1. Soil Physics 2010 Outline Announcements Where were we? Archimedes Water retention curve

2. Soil Physics 2010 Announcements Reminder: Homework 3 is due February 19 Quiz!

3. Soil Physics 2010 Water characteristic curve Water content Wetness, , etc Suction Potential, h, tension, etc

4. Soil Physics 2010 Darcy’s law 5 cm 2 cm 10 cm 4 cm radius = 4 cm Q = K = A =  h =  L = ? ? 16  cm 2 5 cm 10 cm

5. Soil Physics 2010 Fresh water Salt water Where were we? Osmotic potential drying a soil

6. Negative pressure drying a soil Soil Physics 2010 Drying pressure Tube radius The water left in the soil is at equilibrium with the water in the tube

7. 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 pp Filter passes water but not air (what kind of material does that?)

8. 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h

9. 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

10. Soil Physics 2010 Buoyancy We saw this in deriving Stokes’ Law: At terminal velocity, Force up = Force down (Newton’s 1 st law) Force down: Force = Mass * acceleration = (  s -  w )(4/3  r 3 ) * g (Newton’s 2 nd law)

11. Soil Physics 2010 Density difference Force down: Force = Mass * acceleration = (  s -  w )(4/3  r 3 ) * g Density difference * Volume = Mass Density difference Volume Acceleration Mass / Volume = Density

12. Soil Physics 2010 Archimedes Syracuse, Sicily, 287-212 BCE How much water overflows? density of gold: 19,300 kg m -3 density of silver: 10,500 kg m -3

13. Soil Physics 2010 Archimedes Principle 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 ?

14. 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

15. Soil Physics 2010 Water retention curve Basic idea: As a soil dries, its wetness  is related to the water’s energy level h. Water content Wetness, , etc Suction -potential, h, tension, etc

16. 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!

17. 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.

18. 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.

19. 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? (Poiseuille’s law) (Capillary rise equation)

20. 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

21. 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  = 

22. 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 , and mean h = L/2

23. Soil Physics 2010 Then I talked about sponges