Handbook of air conditioning and refrigeration / Shan K

Stack Effect
where � � air density, lb/ft 3 . For air density � � 0.075 lb/ft 3 , if the velocity pressure p v is
expressed in in. WC and the air velocity in fpm or ft/min, according to Eq. (17.9),
and v � 4005 √pv pv �� (17.10)
v
In SI units, if v is expressed in m/s and � in kg/m 3 , then p v is in Pa, and p v can be calculated by
Eq. (17.9). For SI units, g c � 1.
Total Pressure. At any cross-sectional plane perpendicular to the direction of the airflow, the total
pressure of the airstream p t is defined as the sum of the static pressure p s and the velocity pressure
p v, that is,
pt � ps � pv pv � pt � ps (17.11)
From Eq. (17.11) velocity pressure pv is also a kind of pressure difference. The units of pt must be
consistent with ps and pv. In I-P units, it is also indicated in inches WC or WG and in SI units in Pa
absolute (abs.) or gauge (g). Substituting Eq. (17.11) into Eq. (17.7), we see that
(17.12)
Equation (17.12) is another primary equation that relates the pressure loss from friction and other
sources, �p f, and the total pressure p t1 and p t2 at two cross sections of the air duct system.
When an air duct system has an elevation difference and the air temperature inside the air duct is
different from the ambient air temperature, the stack effect exists. It affects airflow at different elevations.
During a hot summer day, when the density of the outdoor air is less than the density of the
cold supply air inside the air duct, the pressure exerted by the atmospheric air column between z 1
and z 2, as shown in Fig. 17.1, is given as
where � o � mean density of the ambient air, lb/ft 3 (kg/m 3 ). And the pressure exerted by the air
column inside the air duct between z 1 and z 2 is
where � i � mean density of the supply air inside the air duct, in lb/ft 3 (kg/m 3 ). If the differences
between the densities inside the air ducts, � 1 and � i, and � 2 and � i, are ignored, substituting these
relationships into Eq. (17.6) yields
and
� v
60� 2
� 5.192(2p vg c)
p 1 � � 1v 1 2
2g c
�
� 2gz 2 � � 1gz 1
g c
� g(� o � � i)(z 2 � z 1)
g c
p t1 � g(� o � � i)(z 2 � z 1)
g c
� 5.192 � 2 � 32.2 p v
0.075
p t1 � p t2 ��p f
p at1 � p at2 � � o g(z 2 � z 1)
g c
� � i g(z 2 � z 1)
g c
AIR SYSTEMS: AIR DUCT DESIGN 17.5
4005� 2
� p 2 � � 2v 2 2
2g c
� p t2 ��p f
� 4458p v
��p f
(17.13)
(17.14)