[3-1] Lee&Schwartz lecture files.pdf

1
Module 1-1
Water Resources and
Groundwater Basics

2
Water Resources
• Why know about water?
• Water availability
• Water issues around the world
• Hydrologic or water cycle

3
Fresh Water: Keeps Life Going
NASA
Wikipedia

4
Learning from History
Prosperity of ancient
civilizations were
dependent upon water
@ 2900 BC

5
Personal Issues
• Water and health
- poor quality water has health implications
- agrochemicals, trace pharmaceuticals
- standing water, mosquitoes West Nile virus:
water-born disease
• Water and safety
- floods can kill
- storm surge with hurricanes
http://www.youtube.com/watch?v=RE7OK9sMDvo&feature=related
http://www.youtube.com/watch?v=fFdDTxlQ3Jc

6
• Water and Money
- choice of a house
- choice of recreational
property
- insurance coverage
- basement flooding
Minn. Public
Radio

7
Water and Business
• Site Development
- formerly used sites contaminated
- costs of flooding, droughts
- industrial processes need reliable water, shut
down in drought
• Risky Sites
- disrupted transportation
- flooded sites

8
Water More Generally
• Water and politics: Water Conflicts
- continuous fights over water everywhere
- whose water will be grabbed how much $$
- Endangered Species Act (ESA) protects critically
endangered species from extinction – FWS, NOAA
- Clean Water Act (CWA) protects quality of
receiving water body through NPDES permit - EPA
• Water and poverty
- people many countries in world suffer from
inadequate water supplies

9
Water Resources

10
Occurrence of water
• Total volume of water: 323 million mi3
• 97% in the ocean
• 3% fresh water
– 68.7% fresh water (~ 9 million mi3) in glaciers and icecaps
– 30.1% fresh water (~2 million mi3) as groundwater
– 0.3% (~45,000 mi3) fresh water as surface water in lakes, rivers,
soils
• Most water unavailable for use
(1 mi3 = 1.1 trillion gallon)

11
Water Resources

12
Water Issues Around the World
• Diversion of rivers for many reasons
• Urbanization
• Water pollution

Marsh Arab
Sumerian and modern Iraqi
reed houses (Mudhif)
Photos from:
ANTHROCIVITIAS.NET
@ 2900 BC

14
Vanishing Marsh Arabs…and the 5,000
years old Civilization
http://www.youtube.com/watch?v=_er85Rs8cMA
https://www.youtube.com/watch?v=w-QJyX8nxOc /

15
http://www.birdlife.org/middle-east/news/miracle-marshes-iraq /

16
- Since 1970s dams upstream in
Turkey, Syria, Iraq have reduced
the flow of the rivers into Iraq

17

18
Urbanization
- impervious
surfaces, all kinds
of pollutants in
urban runoff
- http://www.youtube.com/watc
h?v=BYwZiiORYG8&feature=r
elmfu
http://www.youtube.com/watch?v=ft7s7y-f8Q8

19
Urbanization
- impervious
surfaces, all kinds
of pollutants in
urban runoff
- http://www.youtube.com/watc
h?v=BYwZiiORYG8&feature=r
elmfu
http://www.youtube.com/watch?v=ft7s7y-f8Q8

Water Pollution: Groundwater
• Contamination of groundwater not
uncommon
• A leukemia cluster (8 victims)
identified in Woburn, MA
• Woburn's drinking water supply wells
were contaminated by local
businesses, Riley Tannery (Beatrice
Foods), W.R. Grace, Unifirst
• The families of leukemia victims sued
• TCE, PCE contamination
http://www.youtube.com/watch?v=T7AJLHOnti8&feature=related
- Beatrice foods: altoids, avis, dannon, hunts, samsonite, krispy kreme,
swiss miss, tropicana….

