10.5 Duct Friction, Fitting Losses, and System Balancing

Duct Friction, Fitting Losses, and System Balancing

Choosing a transport velocity and a duct diameter fixes the geometry. Predicting whether the fan can actually move that air requires adding up every friction and fitting loss in the run, and then making the branches balance at the junctions.

1. Duct Friction Losses: Darcy-Weisbach & ACGIH Charts

As air travels through ductwork, mechanical energy is converted into non-recoverable heat via fluid friction against the duct walls and internal turbulent shearing.

Darcy-Weisbach Equation

$h_f = f \cdot \left(\frac{L}{D}\right) \cdot VP$

Where:

• hf = Friction loss in inches of water gauge (in. w.g.)
• f = Dimensionless Darcy friction factor (function of Reynolds number Re and duct roughness ε/D)
• L = Duct length (ft)
• D = Duct hydraulic diameter (ft)
• VP = Velocity pressure in the duct (in. w.g.)

The ACGIH Standard Friction Chart

In industrial hygiene design, friction loss is determined using standard ACGIH Air Friction Charts for round galvanized metal ductwork carrying standard air (0.075 lb/ft³ at 70°F and 29.92 in. Hg). Losses are expressed as friction loss per 100 feet of duct (extin. w.g. / 100 ft):

$h_{\text{friction}} = \left(\frac{\text{Loss per } 100\text{ ft}}{100}\right) \times L_{\text{actual}}$

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2. Fitting and Transition Dynamic Losses

Whenever air changes direction, expands, contracts, or merges, flow separation and turbulent eddy dissipation induce dynamic fitting losses (hL), calculated using the dimensionless loss coefficient (K):

$\mathbf{h_L = K \times VP_d}$

Elbow Aerodynamics: Centerline Radius-to-Diameter Ratio (R/D)

When air negotiates a bend, centrifugal force creates a high-pressure zone along the outer radius and a low-pressure separation bubble along the inner radius, generating severe secondary twin-vortex swirling.

   +-------------------------------------------------------------------------+
   |                  ELBOW RADIUS-TO-DIAMETER RATIO (R/D)                   |
   +-------------------------------------------------------------------------+
   |                                                                         |
   |           Centerline Radius (R)                                         |
   |       <--------------------------->                                     |
   |       +---------------------------+----                                 |
   |       |                           |  ^                                  |
   |       |   .-''''-.                |  | Duct Diameter (D)                |
   |       |  /        \               |  v                                  |
   |       | |  Center  |              +----                                 |
   |       | |   Line   |                                                    |
   |       |  \        /                                                     |
   |       |   '-....-'                                                      |
   |       |                                                                 |
   |       * Optimal LEV Design: R/D = 1.5 to 2.5 (K = 0.15 to 0.24)         |
   |       * Mitered 90° Elbow: R/D = 0.75 (K = 0.75 to 1.30 - AVOID!)        |
   +-------------------------------------------------------------------------+

The aerodynamic severity of an elbow is determined by its Centerline Radius-to-Diameter Ratio (R/D):

$R/D = \frac{\text{Centerline Radius of Elbow }(R)}{\text{Duct Diameter }(D)}$

Exam Key Rule: The optimum economic and aerodynamic elbow design has an R/D ratio between 1.5 and 2.5 (R/D = 2.0 is the ideal target). Designing below R/D = 1.5 dramatically spikes energy loss, while designing above R/D = 2.5 adds unnecessary weight, space, and frictional surface area.

Branch Entry Junctions: Expanding Mains

When a branch duct merges into a main trunk duct:

1. Angle of Entry (heta): Branches must enter at an angle of 30° to 45° relative to the main duct axis (30° is ideal, Kbranch ≈ 0.15--0.18; 45° yields K ≈ 0.28). 90° T-junctions are strictly prohibited in particulate systems (K > 0.80, severe turbulence and dust fallout).
2. Expanded Main Transition: Downstream of the branch junction, the main duct diameter must be expanded so that the combined volumetric flow (Qmain = Q(branch 1) + Q(branch 2)) maintains the exact design transport velocity without creating excessive velocity or causing upstream choking.

   +-------------------------------------------------------------------------+
   |                  BRANCH JUNCTION & EXPANDED MAIN DESIGN                 |
   +-------------------------------------------------------------------------+
   |                                                                         |
   |                         Branch Duct (Q1, D1)                            |
   |                            \                                            |
   |                             \  Angle theta = 30° to 45°                 |
   |                              \                                          |
   |   Upstream Main (Q2, D2)      \    Downstream Expanded Main (Q_total, D3)|
   |   -------------------------\   ---------------------------------------   |
   |                             \  Taper angle <= 30°                       |
   |   ===========================>  ======================================>  |
   |   --------------------------------------------------------------------   |
   |   * Q_total = Q1 + Q2                                                   |
   |   * D3 is expanded to maintain minimum transport velocity at Q_total!   |
   +-------------------------------------------------------------------------+

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3. Duct System Balancing Methodologies

When multiple exhaust branches connect to a common main manifold leading to a single fan, the system will naturally self-equilibrate according to the laws of fluid resistance: air will distribute such that the total static pressure loss through each parallel branch path to the junction is exactly equal (SP(j,1) = SP(j,2)). If the system is designed incorrectly, branches with lower resistance will steal airflow from high-resistance branches, causing the high-resistance branches to drop below minimum transport velocity.

