Environmental Engineering Reference
In-Depth Information
However, if more than one glass tube is measured in order
to determine the direction of flow in the pipe, the heights
must be comparable to a common datum, called the eleva-
tion head. Hence, after Bernoulli's experiments, fluids could
be characterized by knowing their pressure, density, and
elevation. In the mid-1800s, Darcy measured levels of mer-
cury in thin tubes and converted them to equivalent levels of
water with respect to a common surface, the bottom of the
column. These measurements reflected the elevation of
the water level, or head, above the column bottom added
to the elevation of the head above the sand. In other words,
4.3
Flowing Water—The Bernoulli Equation
The flow of fluids is the result of the driving force of gravity
to overcome inertia and the resisting force of friction as the
fluid flows; flow is constant once these two opposing forces
are equal. In groundwater, the hydraulic gradient is what
imparts the gravitational component of flow. Flow is essen-
tially an energy gradient such that water at a higher elevation
has more energy than water at lower elevation. Energy here
means the force multiplied by the distance, or the amount of
work done. The initial energy for flow is attained by eleva-
tion and is called potential energy and by flow called kinetic
energy. Because the rate of groundwater flow is relatively
slow and laminar compared to turbulent surface-water flow,
the kinetic energy is small. Heat as a form of energy in
groundwater normally varies little over space and is consid-
ered a constant.
This understanding of fluid flow as a special condition of
static fluids was not gained easily, however. As late as the
early 1700s, during the time when Harvey was concerned
with the circulation of blood in humans (Chap. 1) and Hales
was concerned with the circulation of water or sap in plants
(Chap. 1; Table 1.3), no device existed to measure the
pressure exerted by the flow of these fluids against their
vessels. Harvey noticed that when a blood vessel was rup-
tured, the level of blood issuing would rise and fall in rhythm
with the contractions and relaxations of the heart. The
French scientist Edm´ Mariotte (Chap. 2) was
experimenting with measuring the pressure of water flowing
out of a pierced pipe. His experimental device was novel and
simple: the water let out of the pipe was allowed to push
against an instrument that contained lead, and when the
amount of lead added was equal to the force of the water
against it Mariotte was able to calculate the pressure of the
water (Guillen 1995). Although useful for measuring fluids
that could be permitted to leak, it would have been a disas-
trous way to measure the blood pressure of humans.
This quest for understanding fluid pressure and its mea-
surement did not go unnoticed by a Swiss mathematician
named Daniel Bernoulli (1700-1782). He published his
work on his theories of fluids called
Hydrodynamics
in
1738. As Darcy did almost 100 years later, Bernoulli
conducted physical experiments with water flowing through
pipes of different sizes and recorded the changes in pressure.
Although the behavior of fluids seems trivial today, during
Bernoulli's time the behavior of fluids was unknown, com-
pared to Isaac Newton's contemporaneous revelations about
the behavior of solids. When Bernoulli added a glass tube to
the side of a pipe that contained flowing water, the water rose
up into the tube until it stopped at a certain elevation: could
this perhaps be where Darcy got his idea to measure the head
in his columns using thin tubes more than 100 years later?
H
¼
elevation head
þ
pressure head
;
and
(4.8)
H
¼
z
þ
ð
P
=r
g
Þ;
(4.9)
mass density (M/L
3
),
g
gravity (L/T
2
), and
where
r ¼
¼
pressure (ML/T
2
). Density,
P
¼
r
, is the mass of a unit
volume of a substance with dimensions (M/L
3
).
In groundwater investigations, Bernoulli's equation can
be used to deduce that the potential of a fluid at any point in a
porous medium can be measured by the head above a com-
mon datum (Fig.
4.7
). This is because gravity,
g
, can be
considered constant among measurements. Instead of using
manometers, hydrogeologists use piezometers, which essen-
tially are pipes with two open ends, or observation wells
consisting of 1- to 4-in. diameter pipes with no more than
10 ft (3.3 m) of slotted pipe, or screen, at the end penetrating
the aquifer. For the measurements to be comparable the
depth from land surface to the end of the pipe, or midpoint
of the slotted section, must be constant. Hence, wells
screened with larger slotted sections or a section that crosses
two aquifers may not be comparable.
4.4
Aquifers
The sand- and water-filled columns used by Darcy enabled
water to flow from the inlet to the outlet pipes. On a much
larger scale in nature, aquifers are sediments that contain
water available to flow to a well in useable volumes. The
study of groundwater flow through sediments, geologic
media, and aquifers is called hydrogeology. Although the
term hydrogeology was first used in a report by J.B. Lamarck
(1802), he used the term to refer to sediments that had been
deposited by water flow. The first use of the term hydroge-
ology to describe groundwater flow in aquifers was in a
paper by J. Lucas (1880). About the same time, the newly
formed USGS adopted the term in published results of
hydrogeologic investigation studies.
Even though the term aquifer is widely used today, C.V.
Theis of the USGS used the term hydropher to describe the
part of the geologic unit that was saturated with groundwater
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