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H3/4
where His the adiabiatichead， Qis the volumerate， and N the speed.
The specific diameter compares head and flow rates in geometrically similar machines at various diameters
DH1/4
Ds -.... (3-4O)
Q
The flow coefficient is the capacity of the flow rate expressed in dimen-sionless form
Q
. -(3-41)
ND3
The pressure coefficient is the pressure or pressure rise expressed in dimensionless form
H
. -(3-42)
N2D2
The previous equations are some of the major dimensionless parameters.For the flow to remain dynamicallysimilar， all the parameters must remainconstant; however， constancy is not possible in a practicalsense， so one must make choices.
In selecting turbomachines the choice of specific speed and specific dia-meter determines the most suitable compressor (Figure 3-8a) and turbine (Figure 3-8b). It is obvious from Figure 3-8a that high-head and low-flow require a positive displacementunit， a medium-head and medium-flow require acentrifugalunit， and high-flow and low-head require an axial-flow unit. Figure 3-8a also shows the efficiency of the various types of com-pressors. This comparison can be made with the different compressors.While results from Figures 3-8a and 3-8b may vary with actual machines， the results do give a good indication of the type of turbomachine required for the head at the highest efficiency.
Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calcula-tions for skin friction and velocity distribution.
When using dimensional analysis in computing or predicting performancebased on tests performed on smaller-scaleunits， it is not physically possible to keep all parameters constant. The variation of the final results will depend on the scale-up factor and the difference in the fluid medium. It is important in any type of dimensionless study to understand the limit of the parameters and that the geometrical scale-up of similar parameters must remain constant.
128 Gas Turbine Engineering Handbook

Figure 3-8b.Turbine map.(Balje，O.E.， ""A Study of Reynolds Number Effects inTurbomachinery，.. Journal of .n.íneerín. for Power， ASMETrans.， Vol.86， SeriesA， p. 227.)
Compressor and Turbine Performance Characteristics 129
Many scale-ups have developed major problems becausestress，vibration， and other dynamic factors were not considered.
Compressor Performance Characteristics
Compressor performance can be represented in various ways. The com-monly accepted practice is to plot the speed lines as a function of the pressure delivered and the flow. Figure 3-9 is a performance map for a centrifugal compressor. The constant speed lines shown in Figure 3-9 areconstant aero-dynamic speedlines， not constant mechanical speed lines.
...
The actual mass flow rates and speeds are corrected by factor ( ，/. ) and
...
(1/，) respectively， reflecting variations in inlet temperature and pressure. The surge line joins different speed lines where the compressor"s operation becomes unstable. A compressor is in surge when the main flow through acompressor reverses direction for short time intervals， during which the back (exit) pressure drops and the main flow assumes its proper direction. This process is followed bya rise in back-pressure， causing the main flow to reverseagain. If allowed topersist， this unsteady process may result in irreparable damage to the machine. .ines of constant adiabatic efficiency (sometimes called efficiency islands) are also plotted on the compressor map. A condition known as ""choke"" indicates the maximum mass flow rate possible through a compressor at operating speed (Figure 3-9). Flow rate cannotbe increased， since at this point it is beyond Mach one at the minimum area of thecompressor， or a phenomenon known as ""stonewalling""occurs， causing a rapid drop in efficiency and pressure ratio.
　
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