Outline
• Announcements
• Where were we?
• Capillary II
Soil Physics 2010
Announcements
• Exams & grades
• Exam answers posted (2/3)
• Homework 3 is due February 19.
Soil Physics 2010
Where were we?
Given this system, with steady-state water flow,
what are the values of the head components at each point?
5 cm
• Atmospheric pressure
at free water surfaces
A
B
25 cm
50 cm
C
F
5 cm
• Elevations easy to read,
• Reference elevation is
arbitrary
• No resistance in tubes
→ same total potential
everywhere within a tube
20 cm
D
10 cm
Soil Physics 2010
E
• Elevation + Pressure =
Total Potential
• Potential gradient is
linear in uniform soil,
steady-state flow
Solving the artificial systems
• Atmospheric pressure at free water surfaces
5 cm
A
B
Pressure
25 cm
50 cm
C
F
10 cm
Soil Physics 2010
0
B
5 cm
20 cm
D
A
C
D
E
E
F
0
Elevation
Total
Potential
Solving the artificial systems
• Elevations easy to read
• Reference elevation is arbitrary
5 cm
A
B
25 cm
50 cm
C
F
5 cm
20 cm
D
10 cm
Soil Physics 2010
E
A
Pressure
Elevation
0
30
B
25
C
0
D
-25
E
-35
F
0
0
Total
Potential
Solving the artificial systems
• No (negligible) resistance in a big tube
→ same total potential everywhere within a tube
5 cm
A
B
Pressure
Elevation
Total
Potential
0
30
30
B
25
30
5 cm
C
0
20 cm
D
-25
0
E
-35
0
0
0
25 cm
50 cm
C
F
D
10 cm
Soil Physics 2010
E
A
F
0
Solving the artificial systems
• Pressure + Elevation = Total Potential
5 cm
A
25 cm
50 cm
Pressure
Elevation
Total
Potential
A
0
30
30
B
5
25
30
B
C
F
D
10 cm
Soil Physics 2010
E
5 cm
C
20 cm
D
25
-25
0
E
35
-35
0
F
0
0
0
0
Solving the artificial systems
• Potential gradient is linear in uniform soil,
steady-state flow
5 cm
A
B
25 cm
50 cm
C
F
5 cm
20 cm
D
10 cm
Soil Physics 2010
E
Pressure
Elevation
Total
Potential
A
0
30
30
B
5
25
30
0
15
C
D
25
-25
0
E
35
-35
0
F
0
0
0
Solving the artificial systems
• Pressure + Elevation = Total Potential
5 cm
A
B
25 cm
50 cm
C
F
5 cm
20 cm
D
10 cm
Soil Physics 2010
E
Pressure
Elevation
Total
Potential
A
0
30
30
B
5
25
30
C
15
0
15
D
25
-25
0
E
35
-35
0
F
0
0
0
Capillary 2
We know 2 things about tubes:
2 cos
h
 w  a  g r
(Capillary rise equation)
 r Dp
Q
8h L
4
(Poiseuille’s law)
Soil Physics 2010
Q discharge
r radius
h viscosity
Dp pressure drop
L length
Capillary 2
We know 2 things about tubes:
2 cos
h
 w  a  g r
(Capillary rise equation)
We also know that height
can be treated as a pressure
(and vice versa)
 r Dp
Q
8h L
4
(Poiseuille’s law)
Soil Physics 2010
Capillary 2
2 cos
h
 w  a  g r
 r Dp
Q
8h L
Now we examine this
height and pressure stuff
in more detail
(but not for flow – we’ll do that
in a week or 2)
Soil Physics 2010
4
Capillary pressure
Recall that force = mass * acceleration:
1 N = 1 kg * 1 m s-2 (Newton’s 2nd law)
Also, pressure is a force per unit area:
Pa, or N m-2
So (w - a) g h is a pressure
kg m
kg
m
3 2
2
m s
ms
Capillary
pressure
Soil Physics 2010
2 cos 
 w   a  g h 
r
Where is this pressure?
Water in the capillary tube system
is at equilibrium, so it has the
same potential everywhere
Pressure + Elevation = Total Potential
So if this water is higher
(elevation), it must have
lower pressure
Specifically, it must have
negative pressure.
Soil Physics 2010
Negative pressure?
Think back to kinds of stress:
• Compressive s
• Tensile
s
This water is
under tension:
Negative pressure
Soil Physics 2010
Meniscus curvature
The meniscus curves toward the
lower pressure – because the
higher pressure is pushing it.
There is a pressure jump across
the meniscus (no distance at all)
1 1 
 w   a  g h  Dpc     
 r1 r2 
Soil Physics 2010
Radii of curvature
of the meniscus
Meniscus curvature
1 1 
 w   a  g h  Dpc     
 r1 r2 
This is the Young-Laplace equation,
of which the capillary rise equation is a
special case
In a system at equilibrium, at a given elevation,
all menisci have the same curvature (1/r1 + 1/r2)
Soil Physics 2010
Water & Energy
We have seen several ways that water
can differ in energy:
Height or elevation
Osmotic
Positive pressure
Negative pressure
Temperature
Soil Physics 2010
Water & Energy in the soil
What does it take to dry a wet soil?
Height or elevation
Osmotic
Positive pressure
Negative pressure
Temperature
Soil Physics 2010
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
Dp
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
Dh
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