

L

WKq

Mathematical dimension of ground water flow

Ground Water

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

Self reading

Unconfined groundwater flow (WR, Chapter 5.5.5)

Confined groundwater flow (WR, Chapter 5.5.6)