Editing Centrifugal compressor (section)

=== Classic turbomachinery similitude ===

Completing the task of following the formal procedure results in generating this classic set of five dimensionless parameters for turbomachinery.<ref name="Shepherd" /> Full-similitude is achieved when each one of the 5 Pi-parameters is equivalent when comparing two different cases. This of course would mean the two turbomachines being compared are similar, both geometrically and in terms of performance.

{| class="wikitable"
|+ Table of Classic dimension-less similitude parameters
|-
| 1
| Flow-coefficient
| <math> \Pi_1 = </math>
| <math> \frac{Q}{N D^3}</math>
|-
| 
| Head-coefficient
| <math> \Pi_2 = </math>
| <math> \frac{g H}{N^2 D^2}</math>
|-
| 3
| Speed-coefficient
| <math> \Pi_4 = </math>
| <math> \frac{N D}{a}</math>
|-
| 4
| Power-coefficient
| <math> \Pi_3 = </math>
| <math> \frac{P}{\rho N^3 D^5}</math>
|-
| 5
| Reynolds-coefficient
| <math> \Pi_5 = </math>
| <math> \frac{\rho N D^2}{\mu}</math>
|}

Turbomachinery analysts gain tremendous insight into performance by comparisons of the 5 parameters shown in the above table. Particularly, performance parameters such as efficiencies and loss-coefficients, which are also dimensionless. In general application, the Flow-coefficient and Head-coefficient are considered of primary importance. Generally, for centrifugal compressors, the Speed-coefficient is of secondary importance while the Reynolds-coefficient is of tertiary importance. In contrast, as expected for pumps, the Reynolds-coefficient becomes of secondary importance and the Speed-coefficient of tertiary importance. It may be found interesting that the Speed-coefficient may be chosen to define the y-axis of Figure 1.1, while at the same time the Reynolds coefficient may be chosen to define the z-axis.