In a double-pipe concentric heat exchanger, the annulus carries one of the fluids between the outer pipe I.D. (D2) and the inner pipe O.D. (assumed approximately equal to its I.D. for thin walls). For heat-transfer calculations, what is the appropriate equivalent (hydraulic) diameter of the annulus expressed in terms of D1 and D2?

Introduction / Context:
The equivalent (hydraulic) diameter is used to convert non-circular flow passages into an “equivalent” circular size so that standard convection correlations can be applied. For the annulus in a double-pipe heat exchanger, knowing this diameter directly impacts Reynolds number, Nusselt number, and the predicted heat-transfer coefficient, all of which are central to exchanger sizing and rating.

Given Data / Assumptions:

• The passage of interest is an annulus formed by two concentric pipes.
• D1 is the inner pipe inside diameter (taken as the relevant inside boundary of the annulus); D2 is the outer pipe inside diameter.
• Walls are thin enough that O.D. and I.D. distinction on the inner pipe does not change the result materially.

Concept / Approach:
The hydraulic diameter is defined as Dh = 4 * (flow area) / (wetted perimeter). For an annulus, area = (π/4) * (D2^2 - D1^2), and wetted perimeter = π * (D2 + D1). Substituting gives Dh = (D2^2 - D1^2) / (D2 + D1) = D2 - D1. This compact result is widely used in heat-transfer and pressure-drop calculations for annular flow.

Step-by-Step Solution:
Write Dh = 4A/P.Compute A_annulus = (π/4) * (D2^2 - D1^2).Compute P_wetted = π * (D2 + D1).Form Dh = [4 * (π/4) * (D2^2 - D1^2)] / [π * (D2 + D1)] = (D2^2 - D1^2)/(D2 + D1) = D2 - D1.

Verification / Alternative check:
Dimensional consistency confirms the result has units of length. Practical calculations using Dh = D2 - D1 reproduce standard handbooks and software outputs for annular flow correlations.

Why Other Options Are Wrong:
(a) is the definition, not the closed-form result; (c) simplifies to D2 + D1, which is incorrect for annuli; (e) doubles the correct value; (d) is unnecessary since a correct closed form exists.

Common Pitfalls:
Confusing (D2 - D1) with (D2 + D1); using the wrong boundary (e.g., outer O.D. rather than I.D.); forgetting that Dh is for convection/pressure-drop correlations, not geometric diameter for area calculations.

Final Answer:
D2 - D1