be controlled to stop or go into an "idle" condition. Maximum allowable speed The maximum operating speed for the compressor. Beyond this value stresses may rise above prescribed limits and rotor vibrations may increase rapidly. At speeds above this level the equipment will likely become very dangerous and be controlled to lower speeds. Dimensional analysis To weigh the advantages between centrifugal compressors it is important to compare 8 parameters classic to turbomachinery. Specifically, pressure rise (p), flow (Q), angular speed (N), power (P), density (ρ), diameter (D), viscosity (μ) and elasticity (e). This creates a practical problem when trying to experimentally determine the effect of any one parameter. This is because it is nearly impossible to change one of these parameters independently. The method of procedure known as the Buckingham π theorem can help solve this problem by generating 5 dimensionless forms of these parameters. These Pi parameters provide the foundation for "similitude" and the "affinity-laws" in turbomachinery. They provide for the creation of additional relationships (being dimensionless) found valuable in the characterization of performance. For the example below Head will be substituted for pressure and sonic velocity will be substituted for elasticity. Buckingham Π theorem The three independent dimensions used in this procedure for turbomachinery are: mass (force is an alternative) length time According to the theorem each of the eight main parameters are equated to its independent dimensions as follows: Classic turbomachinery similitude Completing the task of following the formal procedure results in generating this classic set of five dimensionless parameters for turbomachinery. 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. 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