Water Supply and Treatment

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Water Supply and Treatment
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Average Precipitation
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Water Deficits
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Hydrologic Cycle
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Groundwater Problems
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Groundwater Supplies
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The amount of water stored in an aquifer is equal
to the volume of void spaces between the soil
grains, the porosity
Porosity volume of voids/total volume
The amount of water that can be extracted from
the aquifer is called the specific yield
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Q A v
v superficial velocity
Q A v a v
a area available for flow (pores) v actual
velocity of flow
v Av/a A v L / a L v / porosity
When water flows through a soil it loses energy
just like when it flows through a pipe
(friction, etc.)
h energy, measured as elevation of the water
table in an unconfined aquifer or as the
pressure in a confined aquifer L horizontal
distance in direction of flow
dh/dL
In an unconfined aquifer, the drop in elevation
of the water table with distance is dh/dL. The
elevation of the water surface is the potential
energy of the water. Water flows from higher
elevation to lower elevation, losing energy.
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Flow through a porous medium like a soil is
related to the energy loss using the Darcy
equation
Q K A dh/dL
K coefficient of permeability, m/sec
A cross-sectional area, m2
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A soil sample is installed in a permeameter as in
the figure below. The sample length is 0.1 m
with a cross-sectional area of 0.05 m2. The
pressure on the upstream side is 2.5 m and on
the downstream side is 0.5 m. A flow rate of 2.0
m3/day is observed. What is the coefficient of
permeability, K?
dh/dL (2.5 0.5)/ 0.1 20
K Q / (A dh/dL) 2.0 / (0.05 x 20) 2 m/day
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Drawdown
This is an unconfined aquifer being pumped. As
water flows to the well the area through which
it can travel becomes smaller and smaller,
therefore the velocity gets larger and larger.
This means more loss of energy (the gradient
dh/dL increases) and the slope of the water
surface increases, resulting in a cone of
depression
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Given the cylinder shown at the right, Darcys
law becomes
Q K (2Brw) dh/dL
Separate the variables and integrate
Q BK(h12 h22)/ ln(r1/r2)
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Example
A well is 0.2 m in diameter and pumps from an
unconfined aquifer 30 m deep at an equilibrium
rate of 1000 m3/day. Two observation wells are
located at distances of 50 and 100 m and have
drawdowns of 0.3 and 0.2 m, respectively. What
is the coefficient of permeability and estimated
drawdown at the well?
K Q ln(r1/r2)/B(h12 h22) 1000
ln(100/50)/3.14(29.82 29.72 37.1 m/day
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The radius of the well is 0.2/2 0.1 m. Now
Q (BK(h12 h22) / ln(r1/r2) 3.14 x 37.1
x (29.72 h22)/ln(50/0.1) 1000 m3/day
h2 28.8 m
Since the aquifer is 30 m deep, the drawdown is
30 28.8 1.2 m
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Multiple Wells