1. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 1 Lecture 11 Test next Wednesday (2/24): covers material through Friday Lab this Wednesday: tension and compression

2. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 2 Lecture 11 - Rheology

3. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 3 Chapter 9 Page 239 – 256 Friction of Solids and Flow of Granular Solids Lecture 11 – Friction and Flow

4. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 4 Tribology: the study of friction and interaction between solids with relative motion between 2 surfaces in contact with each other. Lecture 11 – Friction and Flow

5. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 5 original Coulomb’s law: –proportional to normal force (load) –independent of area of sliding surfaces –Independent of velocity –Depends on materials in contact Lecture 11 – Friction and Flow

6. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 6 μ s =static coeff. of friction…predicts force at the point in time when motion is initiated μ d =dynamic coeff. of friction…predicts force required to maintain motion once it is initiated. μ d ≤μ s, these coeff. are dependent on the characteristics of the material Lecture 11 – Friction and Flow

7. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 7 Look at examples in Figure 9.1 (slip-stick motion) Tables 9.1 and 9.2. Lecture 11 – Friction and Flow

8. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 8 angle of repose: –The angle that a material makes with the horizontal when dropped into a bin or allowed to form a pile. Lecture 11 – Friction and Flow

9. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 9 Filling or emptying angle of repose Empting > Filling Lecture 11 – Friction and Flow

10. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 10 Resistance to motion is quantified by… –angle of internal friction Φ i, or –coefficient of internal friction μ i –μ i = tan Φ i Lecture 11 – Friction and Flow

11. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 11 Flow Patterns: Fig. 9.3 Funnel Flow Mass Flow Expanded Flow Lecture 11 – Friction and Flow

12. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 12 Predicting lateral forces on bins: –For shallow bins (D>H) use Rankine equation –For deep bins (H>>>D) use Janssen equation Lecture 11 – Friction and Flow

13. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 13 Example: Estimate the lateral and vertical forces at the bottom of the wall of the following bin… –Bin diameter = 17 m –Fill depth = 40 m –Material = wheat at 17%mc –Concrete bin (wood float finish) Lecture 11 – Friction and Flow

14. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 14 Will work in class on Wednesday Problem1: If the bin of wheat in in the previous example is dried to 9% mc, calculate the increase or decrease in lateral pressure at the base of the bin. You will need to calculate the density using the appropriate formula from Chpt. 2, pg 25). Assume the depth will remain the same after drying. Indicate whether the pressure will increase or decrease.

15. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 15 Problem 2: The Omega Coop’s concrete silo is 90 ft. tall with an ID of 25 ft. (convert units!!!) Part a: Plot the horizontal pressure on the bin walls as a function of height from the ground surface. Assume the bottom of the bin is at the ground surface, the grain is 11.0% mc wheat and the bin is filled to 81 ft. Part b: Calculate the total vertical force at ground level Will work in class on Wednesday

16. 10/15/2015BAE2022/BAE4400 Physical Properties of Biological Materials 16 Problem 3: An elevator manager would like you design a concrete silo with a self-cleaning hopper bottom. The silo is located in Northwest Oklahoma. What is the angle of the hopper relative to a horizontal plane, what is the depth to the bottom of the hopper relative to ground level? What assumptions, if any, did you make? Will work in class on Wednesday

17. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 17 original Coulomb’s law: –proportional to normal force (load) –independent of area of sliding surfaces –Independent of velocity –Depends on materials in contact Lecture 11 – Friction and Flow

18. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 18 Tribology: the study of friction and interaction between solids with relative motion between 2 surfaces in contact with each other. Lecture 11 – Friction and Flow

19. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 19 μ s =static coeff. of friction…predicts force at the point in time when motion is initiated μ d =dynamic coeff. of friction…predicts force required to maintain motion once it is initiated. μ d <μ s, these coeff. are dependent on the characteristics of the material Lecture 11 – Friction and Flow

20. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 20 Look at examples in Figure 9.1 (slip-stick motion) Tables 9.1 and 9.2. Lecture 11 – Friction and Flow

21. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 21 angle of repose: –The angle that a material makes with the horizontal when dropped into a bin or allowed to form a pile. Lecture 11 – Friction and Flow

22. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 22 Filling or emptying angle of repose Lecture 11 – Friction and Flow

23. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 23 Resistance to motion is quantified by… –angle of internal friction Φ i, or –coefficient of internal friction μ i –μ i = tan Φ i Lecture 11 – Friction and Flow

24. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 24 Predicting lateral forces on bins: –For shallow bins (D>H) use Rankine equation –For deep bins (H>>>D) use Janssen equation Lecture 11 – Friction and Flow

25. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 25 Example: Estimate the lateral and vertical forces at the bottom of the wall of the following bin… –Bin diameter = 17 m –Fill depth = 40 m –Material = wheat at 17%mc –Concrete bin (wood float finish) Lecture 11 – Friction and Flow

26. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 26 Will work in class on Wednesday Problem1: If the bin of wheat in in the previous example is dried to 11% mc, calculate the increase or decrease in lateral pressure at the base of the bin. You will need to calculate the density using the appropriate formula from Chpt. 2, pg 25). Assume the depth will remain the same after drying. Indicate whether the pressure will increase or decrease.

27. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 27 Problem 2: The Loyal Coop’s concrete silo is 120 ft. tall with an ID of 20 ft. (convert units!!!) Part a: Plot the horizontal pressure on the bin walls as a function of height from the ground surface. Assume the bottom of the bin is at the ground surface, the grain is 12.0% mc wheat and the bin is filled to 100 ft. Part b: Calculate the total vertical force at ground level Will work in class on Wednesday

28. 10/15/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 28 Problem 3: An elevator manager would like you design a concrete silo with a self-cleaning hopper bottom. The silo is located in Northwest Oklahoma. What is the angle of the hopper relative to a horizontal plane, what is the depth to the bottom of the hopper relative to ground level? What assumptions, if any, did you make? Will work in class on Wednesday