Wells G & H Superfund site, Woburn MA
• Wells installed in 1964.
• Ann Anderson’s son, born in 1968, diagnosed with
leukemia in 1974, and died in 1981.
• Wells found to be contaminated by TCE and PCE in
1979.
• Wells were not used for water supply since then
• Law suits filed against two companies, Beatrice Foods,
and W.R. Grace in 1982 by Schlichtman representing
Ann Anderson et al.
21
http://serc.carleton.edu/NAGTWorkshops/hydrogeo/activities/10688.html

Wells G & H Superfund site, Woburn MA
• 5 Contaminated Sites
– New England Plastics
– Riley Tannery (Beatrice Foods, Inc.
– Hemingway Trucking (Olympia Nominee Trust)
– UniFirst
– Cryovac (W. R. Grace & Co.)
• Beatrice dismissed, Grace settled with $8 million,
22
http://serc.carleton.edu/NAGTWorkshops/hydrogeo/activities/10688.html

23
Water Resources
• Hydrologic cycle

24
Hydrologic Cycle
• What is hydrologic cycle?
– Water circulates on Earth from the oceans to the
atmosphere to land and back to the oceans.
– Hydrologic cycle describes the existence and
movement of water on, in, and above the Earth.
• Where does Earth’s water come from?
– Water set free by magma began to cool down the
Earth’s atmosphere, until it could stay on the surface
as a liquid.
– Volcanic activity kept and still keeps introducing water
in the atmosphere.

25
Hydrologic Cycle
• Endless, global-scale process linking water in
atmosphere, on continents, and in oceans

26
The Hydrologic Cycle - Simplified
• Movement of water
between oceans,
atmosphere, and land
• Water exists as liquid,
vapor, and solid
• Energy needed to power
the cycle is supplied by
___ and ______

27
Key Components - Hydrologic Cycle
1. Precipitation
2. Runoff (Surface & Subsurface)
3. Evaporation
• Evapotranspiration
4. Storage

28
Precipitation - World
• Water in atmosphere returning to Earth in liquid or solid
form (as rain, snow, sleet)
• Most precip result of evaporation over oceans
• Extreme variability in precipitation around world
0 10 50 100 200 500 1000 2500 mm/year

Vapor Pressure
• All liquids and solids have a tendency to
evaporate into a gaseous form, and all gases
have a tendency to condense back to their liquid
or solid form.
• Vapor pressure tendency of particles to escape
from the liquid (or a solid )
• _______ liquids have _____ vapor pressure at
normal temperatures.
• Increases with increasing temperature

30
Precipitation
Three steps to form precipitation:
1. cooling of air to approximately the dew-point temperature:
Warm air holds more vapor.
2. condensation of water vapor into liquid water: cooling +
nuclei (dust, ice or water particles)
3. growth of droplets or crystals into raindrops: collision
Cooling can occur when
(i) air rises over mountains,
(ii) warm air masses rise
above cooler air masses
at front.
http://www.youtube.com/watch?v=bymT5AcV-
C4&feature=related

31
- Collector funnel (8-in)
- Measuring tube: 20 in-long,
collects 2 in rain
- Overflow can (20-in long)
Supporter:
10-12 in long
Standard US precipitation gage:
ID = 8 inch (20.3 cm),
L = 30 in (76.2 cm)
Precipitation - Measurements

32
Doppler Weather Radar
– Produces continuous space/time estimates of
weather variables including precipitation
– Intensity of precipitation is represented by the
color, then calibrated into highly resolved
estimates of precipitation amounts
– Can get weather data from areas where
conventional gages can not be used. – mountains
etc

34
Evaporation
• Process converting water
to water vapor
• Evaporating surfaces
include ocean, lakes,
rivers, pavement, soil,
and wet vegetation
• Evaporation very
important contributor to
water loss in arid regions
• Water levels in lakes near the
Colorado River can drop between
2-4 feet every year due to
evaporation
• 70% of Georgia’s 50 in. of rain
are lost directly to evaporation
Photos from USGS

35
Evaporation
• Net evaporation occurs when the rate of evaporation
exceeds the rate of condensation.
– In equilibrium when air humidity is 100%
• Evaporation from ocean drives Hydrologic Cycle by
providing ~90 % of the moisture in the atmosphere.
• Affected by air temperature, humidity, and movement
– Increases when air temperature is low (T or F)
– Increases when air humidity is high (T or F)
– Increases when air movement is strong (T or F)

36
Transpiration and Evapotranspiration
• Transpiration vaporization
of water found in plant
tissue with removal to
atmosphere
• Evapotranspiration sum of
evaporation from soil
surface and transpiration
from plants From Kansas State University

