Centrifugal pump design and manufacturing has been around for over 200 years. If there were an ideal impeller vane number, it seems likely someone would have discovered it by now. However, just because an ideal vane number has not yet been established is not sufficient reason to consider it doesn’t exist.
Single stage pump and first stage, high suction performance impellers tend to have fewer vanes – often 3, 4 or 5. Multistage pump series stages, pipeline pumps and large, high efficiency pumps tend to have 7 or more impeller vanes. Vane number might be dictated by special application requirements. Such is the case with solids handling impellers which often have just 2 or 3 vanes and sometimes only 1.
I recall an anecdote I heard decades ago from a senior hydraulic engineer that only 3-vane impellers are found across the entire range of specific speeds. The problem, especially for high speed, high head pumps, is a 3-vane impeller produces significantly less head than, say, a 7-vane impeller. Head rise to shutoff and pressure pulsations are also issues.
But thinking about this quasi-factual anecdote, I’ve occasionally considered that an ideal vane number does indeed exist. If there is a magic vane number, what is it? If there could be only one impeller vane number for all pumps, what would it be? Pump engineers think these kinds of thoughts.