Industrial hygiene ventilation systems are balanced using one of two primary methods:

   +-------------------------------------------------------------------------+
   |              BALANCE BY DESIGN VS. BLAST GATE BALANCING                 |
   +-------------------------------------------------------------------------+
   |                                                                         |
   |  1. STATIC PRESSURE BALANCE METHOD ("Balance by Design"):               |
   |     - Branch duct diameters and fitting geometries are precisely sized  |
   |       during engineering design so pressure losses match at junctions.  |
   |     - Target: |SP_branchA - SP_branchB| / min(SP) <= 0.05 (within 5%).  |
   |     - Tamper-proof; no dampers or blast gates to clog or erode.         |
   |     - Permanent, reliable, maintenance-free aerodynamic equilibrium.    |
   |                                                                         |
   |  2. BLAST GATE BALANCING METHOD:                                        |
   |     - Branches are oversized, and adjustable sliding mechanical metal   |
   |       plates (blast gates) are inserted into each branch line.          |
   |     - Gates are manually adjusted during commissioning using Pitot tube.|
   |     - Vulnerabilities:                                                  |
   |       * Severe erosion from abrasive dust impacting the gate lip.       |
   |       * Particulate damming: Dust piles up behind gate, causing clogs.  |
   |       * Unauthorized operator tampering throws whole system off balance.|
   +-------------------------------------------------------------------------+

The 5% Static Pressure Balance Criterion

When calculating junction pressures in the Balance by Design method, two converging branches are considered balanced if their calculated branch static pressures at the junction (SPj) agree within 5%:

$\mathbf{\frac{|SP_{j,\text{Branch 1}} - SP_{j,\text{Branch 2}}|}{\min(SP_{j,1}, SP_{j,2})} \le 0.05 \quad (\le 5\%\text{ difference})}$

If the difference exceeds 5%, the branch with the lower resistance must be corrected by:

1. Decreasing its duct diameter (which increases velocity, velocity pressure, and friction loss).
2. Introducing an engineered restriction (e.g., adding an extra bend or slight length adjustment).
3. Increasing the design airflow through that branch until pressures match.

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4. Worked Step-by-Step Calculation Examples

Worked Example 9.2.1: Sizing Duct Diameter for Minimum Transport Velocity

Problem: A local exhaust hood captures dry silica grinding dust from an abrasive cut-off saw. The hood design requires a capture airflow of Q = 1350 cfm. Silica dust requires a minimum transport velocity of Vtr = 3800 fpm.

1. Calculate the theoretical maximum duct cross-sectional area (Ad) and round duct diameter (D).
2. Select the nearest standard commercial round duct diameter (available in 1-inch increments: 7 in, 8 in, 9 in) that guarantees velocity ≥ Vtr.
3. Calculate the actual operating duct velocity (Vactual) and velocity pressure (VPd) with the selected duct size.

Solution Steps:

1. Calculate theoretical duct area and diameter: $A_d = \frac{Q}{V_{tr}} = \frac{1350\text{ cfm}}{3800\text{ fpm}} = 0.3553\text{ ft}^2$ $D = \sqrt{\frac{4 \cdot A_d}{\pi}} \times 12 = \sqrt{\frac{4 \times 0.3553}{3.14159}} \times 12 = \sqrt{0.4524} \times 12 = 0.6726 \times 12 = 8.07\text{ inches}$

2. Evaluate standard commercial duct sizes:

   • Option A: 9-inch duct (D = 9 in = 0.75 ft): $A_9 = \frac{\pi \cdot (0.75)^2}{4} = 0.4418\text{ ft}^2 \implies V = \frac{1350}{0.4418} = 3056\text{ fpm}$ Evaluation: 3056 fpm < 3800 fpm — UNACCEPTABLE. Silica dust will settle and plug the duct!
   • Option B: 8-inch duct (D = 8 in = 0.6667 ft): $A_8 = \frac{\pi \cdot (0.6667)^2}{4} = 0.3491\text{ ft}^2 \implies V = \frac{1350}{0.3491} = 3867\text{ fpm}$ Evaluation: 3867 fpm > 3800 fpm — PERFECT. Meets transport velocity criterion.

3. Calculate actual operating parameters for 8-inch duct: $V_{\text{actual}} = 3867\text{ fpm}$ $VP_d = \left(\frac{V_{\text{actual}}}{4005}\right)^2 = \left(\frac{3867}{4005}\right)^2 = (0.9655)^2 = 0.9322\text{ in. w.g.}$

Result: An 8-inch diameter duct must be selected, establishing an actual transport velocity of 3867 fpm (VPd = 0.932 in. w.g.).

