1. 10/6/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 1 Chapter 9 Page 239 – 256 Friction of Solids and Flow of Granular Solids Materials Handling

2. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 2 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

3. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 3 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

4. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 4 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

5. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 5 Look at examples in Figure 9.1 (slip-stick motion) Tables 9.1 and 9.2. Lecture 11 – Friction and Flow

6. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 6 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

7. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 7 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

8. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 8 Filling or emptying angle of repose Empting > Filling Lecture 11 – Friction and Flow

9. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 9 Flow Patterns: Fig. 9.3 Funnel Flow Mass Flow Expanded Flow Lecture 11 – Friction and Flow

10. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 10 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

11. 10/6/2015BAE2022/BAE4400 Physical Properties of Biological Materials 11 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

12. 10/6/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 12 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.

13. 10/6/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 13 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

14. 10/6/2015BAE2023 Physical Properties of Biological Materials Fricton and Flow 14 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?