A cylindrical magnet is to be made from Alnico (an iron-aluminium-nickel-cobalt alloy) by powder compaction and sintering. The aspect ratio of the cylinder, \(h / 2 r\), is 2. The coefficient of friction \(\mu\) of the powder with the die wall, if unlubricated, is 0.5 . By what factor will the compaction pressure have fallen at the mid plane of the cylinder because of die wall friction? If, instead, a lubricant is mixed with the powder (it will burn out during sintering), which reduces the coefficient of friction to 0.05 , by how much will the compaction pressure have fallen at the mid plane?