37
Evapotranspiration (ET)
• Evaporation + transpiration (from plant leaves).
• Provides 10% of the moisture in the atmosphere.
• An acre of corn gives off ~3,500 gallons (13,000 L) of
water each day
• Potential evapotranspiration: Max ET assuming water is
there to evaporate.
– Potential ET in Sahara Desert _____ in Daejeon
– Actual ET in desert = ____
• Factors affecting transpiration:
– temperature, humidity, wind, soil moisture, plant type

Tomato leaf stomate, photo from Wikipedia
-Cools down
-Mass flow of water from roots to the leaves

Photo from NASA
Largest rain forest:
8,235,430 km2
Ohio: 116,096 km2

41
• Evaporation: US Weather Service Class A pan:
– OD x L = 4 ft (1.22 m) x 10 in (25.4 cm)
– The pan rests on a leveled, wooden base
– Enclosed by a chain link fence
– Measure water depth, max/min temperature for 24 hours
(pan filled to exactly two inches (5 cm) from the pan top)
– At the end of 24 hours, the amount of water to
refill the pan to exactly two inches from its
top is measured.
– Need rain gage
– Values in a pan > or < (?) Values in a lake
– Pan coefficient : 0.58 – 0.78 (varies with
months)
Evapo-transpiration - Measurements
Photo: Wikipedia

• Evapotranspiration: Lysimeter
– Soil-filled tank on which plants are grown.
– Rate of
– Measure quantity of water added through
precipitation, lost through drainage, storage
changes in tank, runoff
RO
S
Q
P
ET o 




Evapotranspiration - Measurements
ETH, Zurich, Swiss
1. container; 2. concrete
wall; 3. cellar; 4. soil;
5. filter (sand and gravel);
6. electronic scales; 7.
drainage outlet; 8.
moisture sensor; 9.
temperature sensor; 10.
grass

Weighing Lysimeters
• Instrument measure
pieces water budget
∆S = P - ET - RO - Qo
P: rain gage
∆S: weigh column [B]
Qo: collect drainage [C]
RO: collect runoff [D]
(source: USDA Texas; Wikimedia Commons)
ET = P - ∆S - RO – Qo
–Lysimeter data usually
unavailable  empirical
methods are used
∆S
Qo
RO

Soil moisture and evaporation
• Heat conductivity of water >> air
– Heat flux / temperature gradient
• Wetter soils have _______ thermal conductivity than drier
soils
• Would wet soils warm up faster than dryer soils in the sun?
• Evaporation removes ‘warm’ water

Evaporative (Swamp) Cooler
45
- Many in Middle East, SW US
- Invented in Persia, 9 million in Iran
- Hot dry outside air used to evaporate water
- Produce cool moist air
USGS
Wikepidia

46
Runoff
• Surface Runoff: Water flowing
across the land surface as
streams, rivers, and drains after
rain storm or from melting snow
• Subsurface (Groundwater)
Runoff: Water flowing beneath
land surface through sediments
and rock

47
Infiltration
• Process of downward water entry into the soil
• Rate of infiltration sensitive to
– Rain: intensity, duration
– Near-surface condition, previous water content of soil
– Soil type: clays vs. sands
– Topography: plains vs. mountains
– Land use: vegetation vs. impervious surface

48
Surface Runoff
• Surface streams, rivers, drains,
sewers
• Factors affecting runoff
– Type of precipitation (rain, snow)
– Rainfall intensity, amount,
duration, frequency, distribution
over the watersheds
– Land use, vegetation, soil type
– Basin shape, slope, topography
– Ponds, lakes, reservoirs reduce
runoff
– Urbanization

Subsurface Runoff
• Water flows underground through open spaces in soils
and rocks
• Interflow: temporary flow after rain in shallow soil zone
• Groundwater flow: flow of water stored in deeper zone of
water saturation

50
Water Storage
• Water collected in naturally
occurring or manmade
bodies along hydrologic
cycle
• Storage bodies include:
- lakes, reservoirs, wetlands,
aquifers, ice caps

Watersheds or Drainage Basin
- extent of land where water from rain drains downhill
into water storage bodies such as river, lake, or wetlands
http://www.youtube.com/watch?v=xUYWb8XTo58

