1. Lecture 12 – 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

2. Lecture 12 – 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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BAE2023 Physical Properties of Biological Materials Fricton and Flow

3. Lecture 12 – Friction and Flow
Tribology: the study of friction and interaction between solids with relative motion between 2 surfaces in contact with each other.
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

4. Lecture 12 – 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
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

5. Look at examples in Figure 9.1 (slip-stick motion) Tables 9.1 and 9.2.
Lecture 12 – Friction and Flow
Look at examples in Figure 9.1 (slip-stick motion)
Tables 9.1 and 9.2.
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

6. Lecture 12 – 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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BAE2023 Physical Properties of Biological Materials Fricton and Flow

7. Filling or emptying angle of repose
Lecture 12 – Friction and Flow
Filling or emptying angle of repose
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

8. Lecture 12 – 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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BAE2023 Physical Properties of Biological Materials Fricton and Flow

9. Lecture 12 – Friction and Flow
Predicting lateral forces on bins:
For shallow bins (D>H) use Rankine equation
For deep bins (H>>>D) use Janssen equation
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

10. Lecture 12 – 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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BAE2023 Physical Properties of Biological Materials Fricton and Flow

11. BAE2023 Physical Properties of Biological Materials Fricton and Flow
Assignment HW6 Due 2/18
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.
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

12. BAE2023 Physical Properties of Biological Materials Fricton and Flow
Assignment HW6
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
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BAE2023 Physical Properties of Biological Materials Fricton and Flow

13. BAE2023 Physical Properties of Biological Materials Fricton and Flow
Assignment HW6
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?
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BAE2023 Physical Properties of Biological Materials Fricton and Flow