1. BAE2022/BAE4400 Physical Properties of Biological Materials
Lecture 11
Test next Wednesday (2/24): covers material through Friday
Lab this Wednesday: tension and compression
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

2. BAE2022/BAE4400 Physical Properties of Biological Materials
Lecture 11 - Rheology
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

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

4. Lecture 11 – Friction and Flow
Tribology: the study of friction and interaction between solids with relative motion between 2 surfaces in contact with each other.
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

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

6. Lecture 11 – Friction and Flow
μs=static coeff. of friction…predicts force at the point in time when motion is initiated
μd=dynamic coeff. of friction…predicts force required to maintain motion once it is initiated.
μd≤μs, these coeff. are dependent on the characteristics of the material
4/3/2019
BAE2022/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
Look at examples in Figure 9.1 (slip-stick motion)
Tables 9.1 and 9.2.
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

8. Lecture 11 – Friction and Flow
Resistance to motion is quantified by…
angle of internal friction Φi, or
coefficient of internal friction μi
μi = tan Φi
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BAE2022/BAE4400 Physical Properties of Biological Materials

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

10. Filling or emptying angle of repose Empting > Filling
Lecture 11 – Friction and Flow
Filling or emptying angle of repose
Empting > Filling
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

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

12. Lecture 11 – Friction and Flow
Predicting lateral forces on bins:
For shallow bins (D>H) use Rankine equation
For deep bins (H>>>D) use Janssen equation
4/3/2019
BAE2022/BAE4400 Physical Properties of Biological Materials

13. Lecture 11 – Friction and Flow
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)
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BAE2022/BAE4400 Physical Properties of Biological Materials

14. BAE2023 Physical Properties of Biological Materials Fricton and Flow
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.
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

15. BAE2023 Physical Properties of Biological Materials Fricton and Flow
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
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

16. BAE2023 Physical Properties of Biological Materials Fricton and Flow
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?
4/3/2019
BAE2023 Physical Properties of Biological Materials Fricton and Flow