52
52
Watersheds and Streams
• River + tributaries
drain a watershed
• Watershed (drainage
basin) land area that
contributes water to a
stream system
from www.kidsgeo.com

Watersheds and Basins
• Watershed or basin is area where all water that is
under it or drains off of it goes to same place
• Watersheds are smaller areas and basins are bigger
(source USGS)

Exercise 1: Defining Watersheds
• Shaded relief map of Mad
River area
• Reds, browns greys hills
• Green and dark green valley
(1) Are labeled dots in Mad River
watershed?
(a) (b) (c)
(2) Sketch in the boundaries of
the watershed.
a
b
c

57
Water Budget
• Volume water transferred in hydrologic cycle
• Water budget developed for a hydrologic system
e.g., watershed or where water stored e.g.,
surface or ground water
• Calculation involves a direct accounting for the
inflows and outflows of water

58
Water Budget Equation
• Written for control volume
• Watershed, groundwater
(Source USGS)
Input – Output = ∆Storage
P + Qi - ET - Qo= ∆S
- P is precipitation
- Qi is surface and groundwater
water inflow
- ET is transpiration,
- Q0 is surface and groundwater
outflow

60
Water Budget Small Watershed
• Beaverdam Creek, Delmarva Peninsula of
Maryland - USGS
• Description
- 50.5 km2
- sand/silt 21 m thick
- shallow water table
- precipitation 109 cm/yr
(Source USGS)

61
Measurement Approaches
• Precipitation [P] – 12 rain gages
• Stream discharge [D] – sharp crested weir
• Evapotranspiration [ET] – Class A evap. pan
• Change gw storage: ΔSgw – 25 observation wells
• Change sw storage: ΔSsw – stage in 2 ponds
(www.engenious.com)
(source www.eijkelkamp.com)

62
Results as cm/inches over Watershed
• P = 211 cm per 2 yr depth x watershed area = volume
• ET = 127 cm
• D = 79 cm
• ΔS = 5 cm
211 = 127 + 79 + 5
P = ET + D + ΔS
(Source USGS)

Exercise 2: Estimating runoff ratio
• In an average year (water year Oct 1 to Sept.
30) the Mill Creek drainage basin (166.2 mi2)
in OH receives 700 mm of precipitation.
• A stream gauge recorder at the southern end
of the basin records an average stream
discharge of 2.2 m3s-1. (1 mile = 1.61 km).
• Conservation equation for a watershed:
P – Rs – ET = 0
63

Exercise 2: Estimating runoff ratio
(a) What is the volume of water (in m3) evapotranspired
for the year (assume no change in water stored in the
catchment)?
(b) What is the depth of water (in mm) evapotranspired
for the year (assume no change in water stored in the
catchment)?
(c) What is the runoff ratio (Rs/P) for the catchment?
64

65
Safe Yield and Sustainability
• Historical concerns on quantity of water that
could be pumped from watershed
• Concept of ‘Safe Yield’
“The limit to the quantity of water which can
be withdrawn regularly and permanently
without dangerous depletion of the storage
reserve”. [Lee, 1915]

66
• Definition expanded through the years
- Meinzer [1923]: economic aspect
- Conkling [1946]: conditions for safe yield
- Banks [1953]: protection water rights
• ‘Safe Yield’ no unique or constant value
- idea good but implementation difficult
Moving from Safe Yield to Sustainability

67
Sustainability
• Limit groundwater use to levels that can be
sustained over longer term
• Also ambiguous, difficult to define
• Broader than safe yield concepts - considers
role of groundwater in streams, rivers, wetlands
…development and use…that can be maintained
for indefinite time without unacceptable
environmental, social, economic consequences

68
GW/SW Connections
• Concept of safe yield
obsolete because
groundwater and
surface waters
connected
• Depletion gw causes
depletion sw
(Source USGS)

69
Effects of Pumping
[A] Natural system with gw
discharge to stream
[B] Moderate pumping
causes reduced inflow
to stream
[C] Heavy pumping
induces flow from
stream
- streamflow reduced
(Source USGS)
S
Q
Q
ET
R p
o 





