## Shutoff

FIGURE 6A and B Characteristic performance curves of a pump stage, related to velocity diagrams sages as illustrated in Figure 6b for "high Q." However, it fails at "low Q," where recirculating flow develops—indicated by a substantial one-dimensional deceleration or reduction in the fluid velocity relative to those passages—that is, W2 V W1. This is analogous to a diffuser with side walls that diverge too much: the main fluid stream separates from one or both walls and flows along in a narrow portion of the passage in a jet—the rest of the passage being occupied with eddying fluid that can recirculate out of the impeller inlet and exit. Consequently, the real outlet velocity diagram at low Q is the one with the dashed lines and the smaller value of Vu 2, rather than the solid-lined, one-dimensional diagram superimposed on it. This in turn reduces the ideal head at the low-Q point of the curves.

To complicate matters further at low Q, one-dimensional application of this "corrected" outlet velocity diagram via Eq. 14 would produce a pump power consumption curve that passes through the origin of Figure 6a. Such a result (assuming negligible external drag power PD), is known not to occur in a real pump. Rather, superimposed on the jet flow pattern just described is recirculating fluid that leaves the impeller, gives up its angular momentum to its surroundings, and re-enters the impeller to be re-energized.

In other words, the one-dimensional simplifications mentioned after Eq. 12 do not hold at low Q; rather, there is an added "recirculation power," which is the UVu-change experienced by the recirculating fluid integrated over each element of re-entering mass flow rate4. The complexity of this recirculation destroys one's ability to interpret pump performance under such conditions by means of velocity diagrams. Instead, a transition is made from empirical correlations for head and power at "shutoff" or zero net flow rate to the high-Q, one-dimensional analysis, enabling one to arrive at the complete set of characteristic curves for efficiency, power, and head illustrated in Figure 6a. In fact, impeller pressure-rise at shutoff is very nearly what would be expected due to the centrifugal effect of the fluid rotating as a solid body, namely pU22/2. The recirculating flow patterns seem to be merely superimposed with little effect on impeller pressure-rise. This recirculation, on the other hand, does produce some additional shutoff pressure rise in the collecting and diffusing passages downstream of the impeller.

## Survival Treasure

This is a collection of 3 guides all about survival. Within this collection you find the following titles: Outdoor Survival Skills, Survival Basics and The Wilderness Survival Guide.

## Post a comment