Final answer:
To determine the value of the mold constant in Chvorinov's rule, we can use the formula t = k * V/A^(n-1), where t is the solidification time, k is the mold constant, V is the volume of the casting, A is the total surface area of the casting, and n is a constant that depends on the shape of the casting. To find the total solidification time for a cylindrical casting, we can use Chvorinov's rule and the mold constant determined in part (a)
Step-by-step explanation:
(a) Mold Constant:
To determine the value of the mold constant in Chvorinov's rule, we can use the formula:
t = k * V/A^(n-1)
where:
- t is the solidification time
- k is the mold constant
- V is the volume of the casting
- A is the total surface area of the casting
- n is a constant that depends on the shape of the casting
Given that the casting is a cube with a side length of 45 mm, we can calculate the volume (V) and surface area (A) as follows:
V = (45 mm)^3 = 91,125 mm^3
A = 6 * (45 mm)^2 = 12,150 mm^2
Substituting these values into the formula, we have:
155 sec = k * 91,125 mm^3 / (12,150 mm^2)^(n-1)
Simplifying the equation, we can solve for the mold constant (k):
k = 155 sec * (12,150 mm^2)^(n-1) / 91,125 mm^3
(b) Total Solidification Time:
To find the total solidification time for a cylindrical casting, we can use Chvorinov's rule and the mold constant (k) determined in part (a). The formula for the solidification time (t) is:
t = k * V/A^(n-1)
where:
- k is the mold constant
- V is the volume of the casting
- A is the total surface area of the casting
- n is a constant that depends on the shape of the casting
Given that the casting is a cylinder with a diameter (d) of 28.85 mm and a length (l) of 40 mm, we can calculate the volume (V) and surface area (A) as follows:
V = π * (d/2)^2 * l = π * (28.85 mm/2)^2 * 40 mm
A = 2 * π * (d/2) * l + π * (d/2)^2 = 2 * π * (28.85 mm/2) * 40 mm + π * (28.85 mm/2)^2
Substituting these values into the formula, we can compute the total solidification time (t).