Natural Draught Ventilation

Overview

Engineering reference data for Natural Draught Ventilation in HVAC systems.

Key Formulas

Sensible Heat

$Q = \dot{m} c_p \Delta T$

Heat causing temperature change.

Latent Heat

$Q = \dot{m} h_{fg} \Delta\omega$

Heat causing moisture change.

COP (Cooling)

$COP = Q_c / W$

Coefficient of performance.

Variables

Symbol	Description	Unit
$Q$	Heat transfer	W
$\dot{m}$	Mass flow rate	kg/s
$c_p$	Specific heat of air	J/(kg·K)
$\Delta T$	Temperature difference	K

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 $\rho = \frac{353}{273 + t}$: $\rho_o = \frac{353}{273 + (-10)} = 1.342 \, \text{kg/m}^3$ $\rho_i = \frac{353}{273 + 20} = 1.205 \, \text{kg/m}^3$

2. Calculate Duct Air Velocity: $v = \sqrt{\frac{2 g (\rho_o - \rho_i) h}{\frac{\lambda l \rho_i}{d_h} + \Sigma\xi \rho_i}} = \sqrt{\frac{2 \cdot 9.81 \cdot (1.342 - 1.205) \cdot 8}{\frac{0.019 \cdot 3.5 \cdot 1.205}{0.2} + 1 \cdot 1.205}} \approx 3.7 \, \text{m/s}$

3. Calculate Air Flow Volume: $q = \frac{\pi d_h^2}{4} \cdot v = \frac{\pi \cdot (0.2)^2}{4} \cdot 3.7 \approx 0.12 \, \text{m}^3/\text{s}$

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:

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

where:

• $\lambda$ = Darcy-Weisbach friction coefficient
• $l$ = length of duct or pipe (m)
• $d_h$ = hydraulic diameter (m)
• $\Sigma\xi$ = sum of minor loss coefficients

References

• Original Source