Handbook of air conditioning and refrigeration / Shan K

For galvanized steel flat oval ducts with spiral seams, Heyt and Diaz (1975) proposed the
following formula to calculate the circular equivalent for use of the duct friction chart:
Here A is the cross-sectional area of the flat oval duct, in. 2 (mm2 De �
), and is given as
1.55A0.625
P0.25 The dimensions a and b of the flat oval duct are shown in Fig. 17.4c.
17.6 DYNAMIC LOSSES
Elbows
A �
and the perimeter P, in in. (mm), is calculated as
�b2
� b(a � b)
4
AIR SYSTEMS: AIR DUCT DESIGN 17.31
(17.49)
(17.50)
P ��b � 2(a � b) (17.51)
When air flows through duct fittings, such as, elbows, tees, diffusers, contractions, entrances and exits,
or certain equipment, a change in velocity or direction of flow may occur. Such a change leads to flow
separation and the formation of eddies and disturbances in that area. The energy loss resulting from
these eddies and disturbances is called dynamic loss �pdy, in in. WC (Pa). Although a duct fitting is
fairly short, the disturbances it produces may persist over a considerable distance downstream.
In addition to the presence of dynamic loss �pdy, frictional loss �pf occurs when an airstream
flows through a duct fitting. For convenience in calculation, the length of the duct fitting is usually
added to the adjacent duct sections connected with this duct fitting of the same mean air velocity.
When airstreams of the same Reynolds number flow through geometrically similar duct fittings,
that is, in dynamic similarity, the dynamic loss is proportional to their velocity pressure pv. Dynamic
loss may be calculated as
(17.52)
where Co � local loss coefficient or dynamic loss coefficient
� � air density, lb/ft3 (kg/m 3 )
vo � mean air velocity of airstream at reference cross section o, fpm (m/s)
gc � dimensional constant, 32.2 lbm�ft/lbf�s2 �pdy � Copv �
, for SI units, gc � 1
cf � conversion factor, for SI units, cf � 1
C 2
o�vo 2gccf � Co� vo 4005� 2
Because the mean velocity of the airstream may vary at different ends of a duct fitting, C o is always
specified with respect to a velocity of a reference cross section o in the duct fitting.
An elbow is a duct fitting in which the airflow changes direction. Elbows are shown in Figs. 17.9
and 17.10. Consider an elbow that makes a 90° turn in a round duct, as shown in Fig. 17.9a.
Because of the change of airstream direction, centrifugal force is created and acts toward the outer
wall of the duct. When the airstream flows from the straight part of the duct to the curved part, it is
accompanied by an increase in pressure and a decrease in air velocity at the outer wall. At the same
time, a decrease in pressure and an increase in air velocity take place at the inner wall. Therefore, a
diffuser effect occurs near the outer wall, and a bell mouth forms near the inner wall. After turning,
the opposite effect takes place as the airstream flows from the curved part to the straight part of the