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