Alloy parts were cast with a sand mold that took 160 secs for a cube-shaped casting to solidify. The cube was 50 mm on a side. (a) Determine the value of the Chvorinov's mold constant. (b) If the same alloy and mold type were used, find the total solidification time for a cylindrical casting in which the diameter = 25 mm and length = 50 mm.

a) k = 6.4 s/cm²

b) Te = 160 s

Explanation:

a) Given

Solidification time in s: Te = 160 s

L = 50 mm = 5 cm

We use the formula

Te = k*(V/A)ⁿ  

k = Te*(A/V)ⁿ

where

k is the Chvorinov's mold constant

V is casting volume in cm³ = V = L³ = (5 cm)³ = 125 cm³

A is the surface area of the casting in cm² = A = L² = (5 cm)² = 25 cm²

n = 2 (assumed)

⇒  k = 160 s*(25 cm²/125 cm³)²

⇒  k = 6.4 s/cm²

b) Given

D = 25 mm = 2.5 cm  ⇒  R = D/2 = 2.5 cm/2 = 1.25 cm

h = 50 mm = 5 cm

k = 6.4 s/cm²

n = 2

We find the volume as follows

V = π*R²*h ⇒   V = π*(1.25 cm)²*(5 cm) = 24.5436 cm³

and the surface area

A = π*R² = π*(1.25 cm)² = 4.9087 cm²

We apply the equation

Te = k*(V/A)ⁿ  

⇒  Te = (6.4 s/cm²)*(24.5436 cm³/4.9087 cm²)²

⇒  Te = 160 s

more information

explanation:

the equation above shows how temperature f, measured in degrees fahrenheit, relates to a temperature c, measured in degrees celsius. based on the equation, which of the following must be true?

a temperature increase of 1 degree fahrenheit is equivalent to a temperature increase of

5

9

degree celsius.

a temperature increase of 1 degree celsius is equivalent to a temperature increase of 1.8 degrees fahrenheit.

a temperature increase of

5

9

degree fahrenheit is equivalent to a temperature increase of 1 degree celsius.

a) i only

b) ii only

c) iii only

d) i and ii only