GATE 2021 ME (ME2) – Question 47

Casting, Forming and Joining Processes · Casting: patterns, moulds, cores, solidification, riser and gating design, defects · 2 marks · Numerical answer

A cast product of a particular material has dimensions 75 mm × 125 mm × 20 mm. The total solidification time for the cast product is found to be 2.0 minutes as calculated using Chvorinov’s rule having the index, $n=2$. If under the identical casting conditions, the cast product shape is changed to a cylinder having diameter = 50 mm and height = 50 mm, the total solidification time will be _____ minutes (round off to two decimal places).

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Correct answer: 2.82 to 2.84

Explanation

For the block, V=187500 mm³ and A=2(75×125+125×20+75×20)=26750 mm², so V/A=7.00935 mm.

For the cylinder, $V/A=dh/[4h+2d]=50/6=8.33333$ mm. Since t∝(V/A)², new time is $2(8.33333/7.00935)^2=\mathbf{2.83}$ min.