Question

A 75-mm thick square plate and a right circular cylinder with a radius of 100 mm and height of 50 mm each have the same volume. if each is to be cast using a cylindrical riser, which part will take longer time to solidify and require a larger riser to ensure proper feeding of the molten metal?

Answer 1

we know,
time taken for solidification = C(volume/area)
where C is constant .

for cylinder :
volume of cylinder = π r²h
r = 100mm = 0.1 m
h = 50mm = 0.05m
volume of cylinder = π(0.1)²×0.05 =0.00157m³
total surface area of cylinder = 2πr² + 2πrl
= 2π(0.1)² + 2π(0.1)(0.05) = 0.0942 m²
so, time taken for the cylinder = C(Volume/area)
= C(0.00157/0.0942) = (2.78 × 10^-4)C

for square plate ,
h= 75 mm = 0.075m
l = b = x
volume of plate = volume of cylinder
0.075 × x² = 0.00157 m³
x = 0.144m
hence, l = b = 0.144m
volume of square plate = 0.0157 m³ [A/C to question]
total surface area = 2(lb + bh + hl)
= 2(0.144)² + 4(0.144)(0.075)
= 0.0847 m³
so, time taken for square plate = C(volume/area)
= C(0.00157/0.0847) = (3.43 × 10^-4)C

here it is clear that time taken for square plate is larger than cylinder . hence , it will require a larger riser , and the riser will be different sizes.