Outline
• Announcements
• Where were we?
• Archimedes
• Water retention curve
Soil Physics 2010
Announcements
• Reminder:
Homework 3 is due February 19
• Quiz!
Soil Physics 2010
Potential, h, tension, etc
Suction
Water characteristic curve
Water content
Soil Physics 2010
Wetness, q, etc
Darcy’s law
h
Q  KA
L
Q=
K=
A=
h =
L =
?
?
16p cm2
5 cm
10 cm
Soil Physics 2010
5 cm
2 cm
radius = 4 cm
10 cm
4 cm
5 cm
Q  K 16p cm
10 cm
2
Where were we?
Osmotic potential drying a soil
Fresh
water
Soil Physics 2010
Salt
water
Negative pressure drying a soil
2 cos 
 w   a  g h 
r
Drying
pressure
Soil Physics 2010
Tube
radius
The water left in the soil
is at equilibrium with
the water in the tube
Positive pressure drying a soil
The water left in the soil is at
equilibrium with the pressure
difference between the
chamber and the outside
Filter passes water but not air
(what kind of material does that?)
Soil Physics 2010
Drying
pressure
p
Elevation drying a soil
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
Soil Physics 2010
h
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 p r3) * g
(Newton’s 2nd law)
Soil Physics 2010
Density difference
Acceleration
Force down:
Force = Mass * acceleration
= (s-w)(4/3 p r3) * g
Density
difference
Volume
Density difference * Volume = Mass
Mass / Volume = Density
Soil Physics 2010
Archimedes
Syracuse, Sicily, 287-212 BCE
density of gold:
19,300 kg m-3
How much
water
overflows?
Soil Physics 2010
density of silver:
10,500 kg m-3
Archimedes
Principle
density of gold:
19,300 kg m-3
density of silver:
10,500 kg m-3
?
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
Soil Physics 2010
Buoyancy
Eggs sink in fresh water, but float in salt water
A ship sailing from the ocean
to a freshwater port
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:
-potential, h, tension, etc
Suction
• As a soil dries, its wetness q is related to
the water’s energy level h.
Water content
Soil Physics 2010
Wetness, q, etc
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
This is why we’ve been studying tubes?
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.
p r p
Q
8 L
4
Soil Physics 2010
(Poiseuille’s law)
2 cos
h
 w   a  g r
(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.
Soil Physics 2010
Real porous media have
multiply connected pores
(topology & connections again).
With that warning, let’s look at water retention
Start with a soil core
that’s saturated:
Atmospheric
pressure
Known
height
Known dry mass
Known porosity
q =f
Soil Physics 2010
So we know the water’s
potential everywhere
So we know the water’s potential everywhere
L
Atmospheric
pressure (0)
5
Known
height L
0
At saturation:
qf
h=0
Soil Physics 2010
If it can drain out
the bottom, then
q < f, and
mean h = L/2
Then I talked about sponges
Soil Physics 2010