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Natural Draught Ventilation

Reference data and engineering information about natural draught ventilation for hvac systems applications.

naturaldraughtventilation

Overview

Engineering reference data for Natural Draught Ventilation in HVAC systems.

Key Formulas

Sensible Heat

Q=m˙cpΔTQ = \dot{m} c_p \Delta T

Heat causing temperature change.

Latent Heat

Q=m˙hfgΔωQ = \dot{m} h_{fg} \Delta\omega

Heat causing moisture change.

COP (Cooling)

COP=Qc/WCOP = Q_c / W

Coefficient of performance.

Variables

SymbolDescriptionUnit
QQHeat transferW
m˙\dot{m}Mass flow ratekg/s
cpc_pSpecific heat of airJ/(kg·K)
ΔT\Delta TTemperature differenceK

Worked Example: Two-Story House

This example demonstrates calculating air flow due to natural draft in a two-story house.

Given:

  • Height between outlet and inlet air (h): 8 m
  • Outside temperature (t_o): -10 °C
  • Inside temperature (t_i): 20 °C
  • Duct hydraulic diameter (d_h): 0.2 m
  • Duct length (l): 3.5 m
  • Minor loss coefficient sum (Σξ): *1
  • Friction coefficient (λ): *0.019 (for galvanized steel)

1. Calculate Air Densities: Using the density-temperature relation ρ=353273+t\rho = \frac{353}{273 + t}: ρo=353273+(−10)=1.342 kg/m3\rho_o = \frac{353}{273 + (-10)} = 1.342 \, \text{kg/m}^3 ρi=353273+20=1.205 kg/m3\rho_i = \frac{353}{273 + 20} = 1.205 \, \text{kg/m}^3

2. Calculate Duct Air Velocity: v=2g(ρo−ρi)hλlρidh+Σξρi=2⋅9.81⋅(1.342−1.205)⋅80.019⋅3.5⋅1.2050.2+1⋅1.205≈3.7 m/sv = \sqrt{\frac{2 g (\rho_o - \rho_i) h}{\frac{\lambda l \rho_i}{d_h} + \Sigma\xi \rho_i}} = \sqrt{\frac{2 \cdot 9.81 \cdot (1.342 - 1.205) \cdot 8}{\frac{0.019 \cdot 3.5 \cdot 1.205}{0.2} + 1 \cdot 1.205}} \approx 3.7 \, \text{m/s}

3. Calculate Air Flow Volume: q=πdh24⋅v=π⋅(0.2)24⋅3.7≈0.12 m3/sq = \frac{\pi d_h^2}{4} \cdot v = \frac{\pi \cdot (0.2)^2}{4} \cdot 3.7 \approx 0.12 \, \text{m}^3/\text{s}

5 rows
Results for the Natural Draft Example in a Two-Story House
Parameter
Symbol
Value
Heighth8 m
Outside Air Densityρ_o1.342 kg/m³
Inside Air Densityρ_i1.205 kg/m³
Duct Velocityv3.7 m/s
Air Flow Volumeq0.12 m³/s

Source: engineeringtoolbox.com

Note: These equations apply to dry air. For mass flow and energy loss calculations, the effects of air humidity can be significant and must be considered separately.

Major and Minor System Loss

The natural draft force is balanced against the pressure losses in the duct system. The total pressure loss (dp) due to friction (major loss) and fittings (minor loss) is given by:

dp=λ(ldh)ρiv22+Σξ12ρiv2dp = \lambda \left(\frac{l}{d_h}\right) \frac{\rho_i v^2}{2} + \Sigma\xi \frac{1}{2} \rho_i v^2

where:

  • λ\lambda = Darcy-Weisbach friction coefficient
  • ll = length of duct or pipe (m)
  • dhd_h = hydraulic diameter (m)
  • Σξ\Sigma\xi = sum of minor loss coefficients

References

Source: engineeringtoolbox.com