Feeders supply liquid metal to compensate volumetric shrinkage during casting solidification. For this, a feeder has to remain in liquid state longer than the casting and the amount of liquid metal in feeder $($about $15\%$ for uninsulated cylindrical feeders$]$ has to be greater than casting shrinkage volume. The relative solidification time of simple shapes can be compared using the square of their geometric modulus. which is given by the ratio of their volume to cooling surface area. The yleld is given by the ratio of only part weight to full casting weight $($including feeders$).$

$($a$)$ Design a cylindrical feeder for the above casting, with $20\%$ higher modulus $($than the casting$),$ and height$/$diameter ratio of $1\mathrm{.}5.$ Assume feeder bottom is in contact with casting $($hence negligible heat transfer$).$

$[10]$

$($b$)$ Check the shrinkage volume criteria, given the volumetric contraction of the cast metal is $5\%.$ Can this feeder be used to feed another casting? If no$,$ why? If yes, what will be the yield improvement.

$[10]$