70
Case Study – High Plains Aquifer
• High Plains 450,000 km2
- extends from South Dakota to Texas
• Farming late 1800’s difficult - modest rainfall
• Irrigation water from High Plains aquifer
Center-pivot field near Elkhart, Kansas (photos from USGS)

71
High Plains Aquifer
• Tremendous quantity
of water stored
- 3.3 billion acre-feet (1
acre-foot = 1235 m3
• “Old” water recharged
15,000 years ago with
wetter climate
• Pumping caused major
declines in ground-
water levels
(Source USGS)

72
Exercise 3: Water Budget
• Conceptual Model
• Before/After
development
• Flows (x106 ft3/d)
(x2.83x104 m3/d)
(Source USGS)
(Source USGS)

Exercise
(1) Write water balance equations for the aquifer
- Use QNR as natural recharge, QND as natural
discharge, QP as pumpage, and QNR+IR as recharge
and irrigation return flow, as storage change
- Before Development
- After Development
0



 S
Q
Q ND
NR
S
Q
Q
Q P
ND
IR
NR 




S

0
24
24 

330
830
10
510 




74
(2) The figure below shows perennial streams
(flow continually) in Kansas. Why the loss?

75
• Being depleted at a rate of 12
bcm/yr, total depletion to date 325
bcm ~ annual flow of 18 Colorado
Rivers, watering 20% of US
irrigated land.
• Will depleted within decades if
not managed
TAKE HOME POINT
(from USGS)
- aquifers like bank
accounts take out water
faster than put in
- go dry!

Folk Beliefs and Groundwater
77

• Many people believe in water dowsing
• Underground ‘lakes’, ‘underground
streams’
• Scientific view of water below ground!
– how much?
– Of what quality?
– At what rate can it be withdrawn?
– For how long and with what impact on other wells
and on nearby streams?
http://www.youtube.com/watch?v=T7R8ul7vABM

• All you need to know about ground water
Ground Water

80
Ground-Water Occurrence
• pores in unsaturated zone some water - moist
• in saturated zone, water completely fills pores
• saturated / unsaturated zones separated by water
table
(from USGS)

81
• Ultimate source of
water is rain
• Infiltrates into soil
added to
unsaturated zone
- used by plants
- some evaporates
• Excess water
moves down to
ground water
(from USGS)
Where Ground Water Comes From

82
Where Ground Water Goes
• Water moves slowly – 1 foot per day in
permeable deposits
• Flow moves from hills to valleys – “downhill”
to rivers
(from USGS)
http://www.traileraddict.com/trailer/a-river-runs-through-it/trailer

83
Darcy’s Law
• When water flowing,
gradient exists in
hydraulic head
• Flux (q) depends on
gradient and hydraulic
conductivity K
• Water flows from
places where head is
high to places where
head is low

84
Henry Darcy
• Near end of engineering career in France, Henry
Darcy returned hometown of Dijon. During his
earlier work with water flow in pipes (Darcy,
1837), interested in developing an equation for
flow of water through sand.
• Work concerned filtering of water through sand
to remove suspended solids and potentially
purifying the water. His work also related to
design large-scale artificial recharge lagoons
with water from rivers.

Henry Darcy
Appendix, D, Les Fountaines Publiques de la ville de Dijon, 1856
Photo by
Dr. Scott Bair, OSU From Wikipedia, public domain
- 3m x 0.3m
- 2 Hg manometers

86
Darcy’s Experiment
• Poured water through sediment-packed pipes at
some Q (volume of flow per unit time)
• Cylinder with known A (L2)
filled with sand
• Two manometers, separated
by a distance (L)
• Flow rate, Q (L3/T)
• Measured elevation of water
levels in manometers, h1 and
h2 (L) relative to local datum
l


87
Described by Darcy’s Equation
• Written as
where K is constant of proportionality
termed hydraulic conductivity, (h1-h2)/dl is
hydraulic gradient, and Q/A, flow per unit
area is called specific discharge, q,
- units of velocity (L/T)
- also called Darcy velocity
l
h
h
K
A
Q
q




)
( 2
1

88
• Equation states velocity of flow is proportional to
hydraulic gradient, i:
and Darcy’s equation is
written as
dl
dh
l
h
h
i 




