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Unformatted text preview: CE/GEOL 485
Principles of Hydrogeology LECTURE 4
Pressure & Head Lecture Outline
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• Fluid Pressure
Pressure, Energy & Head
Pressure Head in a Static Saturated System
Elevation or Gravitational Head
Total or Hydraulic Head
Measuring Hydraulic Head
Piezometer
Manometer
Pressure Gauge • Hydraulic (Head) Gradients
Pages: 6669, 113122 in Fetter Fluid Pressure
• In a fluid at rest, pressure is a scalar quantity
• This means it is the same in all directions, but can
vary from point to point within the fluid
• In a fluid at rest, pressure, P, is the force exerted by
the fluid per unit area of the fluid P= F
A Dimensions = SI Units = Pa = [M]
[T 2 ][L] N kg.m kg
=
=
m 2 s2 m 2 s2 m English Units = psi = Ψ = pressure head = height of liquid
causing pressure at a point Ψ
Liquid Ψ = P/γ
P = pressure = [L] We can also express energy as:
Energy per unit mass [ML2/T2]/[M] = [L2/T2]
Energy per unit weight [ML2/T2]/[ML/T2] = Head,
Elevation or Gravitational Head, Zg
 in a system at constant pressure, water flows
from high elevation to low elevation
THEREFORE ELEVATION IS ALSO A MEASURE OF ENERGY
& IS REFERRED TO AS GRAVITATIONAL POTENTIAL (OR
GRAVITATIONAL HEAD IN LENGTH UNITS) [M]
[T 2][L] γ = specific weight of liquid γ = ρ water g Energy per unit volume [ML2/T2]/[L3] = Pressure [M/LT2] lbs
in 2 Pressure Head in a Static Saturated System Air Pressure is a Measure of Energy
(or Potential) = [M]
[T 2][L2] Precipitation
Sloping ground
surface Subsurface
Flow •1 Total or Hydraulic Head (hT or h)
What other “forces” can cause flow?
 kinetic effects, i.e., momentum of flowing
water (as described on p. 114115 of
Fetter)
 temperature gradients cause flow because
warm water has lower density than
colder water
 electrical, chemical & osmotic gradients
may also induce water movement Measuring Head
Piezometer – a tubelike device used to measure
hydraulic head, h, at a point in the phreatic zone
under field conditions Tube must be:
 open to liquid at the measurement point In groundwater systems, “other forces”
(including kinetic energy) tend to be small, so
we assume flow is controlled only by the
pressure & gravitational heads, i.e. h= Ψ+z Open to Atmosphere Standpipe Piezometer
• most commonly
used type of field
piezometer
• simple & reliable
• can also be used to
take water samples
& measure aquifer
characteristics Casing
stickup Cap
Ground Surface Water table
Casing (steel, PVC, etc.)
must not leak!
Average
depth
ψ
of
screen h  open to atmosphere at top Annulus, filled with
grout to prevent seepage
along casing Open end, or “short”
screened interval for
water intake  sealed along its length
z Datum Manometer
A tubelike device used to measure hydraulic head, h, at a point in
a sample of saturated porous material
Laboratory version of a piezometer which can be filled with fluids
other than water (e.g., mercury)
Mercury
Manometer Water
Manometer STUDENT PRESENTATION ψ Ψm
P1 P2 •2 Gauge Pressure
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• a gauge measures pressure, P, relative to atmosphere
gauge reading is positive if pressure > atmospheric
gauge reading is negative if pressure < atmospheric
for points at the same elevation, water flows from zones of high
gauge pressure to zones of low gauge pressure Example, flow in a waterfilled pipe
P = 2 Pa Datum P = 10 Pa Pgauge = Ptotal  Patm Which direction is flow? Hydraulic Gradients Pressure Gauge
 also used to measure hydraulic head in the laboratory
 measures pressure relative to atmosphere (Pg = Ptotal  Patm)
 calculate total head using h = Ψ +Z = Pg
+ Zg
γw where γ w = ρwg and Zg = elevation of gauge
Flow Water manometer
ψ Column of
saturated sand
Gauge Pg h
ZZ
Zg Datum  Water always
moves from
high h to low h
 Magnitude of
the driving force
for flow is the
hydraulic
gradient, ∆h/∆x
or ∆h/∆z
 Hydraulic
gradient is a
vector quantity
 Need 2 or more
piezometers to
measure
direction &
magnitude of
flow TAKE HOME MESSAGE
A Practical Definition of Total or Hydraulic Head Q
Ψ READING FOR NEXT LECTURE:
h
Z
Elevation Datum Pages: 219228 in Fetter Total or Hydraulic head = Elevation head + Pressure head Water pressure = air pressure = 0 at the “water table”
i,.e., ψ = 0 and h = z = elevation of the water table •3 ...
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This note was uploaded on 11/10/2011 for the course GEOL 455 taught by Professor Perfect during the Fall '11 term at University of Tennessee.
 Fall '11
 Perfect
 Hydrogeology

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