According to Chvorinov's equation, the solidification time in casting is proportional to V^2.

Explanation:
Chvorinov's equation is an empirical equation used to estimate the solidification time in casting processes. It is based on the assumption that the solidification process is controlled by the rate of heat transfer from the casting material to the mold.

The equation is given as follows:
t = (C * V^2) / A

Where:
t is the solidification time,
C is a constant that depends on the material being cast and the mold properties,
V is the volume of the casting, and
A is the surface area of the casting.

Now, let's understand why the solidification time is proportional to V^2.

1. **Volume of the casting (V):**
The volume of the casting represents the amount of material that needs to solidify. A larger volume means a larger amount of material, which requires more time for solidification.

2. **Surface area of the casting (A):**
The surface area of the casting represents the area through which heat is transferred from the casting to the mold. A larger surface area allows for more efficient heat transfer, leading to faster solidification.

3. **Proportional relationship:**
The equation shows that the solidification time is proportional to V^2. This means that as the volume of the casting increases, the solidification time increases exponentially. This can be explained by considering the heat transfer mechanism.

When the volume of the casting increases, the surface area also increases, but not at the same rate. The increase in surface area is proportional to the square root of the volume, as the surface area is a function of the square of the linear dimensions. Therefore, the heat transfer area increases at a slower rate compared to the volume. As a result, the solidification time increases exponentially with the volume.

In conclusion, Chvorinov's equation states that the solidification time in casting is proportional to V^2. This relationship can be explained by considering the heat transfer mechanism and the relationship between volume and surface area.

T =k.(v/s.a)2