GATE 2018 ME (ME2) – Question 60
A solid cylindrical riser with height equal to diameter is required for sand casting an 80 mm × 120 mm × 20 mm rectangular plate. Casting solidification time is 2 min. Chvorinov’s exponent is 2. For a riser solidification time of 3 min, find its diameter (mm), to two decimal places.
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Correct answer: 42.00 to 52.00
Explanation
Casting volume is $80(120)(20)=192000$ mm³. Surface area is $2(80\times120+80\times20+120\times20)=27200$ mm², so modulus is 7.05882 mm. Chvorinov’s law gives riser modulus $\sqrt{3/2}(7.05882)=8.64526$ mm. For a cylinder of height D counting all surfaces, $V/A=D/6$, giving **D = 51.87 mm**. Excluding its attached base gives $V/A=D/5$ and D = 43.23 mm. Both cooling-area conventions fall within the official 42–52 mm interval.