MECHANICS QUESTION


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“Pattern”- making, allowances and its types

“Pattern”- making, allowances and its types: Pattern: A pattern may be defined as a model of desired casting which when moulded in sand forms an impression called mould. The mould when filled with the molten metal forms casting after solidification of the poured metal. The quality and accuracy of casting depends upon the pattern making. The pattern may be made of wood, metal(cast iron, brass, aluminium and alloy steel.), plaster, plastics and wax. Pattern Allowances: A pattern is always made larger than the required size of the casting considering the various allowances. These are the allowances which are usually provided in a pattern. 1: shrinkage or contraction allowance: The various metals used for casting contract after solidification in the mould. Since the contraction is different for different materials, therefore it will also differ with the form or type of metal. 2: Draft allowance It is a taper which is given to all the vertical walls of the pattern for eas
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Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the SC, BCC, FCC, Diamond and Hexagonal structures. Which structure most efficiently fills space?

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Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the SC, BCC, FCC, Diamond and Hexagonal structures.  Which structure most efficiently fills space?  SC :  It is easy to determine that there is 1 lattice point per unit cell.  The maximum radius that a hard sphere can have is  , where  a  is the lattice constant.  When the radius is this value, then the spheres on the corners of the unit cell just touch each other.  Hence the packing fraction is: B.C.C :  It is easy to determine that there is 2 lattice points per unit cell.  The maximum radius that a hard sphere can have is  , where  a  is the lattice constant.  When the radius is this value, then the spheres on the corners of the unit cell just touch the body-centered sphere.  Hence the packing fraction is: F.C.C :  It is easy to determine that there is 4 lattice points per unit cell.  The maximum radius that a hard sphere can have is  , where  a  is the lattice
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