Duct Sizing Calculator

Velocity and Flow Relationships

Air velocity in ducts relates to flow rate and cross-sectional area:

**Velocity**:

v = (Q)/(A)

where: - v = velocity (m/s or fpm) - Q = volumetric flow rate (m³/s or CFM) - A = cross-sectional area (m² or ft²)

**Round Duct**:

A = (π D^2)/(4)

D = √(\frac4Q)π v

**Rectangular Duct**:

A = W × H

**Recommended Velocities** (to minimize noise and energy): - Supply trunks: 900-1200 fpm (4.6-6.1 m/s) - Supply branches: 600-900 fpm (3.0-4.6 m/s) - Return ducts: 600-800 fpm (3.0-4.1 m/s) - Residential supply: 600-900 fpm - Residential return: 500-700 fpm

Lower velocities for noise-sensitive areas (libraries, bedrooms): 400-700 fpm.

Friction Loss

Pressure drop due to friction in straight ducts:

**Darcy-Weisbach Equation**:

Δ P = f · (L)/(D_h) · (\rho v^2)/(2)

where: - f = friction factor (0.01-0.03 for typical ducts) - L = duct length (m) - D_h = hydraulic diameter (m) - \rho = air density (1.2 kg/m³ standard) - v = velocity (m/s)

**Hydraulic Diameter** (rectangular duct):

D_h = (2WH)/(W + H)

where W = width, H = height.

**Simplified Friction Loss** (per 100 ft or per m):

(Δ P)/(L) = C · Q^1.9 · D^-5.02

Typical pressure drop: 0.08-0.15 in.wg per 100 ft (0.65-1.2 Pa/m)

Lower friction = larger ducts = higher cost but lower fan energy

**Total Pressure Drop**:

Δ P_total = Δ P_friction + Δ P_fittings + Δ P_outlets

Equivalent Diameter

Convert rectangular to equivalent round duct:

**Equal Friction Method**:

D_e = 1.30 · \frac(W · H)^0.625(W + H)^0.25

where D_e, W, H are in inches or mm.

**Equal Area Method**:

D_e = √(\frac4WH)π

**Equal Velocity Method** uses equal area.

The equal friction method is preferred as it maintains similar pressure drop characteristics.

**Aspect Ratio**: Ratio of longer to shorter side.

AR = (W)/(H) \text or (H)/(W) \text (whichever is >1)

Recommended: AR ≤ 4:1 (preferably ≤ 3:1)

High aspect ratios (>4:1) increase friction and reduce performance.

Fitting Losses

Fittings, transitions, and outlets add pressure loss:

Δ P_fitting = C · (\rho v^2)/(2)

where C is the loss coefficient.

**Typical Loss Coefficients**: - 90° elbow (smooth): C = 0.2-0.4 - 90° elbow (mitered): C = 0.8-1.2 - Tee (branch): C = 0.5-1.0 - Transition (gradual): C = 0.05-0.15 - Transition (abrupt): C = 0.3-0.5 - Damper (full open): C = 0.2-0.3 - Grille/diffuser: C = 0.5-2.5

**Total System Pressure**:

Sum straight duct losses and fitting losses:

Δ P_system = Σ (Δ P)/(L) · L_segment + Σ C_i · (\rho v_i^2)/(2)

Add 10-20% safety factor for uncertainties.

Design Methods

**Equal Friction Method**:

1. Select friction loss (typically 0.1 in.wg/100 ft or 0.8 Pa/m) 2. Calculate main trunk size from total CFM 3. Size branches using same friction rate 4. Provides good velocity control 5. Most common for commercial systems

**Static Regain Method**:

1. Convert velocity pressure to static pressure at each junction 2. Maintains nearly constant static pressure 3. Better for long duct runs 4. More complex calculations 5. Used in high-velocity systems

**Velocity Method**:

1. Select maximum velocity for each section 2. Calculate area from A = Q/v 3. Simple but may not optimize energy 4. Common for residential systems

**T-Method (Optimized)**:

Balances first cost (duct material) with operating cost (fan energy) to minimize life cycle cost.

Worked Example

Inputs

• airflow: 1000
• ductLength: 50
• ductType: round
• targetVelocity: 800

Result: Duct Diameter: 14 inches | Actual Velocity: 786 fpm | Friction Loss: 0.069 in.wg | Total Pressure: 0.35 in.wg

Explanation

For 1000 CFM over 50 feet targeting 800 fpm velocity:

**Step 1: Calculate Required Duct Area** A = Q / v = 1000 / 800 = 1.25 ft²

**Step 2: Calculate Round Duct Diameter** D = √(4A / π) = √(4 × 1.25 / 3.14159) = 1.26 ft = 15.1 inches

Select standard size: 14 inches (nearest standard)

**Step 3: Calculate Actual Velocity** A_actual = π × (14/12)^2 / 4 = 1.069 ft² v_actual = 1000 / 1.069 = 935 fpm (slightly higher than target)

**Step 4: Calculate Friction Loss** Using friction chart or equation: Δ P / 100ft = 0.11 in.wg per 100 ft For 50 ft: Δ P = 0.11 × (50/100) = 0.055 in.wg

**Step 5: Calculate Velocity Pressure** P_v = (v/4005)^2 = (935/4005)^2 = 0.054 in.wg

**Step 6: Add Fitting Losses** Assume 2 elbows (C=0.25 each): Δ P_fittings = 2 × 0.25 × 0.054 = 0.027 in.wg

**Step 7: Total Pressure Drop** Δ P_total = 0.055 + 0.027 = 0.082 in.wg

**Assessment**: - Velocity 935 fpm: Good for supply branch (target 600-900) - Friction 0.11 in.wg/100ft: Acceptable (target <0.15) - Total pressure: Low, energy-efficient design

Second Scenario

Inputs

• airflow: 1251
• ductLength: 50
• ductType: round
• targetVelocity: 800

Result: Duct Diameter: 14 inches | Actual Velocity: 786 fpm | Friction Loss: 0.069 in.wg | Total Pressure: 0.35 in.wg

Explanation

This scenario uses different inputs (airflow = 1251, ductLength = 50, ductType = round, targetVelocity = 800) to show how changing one variable affects the duct sizing result. Run the calculator above with these values to get the exact updated output with step-by-step work.