Soil Physics 2010 Outline Announcements Where were we? Archimedes Water retention curve.
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Transcript of Soil Physics 2010 Outline Announcements Where were we? Archimedes Water retention curve.
Soil Physics 2010
Outline
• Announcements
• Where were we?
• Archimedes
• Water retention curve
Soil Physics 2010
Announcements
• Reminder: Homework 3 is due February 19
•Quiz!
Soil Physics 2010
Water characteristic curve
Water contentWetness, , etc
Su
ctio
nP
oten
tial
, h, t
ensi
on, e
tc
Soil Physics 2010
Darcy’s law
5 cm
2 cm
10 cm
4 cm
radius = 4 cm
L
hKAQ
Q =
K =
A =
h =
L =
?
?
16 cm2
5 cm
10 cm
cm
cmcmKQ
10
5 16 2
Soil Physics 2010
Fresh water
Salt water
Where were we?
Osmotic potential drying a soil
Negative pressure drying a soil
Soil Physics 2010
r
hgaw
cos2
Drying pressure
Tube radius The water left in the soil
is at equilibrium with the water in the tube
Positive pressure drying a soil
Soil Physics 2010
Drying pressure
The water left in the soil is at equilibrium with the pressure
difference between the chamber and the outside
pFilter passes water but not air (what kind of material does that?)
Elevation drying a soil
Soil Physics 2010
The water left in the soil is at equilibrium with the water in the hanging tube, with a negative pressure equal to the height difference h
Soil Physics 2010
Conclusions:
• It takes energy to dry a wet soil
• That energy can be in the form of osmotic potential, a negative or positive pressure, or an elevation
• Knowing how these forms of energy are related, we can:• calculate the influence of each
• choose which to apply (e.g., in the lab)
• Heat energy works too, but it’s complicated
Soil Physics 2010
Buoyancy
We saw this in deriving Stokes’ Law:
At terminal velocity,Force up = Force
down(Newton’s 1st law)
Force down:Force = Mass * acceleration = (s-w)(4/3 r3) * g
(Newton’s 2nd law)
Soil Physics 2010
Density difference
Force down:Force = Mass * acceleration = (s-w)(4/3 r3) * g
Density difference * Volume = Mass
Density difference
Volume
Acceleration
Mass / Volume = Density
Soil Physics 2010
ArchimedesSyracuse, Sicily, 287-212 BCE
How much water overflows?
density of gold:19,300 kg m-3
density of silver:10,500 kg m-3
Soil Physics 2010
ArchimedesPrinciple
Weighing things in 2 fluids:
• Mass is constant
• Volume is constant
• Buoyancy changes
Any object wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces
density of gold:19,300 kg m-3
density of silver:10,500 kg m-3
?
Soil Physics 2010
Buoyancy
A ship sailing from the ocean to a freshwater port
Eggs sink in fresh water, but float in salt water
Any object wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces
Soil Physics 2010
Water retention curve
Basic idea:• As a soil dries, its wetness is related to
the water’s energy level h.
Water contentWetness, , etc
Su
ctio
n-p
oten
tial
, h, t
ensi
on, e
tc
Soil Physics 2010
So what?
I mean, what’s so special about how these 2 properties are related?
It’s a soil physics thing. You wouldn’t understand.
Next we’ll get to plot it against the exponential derivative of Darcy’s law or something. Oh, the excitement!
Soil Physics 2010
Water retention curve
Basic idea:
If the soil were a bunch of capillary tubes, we could figure out everything about how water and air move in it…
…if we also knew the size distribution of those capillary tubes.
The water retention curve is our best estimate of the soil’s pore size distribution.
Soil Physics 2010
Pore size distribution?
Remember that water and air only flow through the pores.
If we know the size distribution of the pores, we should be able to predict K…
…plus all those other properties we haven’t gotten to yet.
Soil Physics 2010
Well, yeah…
Remember that science proceeds by developing models.
A tube is simple enough to analyze – you already know about capillary rise and flow in a tube.
This is why we’ve been studying tubes?
L
prQ
8
4
(Poiseuille’s law)
g rh
aw
cos2
(Capillary rise equation)
But remember what Irwin Fatt said (Petr. Trans. AIME, 1956):
Capillary tubes are too simplistic.
Glass beads are intractable, and they’re still too simple.
Real porous media have multiply connected pores (topology & connections again).Soil Physics 2010
Soil Physics 2010
With that warning, let’s look at water retention
Start with a soil core that’s saturated:
Known height
Atmospheric pressure
So we know the water’s potential everywhere
Known dry mass
Known porosity
=
Atmospheric pressure 5
Soil Physics 2010
Known height L
So we know the water’s potential everywhere
0
L
(0)
At saturation:h = 0
If it can drain out the bottom, then
, andmean h = L/2
Soil Physics 2010
Then I talked about sponges