Two cubical castings are made of the same material. Side of small casting is 2 cm while that of bigger one is 4 cm. If small casting solidifies in 2 minutes, what will be the solidification time for bigger casting?
[Use Chvorinove's rule]

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This question was previously asked in

BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

Chvorinov's Rule relates solidification time of a casting to its volume and surface area as:

\( t \propto \left( \frac{V}{A} \right)^2 \)

Given:

Small cube side = 2 cm, Large cube side = 4 cm

Time for small cube to solidify = 2 minutes

Calculation:

Volume of cube = L³ , Surface area = 6L²

So, \( \frac{V}{A} = \frac{L^3}{6L^2} = \frac{L}{6} \Rightarrow t \propto L^2 \)

Now, \( \frac{t_b}{t_s} = \left( \frac{L_b}{L_s} \right)^2 = \left( \frac{4}{2} \right)^2 = 4 \Rightarrow t_b = 4 \times 2 = 8 \, \text{minutes} \)