fluid_mechanics

12.8 Turbines 673
12.7 Fans
Fans are used to
pump air and other
gases and vapors.
When the fluid to be moved is air, or some other gas or vapor, fans are commonly used. Types of
fans vary from the small fan used for cooling desktop computers to large fans used in many industrial
applications such as ventilating of large buildings. Fans typically operate at relatively low rotation
speeds and are capable of moving large volumes of gas. Although the fluid of interest is a
gas, the change in gas density through the fan does not usually exceed 7%, which for air represents
a change in pressure of only about 1 psi 1Ref. 142. Thus, in dealing with fans, the gas density is
treated as a constant, and the flow analysis is based on incompressible flow concepts. Because of
the low pressure rise involved, fans are often constructed of lightweight sheet metal. Fans are also
called blowers, boosters, and exhausters depending on the location within the system; that is, blowers
are located at the system entrance, exhausters are at the system exit, and boosters are located at
some intermediate position within the system. Turbomachines used to produce larger changes in gas
density and pressure than possible with fans are called compressors 1see Section 12.9.12.
As is the case for pumps, fan designs include centrifugal 1radial-flow2 fans, as well as
mixed-flow and axial-flow 1propeller2 fans, and the analysis of fan performance closely follows
that previously described for pumps. The shapes of typical performance curves for centrifugal
and axial-flow fans are quite similar to those shown in Fig. 12.20 for centrifugal and axial-flow
pumps. However, fan head-rise data are often given in terms of pressure rise, either static or total,
rather than the more conventional head rise commonly used for pumps.
Scaling relationships for fans are the same as those developed for pumps, that is, Eqs.
12.32 through 12.35 apply to fans as well as pumps. As noted above, for fans it is common to
replace the head, h a , in Eq. 12.33 with pressure head, p arg, so that Eq. 12.33 becomes
p a
a
rv 2 D 2b a
1 rv 2 D 2b 2
(12.47)
where, as before, the subscripts 1 and 2 refer to any two fans from the family of geometrically
similar fans. Equations 12.47, 12.32 and 12.34, are called the fan laws and can be used to scale
performance characteristics between members of a family of geometrically similar fans. Additional
information about fans can be found in Refs. 14–17.
p a
F l u i d s i n t h e N e w s
Hi-tech ceiling fans Energy savings of up to 25% can be realized
if thermostats in air-conditioned homes are raised by a few
degrees. This can be accomplished by using ceiling fans and
taking advantage of the increased sensible cooling brought on
by air moving over skin. If the energy used to run the fans can
be reduced, additional energy savings can be realized. Most
ceiling fans use flat, fixed pitch, nonaerodynamic blades with
uniform chord length. Because the tip of a paddle moves
through air faster than its root does, airflow over such fan blades
is lowest near the hub and highest at the tip. By making the fan
blade more propeller-like, it is possible to have a more uniform,
efficient distribution. However, since ceiling fans are restricted
by law to operate at less than 200 rpm, ordinary airplane propeller
design is not appropriate. After considerable design effort,
a highly efficient ceiling fan capable of delivering the same
airflow as the conventional design with only half the power has
been successfully developed and marketed. The fan blades are
based on the slowly turning prop used in the Gossamer
Albatross, the human-powered aircraft that flew across the English
Channel in 1979. (See Problem 12.58.)
12.8 Turbines
As discussed in Section 12.2, turbines are devices that extract energy from a flowing fluid. The
geometry of turbines is such that the fluid exerts a torque on the rotor in the direction of its rotation.
The shaft power generated is available to drive generators or other devices.
In the following sections we discuss mainly the operation of hydraulic turbines 1those for
which the working fluid is water2 and to a lesser extent gas and steam turbines 1those for which
the density of the working fluid may be much different at the inlet than at the outlet2.
Although there are numerous ingenious hydraulic turbine designs, most of these turbines can
be classified into two basic types—impulse turbines and reaction turbines. 1Reaction is related to