Which ONE or MORE among the following tube cross-sections shown can be produced by true centrifugal casting method? Note: The cross-sections shown are perpendicular to the axis of rotation. Figures are not to scale.
Show Hint
Remember that in true centrifugal casting the outer shape is set by the mold but the inner bore is always a circle, since it forms from the free liquid surface.
Step 1: Understanding the Physics of True Centrifugal Casting:
In true centrifugal casting, molten metal is poured into a mold that is spinning rapidly about its own axis.
Centrifugal force throws the liquid metal outward, pressing it firmly against the inner wall of the rotating mold cavity.
Because of this, the outer surface of the finished casting always takes the exact shape of the mold cavity, whatever that shape may be.
Step 2: Why the Inner Bore Is Always Circular:
The inner surface of the casting is not touching any mold or core, it is a free liquid surface.
Under rotation, the artificial "gravity" created by centrifugal force acts radially outward and is the same in every direction around the axis.
A free liquid surface under a radially symmetric force field always settles at a constant radius from the axis, which means the inner bore can only ever be a circle, never a polygon.
Step 3: Checking Option (A), outer pentagon and inner pentagon:
Here the inner shape is a pentagon, not a circle.
A pentagonal inner bore can only be produced if a solid core or a specially shaped fixture holds the liquid in that shape, and that is not possible in true centrifugal casting since there is no core.
So option (A) is not achievable by this process.
Step 4: Checking Option (B), outer octagon and inner circle:
The outer shape is fixed by the mold, and an octagonal mold cavity is perfectly achievable by machining.
The inner shape is circular, which matches exactly what the free liquid surface will always form.
So option (B) is achievable.
Step 5: Checking Option (C), outer pentagon and inner circle:
Again the outer shape only depends on how the mold is made, so a pentagonal outer profile is possible.
The inner shape is circular, satisfying the rule from Step 2.
So option (C) is achievable.
Step 6: Checking Option (D), outer circle and inner circle:
This is the most common case, a simple round pipe or tube, made using a circular mold.
The inner surface is naturally circular as expected.
So option (D) is achievable.
Final Answer:
Any cross-section is possible in true centrifugal casting as long as the inner bore is circular, so options (B), (C), and (D) are correct while (A) is not.
\[ \boxed{\text{(B), (C), (D)}} \]
