Final answer:
To calculate the size of a cylindrical riser with equal height and diameter for feeding a steel slab casting using the modulus method, the modulus of the riser should be equal to or greater than that of the slab. For a slab with dimensions 25x25x5 cm, the modulus is approximately 2.98 cm, necessitating a riser height and diameter of at least 23.84 cm.
Step-by-step explanation:
To determine the size of a cylindrical riser necessary to feed a steel slab casting using the modulus method, it can be noted that the riser should have a solidification time that is longer than or at least equal to that of the casting to ensure proper feeding. The modulus of a casting is its volume divided by its surface area. For the cylindrical riser where height (h) and diameter (d) are equal:
- Modulus of riser = (V / A)
Where volume (V) = π(d/2)^2*h, and surface area (A) = π3.14*d^2 + 2*3.14*(d/2)*h. Since d = h, we get:
- Modulus of cylinder = π/4*d^3 / (2*π*d^2)
- Modulus of cylinder = d / 8
For the slab casting with dimensions 25x25x5 cm:
- Modulus of slab = (25*25*5) / (2*(25*25) + 4*(25*5))
- Modulus of slab = 3125 / 1050
- Modulus of slab ≈ 2.98 cm
The size of the riser, therefore, should have a modulus equal to or greater than 2.98 cm which implies:
- h / 8 ≥ 2.98 cm
- h ≥ 2.98 cm * 8
- h ≥ 23.84 cm
Since the height and diameter are equal, both should be at least 23.84 cm to ensure proper feeding of the slab casting by the riser.