)
( 2
1
Ki
q 
KiA
Q 

Directions of Groundwater Flow
• Saw previously groundwater
flows
• Movement implies
differences in energy from
place to place
• More familiar example
- where is energy highest?
- where energy lowest?
(from search-best-cartoons.com)

Gradient in Energy
• Gradient is change in energy per unit length
along the path
• gradient = (E1 – E2)/length
• Calculate gradients for left and right slides
E1 = 10
E2 = 0
E1 = 10
E2 = 0
length = 10
length = 20

• Obvious that gradient important in determining
how fast kid will go down slide
• There is another factor, however
• Kid on left is going twice as fast as kid on right
with same gradient!
E1 = 10
E2 = 0
length = 10
E1 = 10
E2 = 0
length = 10

93
Darcy’s Velocity vs. Pore Velocity
• Darcy’s law
- macroscopic no information
pores
• Darcy velocity assumes flow
occurs over entire surface areas
of soil column
• Water only flows in pore space
- linear velocity > Darcy velocity
l
h
h
K
A
Q
q




)
( 2
1

94
• Linear or pore velocity defined as volumetric
flow rate per unit interconnected pore space:
where ne effective porosity
• Linear velocity is true velocity of water flow in a
porous medium
e
n
q
v 

95
Porosity
• Total porosity:
Vv = volume voids; VT = total
volume sample
• Effective porosity: porosity that is effective in
moving water through the porous medium:
Viv = vol. interconnected voids
• ne ~ nT porous medium; ne << nT fractured
medium
T
v
T V
V
n /

T
iv
e V
V
n /


96
• Well sorted media have
higher porosity than poorly
sorted media
- smaller particles fill void
spaces
• Ranges 0 to 60(%)
• Porosity higher for unlithified
materials than for lithified
materials
• Look at table – what types
deposits are unknown?
Porosity Values

97
Hydraulic Conductivity, K
• Introduced in Darcy’s law as constant of
proportionality relating q to i
• Qualitatively, parameter describes how easily
flow can occur through porous medium
• Large values for permeable units like sand and
gravel and small values for clay or shale
• Units of velocity (L/T), when Q has m3/day,
m/day
l
h
h
K
A
Q
q





)
( 2
1

98
Range K Values
• K amazing parameter
• Varies over more
than 14 orders-of-
magnitude
• Fracturing clay and
till cause 100x
increase in K

99
Directional Properties of K
• Isotropic/anisotropic – describes directional
dependence at point within porous medium
• Homogeneous – K in a given direction is same
from point to point
__________________
_
__________________
_

Intrinsic Permeability, k
• K depends on both properties of porous medium
and fluid (density, viscosity)  for water,
constant fluid properties
• For groundwater, K useful hydraulic property
• For petroleum, fluid properties vary
• k describes ability of media to transmit fluid
• k independent of fluid

Hydraulic Conductivity (K) and
Permeability (ki)
ki = intrinsic permeability,
where N = a factor to account for shape of the passages
(dimensionless); d = mean grain diameter (L)
m = dynamic viscosity (kg-m-1s-1)
– resistance of fluid to flow
– water is "thin", having a lower viscosity, while
vegetable oil is "thick" having a higher viscosity.
r = fluid density (M/L3)
g = gravity constant; Here, rg = driving force of fluid
m
rg
k
K i
 2
Nd
ki  Hubert, 1956 +
Hagen-Poiseuille eq.

102
Hydraulic Head
• Fact that water moves implies an energy
gradient
• Water has greater energy available for flow at
one point than at another
• Energy for flow measured by height of water in
manometer above datum
Called hydraulic head (h)

103
Piezometer
• Piezometer is a device
installed to measure
hydraulic head
• Casing with a perforated
screen
- point of measurement
• Water rises up casing
• Head is elevation of water
surface in casing applied to
measurement point
Elev.

