Handbook of air conditioning and refrigeration / Shan K

The fan power input on the fan shaft, often called the brake horsepower P f, can be calculated as
(15. 6)
When �p tf is expressed in Pa, fan volume flow rate in m 3 /s, fan total efficiency � t is the ratio of air
power P air to fan power input P f on the fan shaft, dimensionless, then constant C � 1, and fan
power input P f is expressed in W. If �p tf is expressed in in. WC, fan volume flow rate is in cfm, fan
total efficiency � t is a dimensionless ratio, then constant C � 6356 and fan power input on the shaft
P is in hp.
From Eq. (15.6), fan total efficiency can also be calculated as
(15.7)
Fan total efficiency is a combined index of aerodynamic, volumetric, and mechanical efficiencies of
a fan. Fan static efficiency � s is defined as the ratio of the product of the fan static pressure �p sf, in
in. WC, and the fan volume flow rate to the fan power input, i.e.,
Air Temperature Increase through Fan
Fan Performance Curves
AIR SYSTEMS: COMPONENTS—FANS, COILS, FILTERS, AND HUMIDIFIERS 15.5
P f � �p tfV˙ f
C� t
� t � �p tf V˙ f
� s � �p sf V˙ f
(15.8)
If air density � a � 0.075 lb/ft 3 , the specific heat of air c pa � 0.243 Btu/lb�°F, and 1 hp � 42.41
Btu/min, the relationship between fan power input and the air temperature increase when it flows
through the fan �T f, in °F, is given as
Pf �
Combining Eqs. (15.6) and (15.9), then, gives
V˙
f �acpa �Tf 42.41
�Tf � 0.00667�ptf � 0.37�ptf � ac pa� t
� �p tfV˙ f
6356P f
6356P f
6356� t
(15.9)
(15.10)
This air temperature rise in a fan when air flows through it is caused by the compression process
and energy losses that occur inside the fan. When air flows through the air duct, duct fittings, and
equipment, the duct friction loss and dynamic losses cause a temperature increase as mechanical
energy is converted to heat energy. However, this temperature increase in the air duct is offset by a
temperature drop caused by the expansion of air due to the reduction of static pressure along the
airflow. Therefore, it is more convenient to assume that the air temperature rise occurs because of
the friction and dynamic losses along the airflow only when air is flowing through the fan.
Fan characteristics can be described by certain interrelated parameters such as volume flow rate,
pressure, power, and efficiency. These characteristics are depicted graphically by fan performance
curves in Fig. 15.2.
Fan characteristic curves usually set the volume flow rate , in cfm (m3 V˙
/s), as the abscissa; and
fan total pressure �p tf, fan static pressure �p sf, fan power input P f, or fan total efficiency � t as the
ordinate. In Fig. 15.2, there are three pressure-volume flow characteristic curves:
� t