For flow in non-circular passages, the equivalent diameter defined for pressure-drop calculations is generally __________ the equivalent diameter used for heat-transfer correlations (because the heated perimeter may differ from the wetted perimeter).

Introduction / Context:
When analyzing non-circular ducts or annuli, engineers use an equivalent (hydraulic) diameter to apply standard pressure-drop and heat-transfer correlations. However, the appropriate diameter can differ depending on whether the focus is momentum (pressure drop) or heat transfer, because the relevant perimeter in each phenomenon may not be the same.

Given Data / Assumptions:

• Non-circular cross section (e.g., rectangular duct, annulus).
• For pressure drop, the wetted perimeter governs shear.
• For heat transfer, the heated perimeter governs convection to/from walls.
• In many practical exchangers, the heated perimeter ≤ wetted perimeter.

Concept / Approach:
The generic hydraulic diameter Dh = 4 * Area / Perimeter. For pressure drop, Perimeter = total wetted perimeter. For heat transfer, Perimeter = heated perimeter only. If heated perimeter is smaller than total wetted perimeter, then 4A / (heated perimeter) is larger than 4A / (wetted perimeter). Therefore, the equivalent diameter for pressure drop tends to be smaller than that for heat transfer.

Step-by-Step Solution:
Step 1: Write Dh,pressure = 4A / P_wetted.Step 2: Write Dh,heat = 4A / P_heated.Step 3: In typical cases, P_heated < P_wetted, so Dh,heat > Dh,pressure.Step 4: Conclude the relation: pressure-drop equivalent diameter is smaller than that for heat-transfer correlations.

Verification / Alternative check:
Annular passages with only the inner wall heated demonstrate Dh,heat computed with the inner perimeter, which is smaller than the sum of inner + outer perimeters used for pressure drop. This yields Dh,heat > Dh,pressure consistently.

Why Other Options Are Wrong:
Greater than: Reverses the typical inequality.Equal to: Only true for special cases where heated and wetted perimeters coincide.Not related to: They are related via area and perimeters.Variable but typically larger: Typical tendency is the opposite for pressure-drop Dh.

Common Pitfalls:
Blindly using a single Dh for both momentum and heat transfer without checking which perimeter applies can lead to errors in predicted friction factor or Nusselt number.

Final Answer:
smaller than