Tube count scaling: keeping number of passes, tube pitch, and tube outer diameter constant, if the shell inside diameter is tripled, the maximum number of tubes that fit is approximately how many times the original?

Introduction / Context:
Quick scaling estimates are useful when comparing exchanger sizes. If pitch and tube diameter remain fixed, the number of tubes that can be accommodated in a circular bundle is roughly proportional to the cross-sectional area available for tubes, and hence to the square of shell diameter.

Given Data / Assumptions:

• Number of passes, pitch, and tube outer diameter are unchanged.
• Tube layout and clearances remain similar (same packing fraction).
• Shell inside diameter increases from D to 3D.

Concept / Approach:
Available tube bundle area scales with D^2. Tripling D increases area by 3^2 = 9. With similar layout and pitch, the tube count scales approximately with area, so the maximum tube count is about 9 times the original, allowing for minor edge effects that are negligible in this estimate.

Step-by-Step Solution:

Verification / Alternative check:
Handy design charts for tube count vs. shell I.D. show near-quadratic scaling, validating the factor-of-nine approximation.

Why Other Options Are Wrong:

• About 3 or 6: underestimates because count scales with area, not diameter.
• Considerably less/more than 9: contradicts geometric scaling when layout consistency is preserved.

Common Pitfalls:
Forgetting that pitch must remain constant; mixing area and diameter proportionalities; ignoring pass-partition and tie-rod space (small corrections only).

Final Answer:
About 9