Exercise 4: Hydraulic Head
• Elevation of ground surface: 1000 m asl
• Depth to water is 25 m
• Total length of piezometer is 50 m
• Water has density of 1000 kg/m3
• What are (a) elevation h, (b) pressure h, (c) total h?
g
v
g
P
z
h
w 2
2



r
Bernoulli’s eq

105
Field Determination Hydraulic Head
80

106
Water Table Observation Well
• Device is not a piezometer
• Purpose to measure
elevation of water table
• Screen is long so water table
always in screened section
• Measurement applied to
water surface

107
Interpretation
• Collection of heads
shows pattern of flow
• Contour head values to
produce equipotential
lines
• Flow lines drawn
perpendicular
• Assumptions
- isotropic
- no flow in/out section

108
Field Interpretation Darcy Equation
• Darcy equation used to estimate quantities of
flow (Q) and groundwater velocities
• Quantity of flow:
• Darcy Velocity:
• Linear groundwater velocity:
dx
dh
K
q 

dx
dh
KA
Q 

dx
dh
n
K
v
e



109
Exercise 5: Application of Darcy’s Law
A 5 m thick sand aquifer has K=1.5x10-3 m/s. Calculate:
(1) Quantity of flow through a unit cross-section
(2) Linear ground water velocity, estimating necessary
parameters
(3) Linear velocity assuming aquifer is fractured shale
ne = 0.001
4000 meters
200 m
180 m

110
Estimating Patterns of Flow
• Shown that is possible to measure
hydraulic head and estimate patterns of
groundwater flow
• Alternative approach is to understand
geologic setting and predict hydraulic head
distribution and patterns of flow
• Application of theoretical approaches to
problems of regional flow developed from
1960s onward

113
• Variety of approaches to solve for
hydraulic head distribution within a
domain
• Graphical or flow net theory
• Solution to differential equation for flow
where h is hydraulic head, x and y
coordinates
0
2
2
2
2






y
h
x
h
Theoretical Approaches

114
• First requirement is to find a domain of interest
- region to solve for head distribution
Region of Interest

115
• Second requirement provide boundary
conditions along the edges of domain
- necessary information to define internal head
distribution
- mainly two: no flow, constant head
Boundary Conditions

116
What Are the Boundary Conditions?
• Chose “natural” set of boundary conditions so
simple
No
Flow
No Flow
Constant Head

117
Flownets
• Graphical solution to Laplace equation
- simple two-dimensional case
- mostly used with simple media
- no layering, isotropic medium
(after Loaiciga & Zekster, 2002)

118
Rules for Flownets
(1) Streamlines perpendicular to equipotential lines
- if contour spacing same, streamlines and
equipotential lines form curvilinear squares
- curved sides, tangent to inscribed circle
(2) Same quantity groundwater flows between
adjacent pairs of flow lines

119
From Jack
Hermance, Brown
University

120
More Suggestions/Rules
(1) In first attempts use only four or five flow tubes
(2) Work holistically on the flownet early, rather
than details
(3) Do simple parts flownet first
(4) Size of the curvilinear squares changes
gradually
(5) No flow boundary is a streamline
Water table streamline when no recharge

121
River
(mean stage 60 ft)
Valley
210 ft 190 170 150 130 110 90 70
200 180 160 140 120 100 80
Flow-Net Concepts
Xsection
Sand
Silty clay
w = 1000 ft
b =
50 ft
• Valley sand with groundwater flow
(Q) to river.
• Create flownet then the flow in
each flow tube (dq) is same.
Q
dq1
dq4
dq2
dq3
Q = dq1 + dq2 + dq3 + dq4

122
Flow-Net Concepts cont’d
ds
dh
dm
A B
C
D
• Designate corners as ABCD with AB = ds
and BC = dm. If the head drop is dh, then
the discharge is dq
dh
dq Kb dm
ds

• Discharge across any vertical plane of aquifer, thickness b
is dq because no water is added or removed from storage
• With inscribed circles, ds = dm and
*
dq Kb dh

• For nf flow tubes, total discharge Q is
* *
f
Q n Kb dh


123
• Draw a flownet for seepage through earthen dam shown here.
Assume homogeneous and isotropic conditions. If the hydraulic
conductivity 0.22 ft/day, what is the seepage per unit width per day?
Assume five flow tubes.
Exercise 6: Flownet

Exercise 7: Flownet
• Average discharge due to ground-water
withdrawals from the Patuxent Formation in
Sparrow Point District in 1945 was 1 million ft3/day.
(Bennett and Meyer, 1952)
• Calculate the transmissivity of the formation.
H
T
n
n
Q
d
f


day
ft
ft
day
ft
H
n
Q
n
T
f
d
/
6667
)
30
)(
15
(
)
/
10
)(
3
( 3
3
6





Exercise 8: Flownets in Heterogeneous
Media
• If width of stream tube remains constant,
segment length of stream tube in higher T is
longer than in lower T zone.

