high pressure pumps
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g behind the last stage.
While the Type a pumps, with their back-to-back impellers, do not require hydraulic balancing and therefore suffer no such volumetric losses, both the gap at the centre of the pump and the one ahead of the second set of impellers do cause additional volumetric losses of their own. At both gaps, roughly half of the pumps’ overall head acts as a differential pressure. In addition, hydraulic losses occurring in the crossovers between the stages also require consideration when comparing pump efficiencies. It has been shown6 that the geometric design of the crossovers has a substantial influence on the hydraulic losses occurring there and, hence, on the pumps’ efficiency. Consequently, for the purposes of this comparison, Type a was postulated as having crossovers that cause as little loss of efficiency as possible while still having defensible dimensions. Moreover, the crossover losses postulated in ETAMAX were balanced out by the data given in ref. 6
With regard to the hub ratio, a (relatively low) ν = 0.3 was assumed for both types of pump. Such a hub ratio is very favorable with respect to efficiency and roughly represents the bottom limit for multistage pumps with impeller geometries that are still mechanically implementable.
Finally, in Figure 4
high pressure pumps
, the calculated maximum achievable overall efficiency values are shown as functions of the nominal flow rate, with the same mechanical efficiency assumed for both types. (The intrinsic advantage offered by a Type b pump with medium-lubricated plain bearings and a single shaft seal has therefore been intentionally omitted from the results shown in Figure 3.)
It is plain to see that, in general, both types of pump:
  reach their best-possible efficiencies for a given flow rate when they have an optimal number of stages, and the achievable efficiencies increase along with the nominal flow rate.
All this yields a significant advantage for Type b pumps as compared with Type a pumps:
  the efficiency advantage of the former increases in inverse proportion to the nominal flow rate for one and the same number of stages,
  the best number of stages for a given nominal flow rate can improve the efficiency by as much as two percentage points, and
  the efficiency is even considerably better for Type b for a postulated equal, but not optimized, number of stages.
Summary
The central element of the so-called ‘core hydraulic system’ of RO-base