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Friction Loss in Ducts (Darcy Equation) Calculator

Friction Loss in Ducts

dimensionless

1. What is a Friction Loss Calculator?

Definition: This calculator computes the friction losses (\( \Delta p_f \)) in a duct using the Darcy equation, accounting for the friction factor, duct length, hydraulic diameter, air density, and velocity.

Purpose: It is used in HVAC design to quantify pressure losses due to friction in ducts, aiding in fan selection, duct sizing, and energy-efficient system design.

2. How Does the Calculator Work?

The calculator uses the following formula for friction loss:

Friction Loss: \[ \Delta p_f = \frac{12 f L}{D_h} \rho \left( \frac{V}{1097} \right)^2 \]

Where:

  • \( \Delta p_f \): Friction losses (in. of water, Pa)
  • \( f \): Friction factor (dimensionless)
  • \( L \): Duct length (ft, m)
  • \( D_h \): Hydraulic diameter (in., m)
  • \( \rho \): Air density (lb_f/ft³, kg/m³)
  • \( V \): Velocity of air (fpm, m/s)

Unit Conversions:

  • Duct Length (\( L \)): ft, m (1 m = 3.28084 ft)
  • Hydraulic Diameter (\( D_h \)): in., m (1 m = 39.3701 in.)
  • Air Density (\( \rho \)): lb_f/ft³, kg/m³ (1 kg/m³ = 0.062428 lb_f/ft³)
  • Velocity (\( V \)): fpm, m/s (1 m/s = 196.850 fpm)
  • Friction Loss (\( \Delta p_f \)): in. of water, Pa (1 in. of water = 248.84 Pa)

Steps:

  • Enter the friction factor (\( f \)), duct length (\( L \)), hydraulic diameter (\( D_h \)), air density (\( \rho \)), and air velocity (\( V \)), and select their units.
  • Convert \( L \), \( D_h \), \( \rho \), and \( V \) to ft, in., lb_f/ft³, and fpm, respectively.
  • Calculate the friction loss using the formula, with constants 12 and 1097.
  • Convert the result to the selected unit (in. of water or Pa).
  • Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Friction Loss Calculation

Calculating friction loss is crucial for:

  • HVAC System Design: Determines pressure drops in ducts, guiding fan and duct sizing for adequate air flow.
  • Energy Efficiency: Minimizes energy consumption by optimizing duct design to reduce friction losses.
  • System Performance: Ensures proper air distribution for ventilation and thermal comfort.

4. Using the Calculator

Examples:

  • Example 1: For \( f = 0.02 \), \( L = 40 \, \text{ft} \), \( D_h = 24 \, \text{in.} \), \( \rho = 0.075 \, \text{lb_f/ft³} \), \( V = 600 \, \text{fpm} \), friction loss in in. of water:
    • \( \Delta p_f = \frac{12 \times 0.02 \times 40}{24} \times 0.075 \times \left( \frac{600}{1097} \right)^2 \approx 0.4 \times 0.075 \times 0.29924 \approx 0.008977 \)
    • Since 0.008977 < 10000 and > 0.00001, display with 5 decimal places: \( 0.00898 \)
  • Example 2: For \( f = 0.025 \), \( L = 12 \, \text{m} \), \( D_h = 0.5 \, \text{m} \), \( \rho = 1.2 \, \text{kg/m³} \), \( V = 5 \, \text{m/s} \), friction loss in Pa:
    • Convert: \( L = 12 \times 3.28084 \approx 39.37008 \, \text{ft} \)
    • \( D_h = 0.5 \times 39.3701 \approx 19.68505 \, \text{in.} \)
    • \( \rho = 1.2 \times 0.062428 \approx 0.074914 \, \text{lb_f/ft³} \)
    • \( V = 5 \times 196.850 \approx 984.25 \, \text{fpm} \)
    • \( \Delta p_f = \frac{12 \times 0.025 \times 39.37008}{19.68505} \times 0.074914 \times \left( \frac{984.25}{1097} \right)^2 \approx 0.60003 \times 0.074914 \times 0.80384 \approx 0.03613 \, \text{in. of water} \)
    • Convert to Pa: \( 0.03613 \times 248.84 \approx 8.9906 \)
    • Since 8.9906 < 10000 and > 0.00001, display with 5 decimal places: \( 8.99060 \)
  • Example 3: For \( f = 0.015 \), \( L = 50 \, \text{ft} \), \( D_h = 12 \, \text{in.} \), \( \rho = 0.08 \, \text{lb_f/ft³} \), \( V = 800 \, \text{fpm} \), friction loss in in. of water:
    • \( \Delta p_f = \frac{12 \times 0.015 \times 50}{12} \times 0.08 \times \left( \frac{800}{1097} \right)^2 \approx 0.75 \times 0.08 \times 0.53176 \approx 0.0319056 \)
    • Since 0.0319056 < 10000 and > 0.00001, display with 5 decimal places: \( 0.03191 \)

5. Frequently Asked Questions (FAQ)

Q: What does friction loss in ducts represent?
A: Friction loss (\( \Delta p_f \)) quantifies the pressure drop due to air friction against duct walls, affecting the energy required to move air through an HVAC system.

Q: How can I determine the friction factor?
A: The friction factor (\( f \)) is typically obtained from the Moody chart or empirical correlations (e.g., Colebrook equation) based on duct roughness and Reynolds number.

Q: Why is friction loss important in HVAC design?
A: It impacts fan power requirements and system efficiency, guiding duct design to minimize pressure losses and ensure adequate air flow.

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