Question

Total solidification times of three casting geometries are to be compared: (1) a sphere with diameter = 10 cm, (2) a cylinder with diameter and length both = 10 cm, and (3) a cube with each side = 10 cm. The same casting alloy is used in all three cases. (a) Determine the relative solidification times for each geometry. (b) Based on the results of part (a), which geometric element would make the best riser? (c) If the mold constant = 3.5 min/cm2 in Chvorinov’s rule, compute the total solidification time for each casting.

Answer 1

Answer:

a) See Below

b) See Below

c) See Below

Step-by-step explanation:

The relative solidification time is given by formula  $t_s=C_m(\frac{V}{A})^2$

Where C_m is the Chvorinov's constant given as 3.5

V is Volume

A is Surface Area

a)

Sphere:

Volume = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3 = 523.6$

Surface Area = $4\pi r^2=4\pi (5)^2 = 314.16$

Now putting in the formula:

Relative Solidification Time of Sphere = $t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{523.6}{314.16})^2\\t_s=9.72$ minutes

Relatively, We can say t_s = 2.778 * C_m

Cube:

Volume = 10^3 = 1000

Surface Area = 6x^2 = 6(10)^2 = 600

Relative Solidification Time of Cube = $t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{1000}{600})^2\\t_s=9.72$  minutes

Relatively, We can say t_s = 2.778 * C_m

Cylinder:

Volume = $\pi r^2 h = \pi (5)^2 (10)=785.4$

Surface Area = $2\pi r^2 + 2\pi r h=471.24$

Relative Solidification Time of Cylinder = $t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{785.4}{471.24})^2\\t_s=9.72$

Relatively, We can say t_s = 2.778 * C_m

b)

All of them have same relative solidification time. So we can say that all 3 of them are good for making risers.

c)

Since, we had

Relatively, We can say t_s = 2.778 * C_m

we get:

t_s = 2.778 * C_m = 2.778 * 3.5 = 9.72 minutes