Handbook of air conditioning and refrigeration / Shan K

T Method
planes 1 and 2, and the volume flow rates, and A1 and A2 the cross-sectional areas. The total
pressure loss in duct section 1-2 consists of the duct friction loss �pf1-2 and the dynamic loss of the
main airstream flowing through the diverging tee �p1c,s. The relationship between the total pressure
at planes 1 and 2 can be expressed as
(17.77)
because pt � ps � pv. Ignore the difference between air densities �1 and �2. Let �pf1-2 ��pf,uL1-2. Here L1-2 represents the length of the duct section 1-2, in ft (m). If the static pressures at planes 1
and 2 are equal, that is, ps1 � ps2, then
(17.78)
If v is expressed in fpm and �pf,u in in. WC per 100 ft, � � 0.075 lb/ft 3 , and gc � 32.2
lbm�ft/lbf�s2 ��p
2g
f,uL1-2 �
c
, the mean air velocity of the sized duct section is
C V˙
1 V˙
2
pt1 � pt2 ��pf1-2 ��p1 c,s
2
1 c,s� v 1 1
2gc In SI units,
� 1(v 1 2 � v2 2 )
v 2 � [(1 � C 1 c,s) v 1 2 � 1.6 � 10 5 �pf,uL 1-2] 0.5
v 2 �� (1 � C 1 c,s)v 1 2 � 2�pf,uL 1-2
(17.79)
(17.79a)
with v1 and v2 both in m/s, �pf,u in Pa/m, L1-2 in m, and � in kg/m 3 .
For any duct section between cross-sectional planes n � 1 and n, if the total local loss coefficient
of the duct fittings is Cn, excluding the local loss coefficient C (n�1)c,s, the mean air velocity of
the sized duct section is
vn �� (17.80)
Because vn�1, �n, Ln, and Cn are known values, by using iteration methods, vn can be determined.
The dimension of the duct section and its rounded standard size can also be determined.
The static regain method can be applied only to supply duct systems. It tends to produce a more
even static pressure at the common end of each diverging tee or wye leading to the corresponding
branch takeoff, which is helpful to the system balance. It does not consider cost optimization. The
main duct sections remote from the fan discharge often have larger dimensions than those in the
equal-friction method. Sound level and space required should be checked against determined air
velocity and dimension.
When one is using the static regain method to size air ducts, it is not recommended to allow only
part of static regain to be used in the calculation.
[(1 � C 2 5
(n�1) c,s)vn�1 � 1.6 � 10 �pf,uLn] 1 � C � n
0.5
The T method, first introduced by Tsal et al. (1988), is an optimizing procedure to size air ducts by
minimizing their life-cycle cost. It is based on the tree-staging idea and is therefore called the T
method. The goal of this method is to optimize the ratio between the velocities in all sections of the
duct system. The T method consists of the following procedures:
1. System condensing—condensing various duct sections of a duct system into a single imaginary
duct section having the same hydraulic characteristics and installation costs as the duct system
�
AIR SYSTEMS: AIR DUCT DESIGN 17.55
� 0.5