Handbook of air conditioning and refrigeration / Shan K

22.34 CHAPTER TWENTY-TWO
�a � air density, lb/ft3 (kg/m 3 )
� air supply volume flow rate, cfm (m3 /s)
Ao � cross-sectional area of free air passage in stairwell, ft2 (m2 )
and the ratio R of the area of free flow passage (orifice) to the interior cross-sectional area of the
stairwell As, in ft2 (m2 V˙
), can be calculated as
R � Ao/As (22.13)
In Eq. (22.12), De, in ft (m), indicates the circular equivalent of the stairwell, and it can be calculated as
De � (22.14)
where Ps � perimeter of the cross-sectional area of the stairwell, ft (m).
The pressure drop coefficient is K. It is mainly a function of the configuration of the stairwell
and the occupant density on the stairs. According to the experimental results of Achakji and Tamura
(1988), for a stairwell tested under the following conditions
4As Ps ● With a cross-sectional area of 134 ft2 (12.5 m2 )
● A floor height of 8.5 ft (2.6 m)
● An occupant density of 0.18 person/ft 2 (2.0 persons/m 2 )
the frictional loss of airflow per floor �p f,s has the following values:
vo, fpm (m/s) �pf,s, in. WC (Pa)
Open-tread stair, bottom injection 879 (4.47) 0.128 (32)
659 (3.35) 0.070 (17.5)
439 (2.23) 0.032 (8)
Closed-tread stair, bottom injection 1055 (5.36) 0.200 (50)
848 (4.31) 0.116 (29)
527 (2.68) 0.05 (12.5)
Here v o represents the air velocity calculated based on the free flow area, in fpm (m/s). The difference
in �p f,s between top and bottom injection is small if other conditions remain the same.
When calculating the system pressure loss of a stairwell pressurization system with multiple injection
�p sy, in in. WC (Pa), as shown in Fig. 22.6, is calculated as
�p sy ��p a � b ��p b � o
(22.15)
where �p a � b, �p b � o � pressure loss between points a and b and points b and o, respectively, in.
WC (Pa) Pressure loss �p b � o usually varies between 0.10 and 0.40 in. WC (25 and 100 Pa) and is
only a small portion of the system pressure. However, it is difficult to calculate accurately because
of complicated airflow paths at various operating conditions and the influence of outdoor conditions.
Pressure loss �p a � b should be calculated between points a and b according to the procedure
described in Chap. 17, including the velocity pressure at the supply inlet, and �p b � o should be estimated
as 0.4 in. WC (100 Pa). The calculated system pressure �p sy should be multiplied by a
safety factor 1.2. The actual �p b � o can be adjusted during acceptance testing.
In a stairwell pressurization system with a bottom single injection, as shown in Fig. 22.8a, the
maximum pressure difference between the stairwell and outdoors often occurs at the top of the
stairwell �p c � o because the cross section of the stairwell is constant. The system pressure can
therefore be calculated as
�p sy ��p a � b ��p b � c ��p c � o
(22.16)