particle technology lecture ## - bangladesh …teacher.buet.ac.bd/tanvir/particle1.pdf · angle of...
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PARTICLE TECHNOLOGYLecture ##
K. M. Tanvir Ahmmed
Lecturer, ChE, BUET
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Angle of Repose, αr
• When bulk granular materials are poured onto a horizontal surface, a conical pile will form
• The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose
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Angle of Repose
• Lower the angle of repose, the more free flowing is the material
– Very free flowing granules: 25° < β < 30°
– Free-flowing granules: 30° < β < 38°
– Fair to passable flow of powders: 38° < β < 45°
– Cohesive solids: 45° < β < 55°
– Very cohesive solids: 55° < β < 70°
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Angle of Repose
• Angle of repose is sensitive to the condition of the supporting surface - the smoother the surface the smaller the angle
• Angle of repose is also sensitive to moisture -it tends to increase the angle of repose
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Angle of Repose
• Used in the design of equipment for the processing of particulate solids
– may be used to design an appropriate hopper or silo to store the material
– It can also be used to size a conveyor belt for transporting the material
– It can also be used in determining whether or not a slope will likely collapse
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Angle of Repose
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Angle of Repose
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Angle of Internal Friction, αm
• The angle of internal friction is the ability of particles to withstand a shear stress
• Defined as the equilibrium angle between flowing particles and stationary solids in a bin
• The tangent of this angle is the coefficient of friction, μ’
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Angle of Repose & Internal Friction
• If the mass are truly homogeneous both angles are equal
• In practice, the angle of repose is smaller than the angle of internal friction
-Moisture content
-Degree of Packing
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Pressures in Masses of Particles
• The minimum pressure in a solid mass in the direction normal to that of the applied pressure
• Ratio of the normal pressure to the applied pressure is a constant K´
• K´ depends on
-Shape and interlocking tendencies of the particles
-Stickiness of the grain surfaces
-Degree of packing of the material
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Storage of Solids
• Open storage areas are used for the high range because of their lower cost
• In low- and medium-capacity ranges partially or totally enclosed storage is used
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Bulk Storage - Stockpiles
• Stacked on a concrete or earthen pad
• May be covered by a roof structure or left uncovered
• Formed using various overhead conveyors
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Silo!
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Bin Storage
• Cylindrical or rectangular vessels of concrete or metal
• Silo is tall and relatively small in diameter
• Bin is not so tall and usually fairly wide
• Hopper is small bin with a slopping bottom
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Pressures in Circular Bin
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Janssen's Equations for Bins
• One cannot solve Eq. ## directly since it contains two unknowns, the average vertical Pv and the average tangential stress PL. To obtain a solution, additional information is required as a correlation between the two stresses. Janssen proposed such a correlation in the form
• PL / Pv = K’ ----------1
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Janssen's Equations for Bins
• where K’ is the so-called Janssen constant. Eq. (1) implies a constant relationship between the two average stresses, independent of the geometry of the slice and, while there is no physical reason that such a relationship should hold, it was found in practice that for routine industrial calculations the results are reasonably accurate.
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Janssen's Equations for Bins
• At very small distances, close to the upper surface of the bin, one can expand the exponential function
• It yields the vertical stress Pb = ZT (g/gc)ρb. This is exactly the stress encountered in a static fluid of constant density as one moves down from its surface and is the so-called hydrostatic pressure.
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Pressures in fluids and stresses in bulk solids (in principle)
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Mass Flow & Tunnel Flow
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Mass Flow
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Core Flow/Tunnel Flow
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ADIOS
• N. B. Most of the pictures are taken from English Wikipedia. This document is prepared for educational purposes only.
• For first section of this presentation the author is expressing his indebtedness to Ashfaq M. Ansery.