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Worked Example 9.2.2: Total Pressure Loss Across a Duct Branch Run

Problem: An LEV branch carrying Q = 1200 cfm of air laden with limestone dust through a 7.5-inch diameter round duct (Ad = 0.3068 ft², Vd = 3911 fpm, VPd = 0.9536 in. w.g.) comprises the following components:

• Tapered intake hood (Fh = 0.15)
• 60 feet of straight galvanized duct (friction loss rate from ACGIH chart = 2.80 in. w.g. / 100 ft)
• Two 90° stamped elbows (R/D = 2.0, Kelbow = 0.19 each)
• One 30° branch entry fitting into the main (Kbranch = 0.18)

Calculate the total static pressure required at the branch junction (SPjunction).

Solution Steps:

1. Calculate Hood Static Pressure (SPh): $h_e = F_h \times VP_d = 0.15 \times 0.9536 = 0.1430\text{ in. w.g.}$ $|SP_h| = VP_d + h_e = 0.9536 + 0.1430 = 1.0966\text{ in. w.g.}$

2. Calculate Straight Duct Friction Loss (hfriction): $h_{\text{friction}} = \left(\frac{2.80\text{ in. w.g.}}{100\text{ ft}}\right) \times 60\text{ ft} = 1.6800\text{ in. w.g.}$

3. Calculate Dynamic Fitting Losses (helbows + hbranch): $h_{\text{elbows}} = 2 \times (K_{\text{elbow}} \times VP_d) = 2 \times (0.19 \times 0.9536) = 2 \times 0.1812 = 0.3624\text{ in. w.g.}$ $h_{\text{branch}} = K_{\text{branch}} \times VP_d = 0.18 \times 0.9536 = 0.1716\text{ in. w.g.}$ $h_{\text{fittings, total}} = 0.3624 + 0.1716 = 0.5340\text{ in. w.g.}$

4. Calculate Total Branch Static Pressure at Junction (|SPj|): $|SP_j| = |SP_h| + h_{\text{friction}} + h_{\text{fittings, total}}$ $|SP_j| = 1.0966 + 1.6800 + 0.5340 = 3.3106\text{ in. w.g.}\implies SP_j = -3.31\text{ in. w.g.}$

Result: The total suction static pressure required at the junction to pull the design airflow through this branch is -3.31 in. w.g.

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Worked Example 9.2.3: Static Pressure Balance by Design at a Junction

Problem: Two LEV branches merge at Junction J:

• Branch 1 (Lead oxide hood): Design flow Q1 = 800 cfm. Sized with a 6-inch duct (V1 = 4074 fpm). Calculated static pressure at the junction is SP(j,1) = -3.45 in. w.g.
• Branch 2 (Solder pot hood): Design flow Q2 = 1100 cfm. Initial layout calculation with an 8-inch duct (V2 = 3151 fpm) yields a calculated junction static pressure of SP(j,2) = -2.80 in. w.g.

1. Evaluate whether the system meets the 5% Balance by Design criterion.
2. If unbalanced, calculate the actual airflow that would be pulled through Branch 2 if fabricated as initially sized.
3. Propose the engineering redesign required to balance the junction without blast gates.

Solution Steps:

1. Check 5% Balance Criterion: $\Delta SP = \frac{|SP_{j,1} - SP_{j,2}|}{\min(SP_{j,1}, SP_{j,2})} = \frac{|3.45 - 2.80|}{2.80} = \frac{0.65}{2.80} = 0.2321 \quad (23.2\% > 5\%)$ Status: UNBALANCED. Branch 2 has significantly lower resistance than Branch 1.

2. Calculate actual self-equilibrating airflow in Branch 2: Because the system will naturally balance to the higher static pressure (-3.45 in. w.g.), Branch 2 will draw excess air: $Q_{\text{actual, 2}} = Q_{\text{design, 2}} \times \sqrt{\frac{SP_{j,1}}{SP_{j,2}}} = 1100\text{ cfm} \times \sqrt{\frac{3.45}{2.80}} = 1100 \times \sqrt{1.2321} = 1100 \times 1.110 = 1221\text{ cfm}$ Consequence: Branch 2 draws 1221 cfm instead of 1100 cfm, which steals capacity from the main fan and may cause Branch 1 to drop below its required transport velocity!

3. Engineering Redesign for Static Pressure Balance:

   • Redesign Branch 2 using a 7-inch duct instead of an 8-inch duct (A7 = 0.2673 ft², V = 1100 / 0.2673 = 4115 fpm).
   • Recalculating friction and fitting losses in Branch 2 with the 7-inch duct increases its junction loss to SP(j,2)' = -3.42 in. w.g.
   • Re-evaluating balance: Δ SP' = (|3.45 - 3.42|)/3.42 = 0.03/3.42 = 0.0088 = 0.88% ≤ 5%.

Result: Resizing Branch 2 to a 7-inch duct establishes aerodynamic balance within 0.88%, ensuring stable design airflow through both hoods without blast gates.