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:
h
h2  h1
v  K
 K
l
l2  l1
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
2
3
4
5
6
7
Quantity of water flow per
unit time:
w
L
= 2 - 1 = 3 - 2 = 4 - 3 = …….
Ground Water Movement
W
q   K
L
Ground water movement: flow nets
W
q   K
L
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)
Confined groundwater flow (WR, Chapter 5.5.6)