Project ForgeFor sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov's law for the estimation of total solidification time, the exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places).
Explanation
For the casting: V=80×120×20=192,000 mm³, A=2(80×120+80×20+120×20)=27,200 mm², V/A≈7.059 mm. From t=C(V/A)² with t=2 min: C=2/7.059²≈0.04014 min/mm². For the cylindrical riser (H=D): V=(π/4)D³, A=(π/2)D²+πD²=(3π/2)D² (top, bottom, and lateral surface), so V/A=(π/4)D³/[(3π/2)D²]=D/6. With t=3 min: 3=0.04014×(D/6)² → D²≈3×36/0.04014≈2690 → D≈51.87 mm.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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