Transcript Lecture 19 Material Handling

Materials Handling
Chapter 9 Page 239 – 256
Friction of Solids and Flow of Granular Solids
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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.
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Lecture 11 – Friction and Flow
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original Coulomb’s law:
Ft  Fn
Ft =force acting in opposite direction of relative motion
Fn =normal force exerted on the object
 = static or dynamic coefficient of friction
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proportional to normal force (load)
independent of area of sliding surfaces
Independent of velocity
Depends on materials in contact
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Lecture 11 – Friction and Flow
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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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Lecture 11 – Friction and Flow
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Look at examples in Figure 9.1 (slip-stick
motion)
Tables 9.1 and 9.2.
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Lecture 11 – Friction and Flow
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Resistance to motion is quantified by…
– angle of internal friction Φi, or
– coefficient of internal friction μi
– μi = tan Φi
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Lecture 11 – Friction and Flow
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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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Lecture 11 – Friction and Flow
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Filling or emptying angle of repose
Empting > Filling
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Lecture 11 – Friction and Flow
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Flow Patterns: Fig. 9.3
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Funnel Flow
Mass Flow
Expanded Flow
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Lecture 11 – Friction and Flow
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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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Lecture 11 – Friction and Flow
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Example: Estimate the lateral and vertical forces
at the bottom of the wall of the following bin…
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Bin diameter = 17 m
Fill depth = 40 m
Material = wheat at 17%mc
Concrete bin (wood float finish)
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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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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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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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