Soil Physics 2010

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

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

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

4. Darcy’s law 5 cm 2 cm radius = 4 cm 10 cm 4 cm Q = K = A = Dh = DL = ? ? 16p cm2 5 cm 10 cm Soil Physics 2010

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

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

7. Positive pressure drying a soil The water left in the soil is at equilibrium with the pressure difference between the chamber and the outside Drying pressure Filter passes water but not air (what kind of material does that?) Dp Soil Physics 2010

8. Elevation drying a soil Dh 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

9. 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

10. Buoyancy We saw this in deriving Stokes’ Law: At terminal velocity, Force up = Force down (Newton’s 1st law) Force down: Force = Mass * acceleration = (rs-rw)(4/3 p r3) * g (Newton’s 2nd law) Soil Physics 2010

11. Density difference Acceleration Density difference Volume Force down: Force = Mass * acceleration = (rs-rw)(4/3 p r3) * g Density difference * Volume = Mass Mass / Volume = Density Soil Physics 2010

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

13. 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

14. 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

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

16. 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

17. 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

18. 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

19. 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. (Capillary rise equation) (Poiseuille’s law) Soil Physics 2010

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: Atmospheric pressure Known height Known dry mass Known porosity q = f So we know the water’s potential everywhere Soil Physics 2010

22. So we know the water’s potential everywhere L (0) 0 Atmospheric pressure 5 Known height L If it can drain out the bottom, then q < f, and mean h = L/2 At saturation: q = f h = 0 Soil Physics 2010

23. Then I talked about sponges Soil Physics 2010