Hopper/heads geometry in process vessels: the included apex angle commonly used for CONICAL BOTTOM HEADS on chemical process equipment is approximately

Introduction / Context:
Conical bottoms are used in tanks and reactors to aid solids discharge, liquid draining, and phase separation. The cone angle affects flow, holdup, and fabrication. A commonly adopted included apex angle balances mass flow of bulk solids and manufacturability. This question checks the typical rule-of-thumb value used in general-purpose chemical equipment.

Given Data / Assumptions:

• Standard storage/mixing vessels and reactors handling liquids, slurries, or bulk solids.
• No special flow-promoting inserts are assumed.
• Included apex angle is the total cone angle at the tip (not half-angle).

Concept / Approach:

For many services, an included cone angle near 60° (half-angle 30°) provides reliable draining and reduces stagnant zones. For bulk solids, this angle also helps approach mass flow for many materials (subject to wall friction and cohesion), while avoiding excessively tall cones (as with very shallow angles).

Step-by-Step Solution:

Verification / Alternative check:

Vendor catalogs and plant standards frequently specify ~60° cones for general service unless material testing suggests otherwise.

Why Other Options Are Wrong:

20° or 40° produce very tall cones; 80° or 120° are very blunt and tend to trap material or liquid.

Common Pitfalls:

Confusing included angle with half-angle; failing to consider liner friction or coatings for difficult powders.

Final Answer:

60°