Exercise 8 - Continued
• Calculate the flow rate ( Q) and the length L2.
Assume that

m
L
W
W 10
1
2
1 





day
m
m
m
m
m
day
m
L
W
h
T
Q /
5000
)
10
(
)
10
(
)
1
)(
50
)(
/
100
( 3







m
m
m
m
m
day
m
L
T
T
L 20
)
10
(
)
50
)(
100
(
)
50
)(
/
200
(
1
1
2
2 






128
Shown on next page hydrogeologic cross-
section showing hydraulic head and water table
elevation measurements
(1) Work in teams of two and on figure draw
water-table and pattern of flow
(2) On the figure, mark recharge and discharge
areas
(3) Explain why flow in the deeper unit is
different than flow in the shallow unit
(4) When discharge occurs at the ground
surface, what forms might it take?
Exercise 9: Hydrogeologic Cross-section

130
• Map of potentiometric surface
- constructed for a single aquifer
- contour heads for piezometers in aquifer
• Designed to show how groundwater is flowing
Potentiometric Surface
Only a map view for single aquifer

131
• Important points when using potentiometric map:
- potentiometric surface only exists for single
aquifer
- map assumes that flow is horizontal
- if aquifer gets thicker in direction of flow,
equipotentials will become ______ spaced
Mapping Flow in Geological Systems

132
Regional Groundwater Flow
• Issues of flow studied at two scales
- local scale response aquifer to pumping
- large scale flow over hundreds of kilometers
• Latter topic is regional groundwater flow
• Basic unit for analysis is groundwater basin
- three-dimensional closed system, which
contains all flow paths followed by water
recharging basin

133
Hubbert’s Classical Figure
• Famous picture in groundwater science
- one or two complete groundwater basins
- basin closed with no flow through left, right,
bottom boundaries
From Hubbert (1940)

134
Definitions
• Water table - top saturated groundwater (gw)
system along which pressure is atmospheric
• Recharge area - region where flow is directed
downward away from water table (wt)
• Discharge area - flow upward toward wt
On the following figure from Freeze and Witherspoon (1967) label recharge and
discharge areas.

136
Water-table and Regional GW Flow
• Toth (1962) extended Hubbert’s theoretical
model by solving Laplace’s Equation analytically

137
Problem Formulation
• Laplace’s equation written as:
• Boundary conditions on three sides
- lower boundary is impervious unit
- lateral boundaries are groundwater divides
• Top boundary
- sinusoidal fluctuation on regional slope
0
2
2
2
2






y
h
x
h

138
)
2
sin
'
(
)
,
( 0

x
b
L
x
B
z
z
x
h 


L
x
B'
= regional slope
= local relief superimposed on regional slope

x
b
2
sin
B’

140
1. If local relief is negligible and there is only a
general slope of topography  only regional
systems will develop
Important Conclusions of Toth’s work:

141
2. If regional slope negligible  only local systems
develop. Greater relief produces deeper local
systems

142
3. Given both local relief and regional slope,
local, intermediate and regional systems will
develop
4. Regional flow systems characterized by
- long paths with slow, deep circulation
- water highly mineralized with elevated
temperature at discharge area

143
5. Local flow systems:
- short flow paths (less mineralized).
- temperature of discharge at mean annual
air temp.
- areas of rapid circulation of groundwater

144
Results of Freeze and Witherspoon
1) Confirmed Toth’s analytical work

145
2) Looked at hydraulic conductivity contrasts
(from Freeze and Witherspoon, 1967, Water Resour. Res.)

146
GW/SW Interactions
(A) Discharge Lake (B)
Recharge Lake (C)
Flow-through Lake
(from USGS)

148
Mapping Regional Groundwater Flow
• Piezometer nests: collection of piezometers at
different depths
• h varies in space/ time
• Measure at same time (snap shot), time element
removed
• We want to represent the 3-D field in 2-D
diagram

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