Hydraulic versus thermal equivalent diameter: In non-circular flow passages and tube bundles, the equivalent diameter used for pressure-drop calculations is typically __________ the equivalent diameter used for heat-transfer correlations.

Introduction / Context:Engineers often use an “equivalent” or “hydraulic” diameter to apply circular-tube correlations to non-circular passages (ducts, annuli, and shell-side crossflow through tube bundles). Depending on how flow area and wetted perimeter are defined, the effective diameters for heat transfer and for frictional pressure drop can differ.

Given Data / Assumptions:

• Crossflow over tube bundles or non-circular ducts where minimum free-flow area matters.
• Heat-transfer De may be based on overall wetted perimeter; pressure-drop De frequently references minimum flow area between obstructions.
• Same physical geometry but different correlation requirements.

Concept / Approach:For many exchanger geometries, especially on the shell side, the equivalent diameter selected for pressure-drop correlation accounts for the minimum cross-sectional flow area, which is smaller than the area basis often used for heat-transfer De. As a result, De(pd) < De(ht) in common design handbooks, reflecting more restrictive passages that govern friction losses.

Step-by-Step Solution:Define De(ht) and De(pd) per geometry-specific standards.Recognize that friction is sensitive to constrictions; heat transfer tends to average over wetted surfaces.Therefore, De for pressure drop is typically smaller than that for heat transfer.Select 'smaller than'.

Verification / Alternative check:Shell-side design methods (e.g., TEMA/standards) provide distinct De expressions; example tables often show the pressure-drop De computed with minimum flow area, yielding a smaller value than the De used in heat-transfer j-factor correlations.

Why Other Options Are Wrong:'Equal to' disregards the differing definitions.

'Greater than' contradicts typical minimum-area basis for friction.

'Not related to' is incorrect; both are related but not identical.

Common Pitfalls:

• Using a single De for both phenomena, leading to mispredicted ΔP or U.
• Ignoring baffle cut, pitch, and pattern effects on free-flow area.

Final Answer:smaller than