Hydraulic diameter concept: for steady flow through a duct of constant noncircular cross-section with flow area A and wetted perimeter P, which expression defines the equivalent (hydraulic) diameter?

Introduction / Context:
The hydraulic (equivalent) diameter allows engineers to apply circular-tube correlations to noncircular ducts by mapping geometry via area and wetted perimeter. This is widely used for heat transfer and pressure drop calculations in channels, manifolds, and HVAC ducts.

Given Data / Assumptions:

• Fully wetted perimeter P with internal flow.
• Constant cross-section with flow area A.
• Turbulent/laminar correlations typically expressed in terms of Re and Nu using Dh.

Concept / Approach:
The standard definition is Dh = 4 A / P. This preserves key dimensionless groups and reduces to the tube inside diameter for a circular tube (A = πD^2/4, P = πD → Dh = D). Using any other ratio would distort Reynolds number and friction factor predictions for noncircular ducts.

Step-by-Step Solution:

Verification / Alternative check:
Standard fluid mechanics and heat transfer texts present Dh = 4A/P as the universal definition for internal flows.

Why Other Options Are Wrong:

• A/P or P/A change dimensions improperly.
• 4 P/A is inverse of the correct form.
• A alone lacks perimeter information and is not a length scale.

Common Pitfalls:
Using external perimeter instead of wetted perimeter; misapplying Dh to partially filled conduits where free surface exists.

Final Answer:
4 A/P