Lecture 14 Announcements HW#11 Due Monday 2/26 Monday’s lecture by Dr. Brusewitz (movie about processing in the cotton industry) HW#12 Due Monday 3/5 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Electromagnetic properties (cont) 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 original Coulombs laws: proportional to normal force (load) independent of area of sliding surfaces Independent of velocity Depends on materials in contact 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Sherwood’s concepts of friction: FF is force acting in a plane containing the contact point or points and in such a manner as to resist relative motion FF is composed of 2 components…a force to deform or shear the asperities and a force req’d to overcome adhesion or cohesion between the surfaces FF is directly proportional to actual contact area FF depends on velocity to the degree of temperature change FF depends on nature of matl’s in contact FF is independent of surface roughness, except for extremes 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 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 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Tribology: the study of friction and interaction between solids with relative motion between 2 surfaces in contact with each other. Look at examples in Tables 9.1 and 9.2. Notice how moisture content changes friction coeff. 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 angle of repose: The angle that a material makes with the horizontal when dropped into a bin or allowed to form a pile. 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Filling or emptying angle of repose 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Resistance to motion is quantified by… angle of internal friction Φi, or coefficient of internal friction μi μi = tan Φi 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Predicting lateral forces on bins: For shallow bins (D>H) use Rankine equation For deep bins (H>>>D) use Janssen equation 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

Friction and Flow of Granular Solids, pg. 239 - 255 Example: Estimate the lateral and vertical foces at the bottom of the wall of the following bin… Bin diameter = 17m Fill depth = 40 m Material = wheat at 17%mc Concrete bin 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials Assignment HW11 Problem1: If the bin of wheat in in the previous example slide 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. 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials Assignment HW11 Problem 2: The Omega Coop’s concrete silo is 110 ft. tall with an ID of 28 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 98 ft. Part b: Calculate the total vertical force at ground level 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials Assignment HW11 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? 9/22/2018 BAE2022/BAE4400 Physical Properties of Biological Materials