The natural draft force will be balanced to the major and minor loss in ducts , inlets and outlets. The major and minor loss in the system can be expressed as
dp = λ (l / d h ) ( ρ r v 2 / 2) + Σξ 1/2 ρ r v 2 (3)
where
dp = pressure loss (Pa, N/m 2 , lb f /ft 2 )
λ = Darcy-Weisbach friction coefficient
l = length of duct or pipe (m, ft)
d h = hydraulic diameter (m, ft)
Σ ξ = minor loss coefficient (summarized)
Equation (1) and (3) can be combined to express the air velocity through the duct
v = [(2 g ( ρ o - ρ r ) h ) / ( λ l ρ r / d h + Σ ξ ρ r )] 1/2 (4)
Equation (4) can also be modified to express the air flow volume through the duct
q = π d h 2 /4 [(2 g ( ρ o - ρ r ) h ) / ( λ l ρ r / d h + Σ ξ ρ r )] 1/2 (5)
where
q = air volume (m 3 /s)
The calculator below can be used to calculate the air flow volume and velocity in a duct similar to the drawing above. The friction coefficient used is 0.019 which is appropriate for normal galvanized steel ducts.
Calculate the air flow caused by natural draft in a normal family house with two floors. The height of the hot air column from ground floor to outlet air duct above roof is approximately 8 m . The outside temperature is -10 o C and the inside temperature is 20 o C .
A duct of diameter 0.2 m goes from 1. floor to the outlet above the roof. The length of the duct is 3.5 m . Air leakages through the building are neglected. The minor coefficients are summarized to 1.
The density of the outside air can be calculated as
ρ o = (1.293 kg/m 3 ) (273 K) / ((273 K) + (-10 o C))
= 1.342 kg/m 3
The density of the inside air can be calculated as
ρ r = (1.293 kg/m 3 ) ( 273 K) / ((273 K) + (20 o C))
= 1.205 kg/m 3
The velocity through the duct can be calculated as
v = [(2 (9.81 m/s 2 ) ((1.342 kg/m 3 ) - (1.205 kg/m 3 )) (8 m)) / ( 0.019 (3.5m)(1.205 kg/m 3 )/(0.2 m) + 1 (1.205 kg/m 3 ) )] 1/2
= 3.7 m/s
The air flow can be calculated as
q = (3.7 m/s) 3.14 (0.2 m) 2 / 4
= 0.12 m 3 /s
that these equations can be used for dry air, not for mass flow and energy loss calculations where air humidity may have vast effects.
Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more.
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The size of chimney vs. boiler's heat load.
Chimneys and fireplaces for stoves burning wood or coal as fuel.
Friction loss coefficients in pipes, tubes and ducts.
The Darcy-Weisbach equation can be used to calculate the major pressure and head loss due to friction in ducts, pipes or tubes.
Minor pressure and head loss in pipes vs. equivalent length in tubes and duct systems.
Recommended air velocities in HVAC ducts.
Estimated infiltration heat losses from buildings.
The stack or flue effect occurs when the outdoor temperature is lower than indoor temperature.
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