soil physics 2010
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Outline. Announcements Todd on aggregates Saturated flow of water. Soil Physics 2010. Announcements. No office hours today Reminder: Homework due Feb. 10 Reminder: Exam Feb. 12 - PowerPoint PPT PresentationTRANSCRIPT
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Soil Physics 2010
Outline
• Announcements
• Todd on aggregates
• Saturated flow of water
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Soil Physics 2010
Announcements
• No office hours today
• Reminder: Homework due Feb. 10
• Reminder: Exam Feb. 12
• Example exam is now posted. Don’t panic! I covered material in a different order that year, and the class was not dual-listed at the 400-level.
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Soil Physics 2010
Todd on Aggregates
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Soil Physics 2010
Saturated flow
When is the soil saturated?
Near the surface under heavy rain
Confined aquifer
Under a lake or stream
Recharge basin
Go deep enough…
It turns out that the saturated flow equations are just special (simpler) cases of flow more generally.
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Soil Physics 2010
The city of Dijon1800
Ancient capitol fallen on hard times
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Soil Physics 2010
Paris
Dijon
Lyon
France, 1800s
Political turmoil:• 1804 - 1815 First Empire - Napoleon
• 1815 - 1830 Restoration - Louis XVIII - Charles X
• 1830 - 1848 Bourgeois Monarchy - Louis-Philippe
• 1848 – 1851 Second Republic
• 1852 - 1870 Second Empire - Napoleon III
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Soil Physics 2010
Henry Darcy
Fellow students at L’École des Ponts et Chaussées*:
CauchyChézy
ColiolisDupuitFresnelNavierPitot
St. Venant
Henry graduated 12th in his class. He had been 1st, but he got violently upset
with a chemistry professor over a question about
cooking.* The school of Bridges and Roads
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Soil Physics 2010
Most famous publication
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Soil Physics 2010
Darcy’s experimentreported in Appendix D ofLes Fontaines Publiques…
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Henry Darcy
“One does not get the main square in town named in one’s
honor on the basis of some column experiments.”
-- Allan Freeze, 1994Soil Physics 2010
• Public water supply in Dijon: clean, reliable, gravity flow 12 km to 142 public fountains
• 4 km railroad tunnel allowed the main Paris-Lyon track to pass through Dijon
• Several large bridges near Dijon
• Improvements to the Pitot tube
• Extensive studies on:Flow through open channelsFlow through pipesRoad construction
• Near the end of his life, a few studies on flow through sand
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Henry Darcy
Soil Physics 2010
“As much as possible, one should favor the free drawing of water because it is necessary for public health. A city that cares for the interest of the poor class should not limit their water, just as daytime and light are not limited.”
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Soil Physics 2010
Darcy’s experiment
1 m3
2.5 m
• Column filled with sand to different depths
• Different water pressures applied across column
• Discharge Q measured (volume of water / time)
• Experiment repeated with different sands
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Soil Physics 2010
Darcy’s 3 observations:
1: Q cross-sectional Area2: Q drop in (pressure + elevation)3: Q 1 / flow distance
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State of the art
Soil Physics 2010
For slow flow through a pipe,
Q dischargeR radius viscosityp pressure dropL length
L
pRQ
8
4
Mean velocity isL
pRu
8
2
(Poiseuille’s law)
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Soil Physics 2010
Darcy’s 1st observation
1: Q cross-sectional Area2: Q drop in (pressure + elevation)3: Q 1 / flow distance
Assume zero resistance in pipes
Darcy’s experiments used a vertical column, but a horizontal column is simpler.
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Soil Physics 2010
Darcy’s 2nd observation
1: Q cross-sectional Area
2: Q drop in (pressure + elevation)3: Q 1 / flow distance
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Pressure = Elevation?
When you swim underwater, your ears feel pressure
Why doesn’t the water at the bottom of the pool – under lots of pressure – shoot up to the top?
The energy is the same all through the pool. Surface water has elevation; deep water has pressure.
Dep
th
Pressure
Elevat
ion
Soil Physics 2010
Pressure+ Elevation
Energy
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Soil Physics 2010
Darcy’s 3rd observation
1: Q cross-sectional Area2: Q drop in (pressure + elevation)
3: Q 1 / flow distance
L
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Soil Physics 2010
Darcy’s Law as he wrote it
L
zhzhKAQ 2211
HeightWater
pressure
Water volume / unit
time
Length of flow
Cross-sectional area of flow
Proportionality coefficient:Hydraulic
conductivity
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Soil Physics 2010
Units in Darcy’s Law
L
zhzhKAQ 2211
L
LLL
T
L
T
L 2
3
UnitlessVelocity
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Soil Physics 2010
Key implications of Darcy’s law: 1
L
hhKAQ 12
For flow through a uniform medium, the hydraulic gradient is constant.
02 h
Taking the derivative of Darcy’s law,
gives the Laplace equation,
hKq
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Soil Physics 2010
Key implications of Darcy’s law: 2
The flow is linearly proportional to the gradient.This puts Darcy’s law into the same class as several other equations:
Hooke’s law (elasticity)
Darcy’s law (hydraulic conductivity)
Ohm’s law (electrical conductivity)
Fourier’s law (heat conduction)
Fick’s law (diffusion)
hKq
Vj Tqh CDf
E
1
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Soil Physics 2010
Key implications of Darcy’s law: 3
K is a property of the medium*.
The hydraulic conductivity K is not changed by whether the water flows up instead of down, or by having a greater or smaller gradient, or by the pressures or elevations themselves.
In fact, K can often be predicted with reasonable accuracy, given some other information about the medium. For example, the porosity and the grain size or pore size distribution allow a fair estimate.
* Also of the fluid – see later