Question

A casting of size 100 × 100 × 100 mm³ solidifies in 20 minutes. Find out the solidification time for casting of size 100 × 100 × 50 mm³ under same condition.
1. 16.3 minutes
2. 14.3 minutes
3. 12.3 minutes
4. 11.3 minutes

Answer 1

Correct Answer - Option 4 : 11.3 minutes

Concept:

Solidification time

\({t_s} = K \times {\left( {\frac{V}{{SA}}} \right)^2}\)

where, V = volume of casting, SA = surface area of casting, K = solidification factor

• Volume represents the amount of heat content
• The surface area represents the amount of heat transfer

Calculation:

Given:

Casting 1

Length = 200 mm, Breadth = 200 mm, Height = 70 mm

Solidification time (ts) for casting 1 = 10 min

\(20 = K \times {\left( {\frac{{100 \times 100 \times 100}}{{2 \times \left( {10000 + 10000 + 10000} \right)}}} \right)^2} \Rightarrow K = 0.072\)

Casting 2

Length = 100 mm, Breadth = 100 mm, Height = 50 mm

Solidification time (ts) for casting 2 

\({t_s} = 0.072\; \times {\left( {\frac{{100 \times 100 \times 50}}{{2 \times \left( {10000 + 5000 + 5000} \right)}}} \right)^2} = 11.25\;min\)