fluid_mechanics

12.10 Chapter Summary and Study Guide 691
Corrected mass flow rate, lb m /s
50
49
48
47
46
45
44
43
42
41
Corrected mass flow rate, kg/s
23.0
22.5
22.0
21.5
21.0
20.5
20.0
19.5
19.0
18.5
Corrected speed as percent
of design speed
40
50
60
70
80
90
100
110
40
39
18.0
17.5
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3
Ratio of inlet–total to exit–total pressure
F I G U R E 12.40
Typical compressible flow turbine
performance “map.” (Ref. 20)
Turbine performance
maps are
used to display
complex turbine
characteristics.
Because of the reduction of static pressure in the downstream direction, the gas expands, and
the flow passage area must increase from the inlet to the outlet of this turbine. This is seen in Fig.
12.39b.
Performance data for compressible flow turbines are summarized with the help of parameters
derived from dimensional analysis. Isentropic and polytropic efficiencies 1see Refs. 2, 3, and
202 are commonly used as are inlet-to-outlet total pressure ratios 1p 01p 02 2, corrected rotor speed
1see Eq. 12.552, and corrected mass flowrate 1see Eq. 12.542. In Fig. 12.40 is shown a compressible
flow turbine performance “map.”
12.10 Chapter Summary and Study Guide
turbomachine
axial-, mixed-, and
radial-flow
velocity triangle
angular momentum
shaft torque
Euler turbomachine
equation
shaft power
centrifugal pump
pump performance
curve
overall efficiency
system equation
head rise
coefficient
power coefficient
flow coefficient
pump scaling laws
specific speed
impulse turbine
reaction turbine
Pelton wheel
Various aspects of turbomachine flow are considered in this chapter. The connection between fluid
angular momentum change and shaft torque is key to understanding how turbo-pumps and turbines
operate.
The shaft torque associated with change in the axial component of angular momentum of a
fluid as it flows through a pump or turbine is described in terms of the inlet and outlet velocity
triangles diagrams. Such diagrams indicate the relationship among absolute, relative, and blade
velocities.
Performance characteristics for centrifugal pumps are discussed. Standard dimensionless
pump parameters, similarity laws, and the concept of specific speed are presented for use in pump
analysis. How to use pump performance curves and the system curve for proper pump selection
is presented. A brief discussion of axial-flow and mixed-flow pumps is given.
An analysis of impulse turbines is provided, with emphasis on the Pelton wheel turbine. For
impulse turbines there is negligible pressure difference across the blade; the torque is a result of
the change in direction of the fluid jet striking the blade. Radial-flow and axial-flow reaction turbines
are also briefly discussed.
The following checklist provides a study guide for this chapter. When your study of the entire
chapter and end-of-chapter exercises has been completed you should be able to
write out meanings of the terms listed here in the margin and understand each of the related
concepts. These terms are particularly important and are set in italic, bold, and color type in
the text.
draw appropriate velocity triangles for flows entering and leaving given pump or turbine
configurations.