Student Laboratory Exercise: Deterministic Duct Aerodynamics & Friction Sizing

1. Pedagogical Learning Objectives

Upon successful completion of this laboratory module, students will be able to:

Formulate the Darcy-Weisbach friction equation and Colebrook-White implicit friction factor relation across laminar, transitional, and fully rough turbulent flow regimes (Re = 2,000 to 100,000).
Quantify hydraulic diameter (D_h) and Huebscher equivalent rectangular duct diameter (D_e) across varying duct aspect ratios (1:1 to 4:1).
Evaluate friction loss discrepancies between classical 0.10 in. wg / 100 ft equal friction sliding rules and exact numerical solutions at varying air densities.
Benchmark flexible duct sag and compression derating penalties against SMACNA and ASHRAE standard duct runs.

2. Theoretical Background & Mathematical Physics

Airflow pressure loss in straight ductwork is governed by the Darcy-Weisbach formulation:

ΔP = f · (L / D_h) · (ρ · V² / 2)

Where:

ΔP = Total friction pressure loss (Pa or in. wg)
f = Darcy friction factor (dimensionless)
L = Total duct length (m or ft)
D_h = Hydraulic diameter = 4A / P
V = Mean air velocity (m/s or FPM)
ρ = Standard air density (0.075 lb/cu ft at standard temperature and pressure)

The friction factor f is determined iteratively via the Colebrook-White implicit equation:

1 / √f = -2 · log₁₀ [ (ε / (3.7 · D_h)) + (2.51 / (Re · √f)) ]

Where:

ε = Material absolute surface roughness (0.0003 ft for galvanized sheet metal, 0.003 ft for wire-helix flexible duct)
Re = Reynolds number = (ρ · V · D_h) / μ
μ = Dynamic viscosity of air (1.21 × 10⁻⁵ lb/ft·s at 70°F)

3. Laboratory Apparatus & Interactive Simulation Workbench

Students execute numerical airflow measurements using the validated deterministic engine:

Primary Simulation Instrument:
Open the live simulation instrument at HVACLogic Deterministic Duct Aerodynamics & Friction Workbench.

4. Step-by-Step Experimental Protocol

Step 1: Set airflow volume to 1,200 CFM and duct shape to Round. Input standard galvanized steel roughness (0.0003 ft). Record calculated velocity (FPM), round diameter (inches), velocity pressure (in. wg), and friction rate per 100 ft.
Step 2: Switch to Rectangular duct geometry with a 12-inch fixed height. Compute the Huebscher equivalent rectangular width and observe the aspect ratio effect on static pressure drop.
Step 3: Modify material roughness to Flexible Duct (ε = 0.003 ft) under 15% uncompressed sag. Record the dramatic +55% to +70% surge in total friction loss compared to rigid sheet metal at identical CFM.

5. Student Data Collection Matrix

Operating Scenario	Duct Geometry	Velocity [FPM]	Velocity Press. [in. wg]	Friction Rate [in. wg / 100 ft]	Flow Regime
Scenario 1: Rigid Round Sheet Metal	14" Round (1,200 CFM)	1,123 FPM	0.078 in. wg	0.080 in. wg / 100 ft	Re ≈ 137,000 (Turbulent)
Scenario 2: Rectangular Sheet Metal	18" x 10" Rect (1,200 CFM)	960 FPM	0.057 in. wg	0.065 in. wg / 100 ft	D_e = 14.3 in.
Scenario 3: Wire-Helix Flex (15% Sag)	14" Flex (1,200 CFM)	1,123 FPM	0.078 in. wg	0.142 in. wg / 100 ft	+77.5% Friction Penalty

6. Post-Lab Analytical Assessment

Aspect Ratio & Wetted Perimeter: Explain why the Huebscher equivalent diameter equation yields a larger cross-sectional area for rectangular ducts compared to equivalent round ducts at identical friction rates and flow volumes.
Turbulent Eddies in Flexible Ducting: In flexible duct installations, why does un-tensioned installation and compression create localized turbulence eddies that dwarf standard boundary-layer friction?
Elevation Air Density Correction: How does high-elevation installation (e.g. Denver, CO at 5,280 ft where air density drops to 0.062 lb/cu ft) alter the required CFM to deliver equivalent sensible heating/cooling capacity?

7. Instructor Notes & Pedagogical Solutions Guide

Estimated Duration: 60 minutes in laboratory session or independent coursework.

Prerequisites: Fluid mechanics fundamentals, conservation of mass (Q = A · V), Reynolds number definition.

Key Takeaway: Standard residential sliding rules assume rigid smooth sheet metal and will drastically undersize flexible duct runs if sag deratings are neglected.