Fan laws can be used in many cases to estimate performance for small changes in speed and flow, but care and judgment must be used. Using these laws is risky, and should be done cautiously.
The fan laws state that inlet volume is proportional to speed, and that head is proportional to the speed squared. These laws are based on the assumption that the fluid is non-compressible. Fan laws may be inaccurate when testing the performance level of multistage compressors at off-design speeds. ( Figure 200-16 illustrates this error.) Similar errors could be incurred in estimating surge volumes using the fan laws.
To illustrate, assume a 10% mass flow reduction to the first stage. If all other inlet conditions remain the same, volume flow will also be reduced by 10%. Since mass flow was reduced by 10%, the second stage will also see a 10% flow reduction. (Figure 200-13 shows that flow reduction results in an increased discharge pressure from the first stage.) Since volume is inversely proportional to pressure, the volume to the second stage will be reduced further in proportion to the increased discharge pressure from the first stage. The second stage will have a similar effect on the third stage and so on. Deviation from the ideal gas laws will increase significantly as the number of compressor stages increases.