Soil Physics 2010

1. Outline • Announcements • Where were we? • Capillary II Soil Physics 2010

2. Announcements • Exams & grades • Exam answers posted (2/3) • Homework 3 is due February 19. Soil Physics 2010

3. Where were we? Given this system, with steady-state water flow, what are the values of the head components at each point? • Atmospheric pressure at free water surfaces A 5 cm B • Elevations easy to read, • Reference elevation is arbitrary 25 cm 50 cm • No resistance in tubes • → same total potential everywhere within a tube C F 5 cm 20 cm • Elevation + Pressure = Total Potential D 10 cm E • Potential gradient is linear in uniform soil, steady-state flow Soil Physics 2010

4. Solving the artificial systems • Atmospheric pressure at free water surfaces A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

5. Solving the artificial systems • Elevations easy to read • Reference elevation is arbitrary A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

6. Solving the artificial systems • No (negligible) resistance in a big tube • → same total potential everywhere within a tube A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

7. Solving the artificial systems • Pressure + Elevation = Total Potential A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

8. Solving the artificial systems • Potential gradient is linear in uniform soil, steady-state flow A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

9. Solving the artificial systems • Pressure + Elevation = Total Potential A 5 cm B 25 cm 50 cm C F 5 cm 20 cm D 10 cm E Soil Physics 2010

10. Capillary 2 We know 2 things about tubes: (Capillary rise equation) Q discharge r radius h viscosity Dp pressure drop L length (Poiseuille’s law) Soil Physics 2010

11. Capillary 2 We know 2 things about tubes: (Capillary rise equation) We also know that height can be treated as a pressure (and vice versa) (Poiseuille’s law) Soil Physics 2010

12. Capillary 2 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

13. 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 (rw - ra) g h is a pressure Capillary pressure Soil Physics 2010

14. 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

15. Negative pressure? Think back to kinds of stress: • Compressive s • Tensile s This water is under tension: Negative pressure Soil Physics 2010

16. 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) Radii of curvature of the meniscus Soil Physics 2010

17. Meniscus curvature 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

18. 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

19. 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

20. Osmotic potential drying a soil Fresh water Salt water Soil Physics 2010

21. 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

22. 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

23. 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

24. 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