Question

A casting size 400 mm × 200 mm × 140 mm solidifies in 20 min the solidification time for a casting 400 mm × 200 mm × 35 mm under similar conditions is

• A. 3.3 min
• B. 2 min
• C. 4 min
• D. 8.1 min

Answer 1

The correct option is A 3.3 min

$\text{Solidification time}{T}_1\text{for casting -1 is}k{\left(\frac{V}{A}\right)}_1^2$

$T_1=k{\left(\frac{400\times 200\times 140}{2(400\times 200+400\times 140+200\times 140)}\right)}^2$

$\text{= 1165.97 k}$

$\text{Similarly for casting 2, we have}$

$T_2=k{\left(\frac{400\times 200\times 35}{2(400\times 200+200\times 35+35+400)}\right)}^2$

$\frac{T_1}{T_2}=\frac{1165.97k}{192.13k}$

$\text{But given,}{T}_1=20min$

$\text{So, we get}$

$T_2=\frac{20\times 192.13}{1165.97}=3.29min\approx 3.3min$