where the subscript n designates values for the best efficiency point. Figures 8, 9, and 10 show approximate performance curves normalized on the conditions of best efficiency and for a wide range of specific speeds as defined in Table 2. These curves are applicable to pumps of any size because absolute magnitudes have been eliminated. In Figure 8, curves 1 and 2 exhibit a rising head or unstable characteristic where the head increases with increasing flow rate over the lower part of the flow rate range. This may cause instability at heads greater than the shutoff value, particularly if two or more pumps are operated in parallel. Curve 3 exhibits an almost constant head at low flow rates and is often called a flat characteristic. Curves 4 to 7 are typical of a steep or stable head characteristic, in which the head always decreases with increasing flow rate. Although the shape of the head-flow curve is primarily a function of the specific speed, the designer has some control through selection of the vane angle b2 number of impeller vanes nb, and capacity coefficient f = cm2/u2, as described in Section 2.1 (see also Figure 2). For pumps having a single-suction specific speed approximately 5000 (1.83) and higher, the power is at its maximum at shutoff and decreases with increasing flow rate. This may require an increase in the power rating of the driving motor over that required for operation at normal capacity.

Efficiency The efficiency h is the product of three component efficiencies (defined in Section 2.1):

The mechanical efficiency hm accounts for the bearing, stuffing box, and all disk-friction losses including those in the wearing rings and balancing disks or drums if present. The volumetric efficiency hv accounts for leakage through the wearing rings, internal labyrinths, balancing devices, and glands. The hydraulic efficiency hh accounts for liquid friction losses in all through-flow passages, including the suction elbow or nozzle, impeller, diffusion vanes, volute casing, and the crossover passages of multistage pumps. Figure 11 shows an estimate of the losses from various sources in double-suction single-stage pumps having at least 12-in (30-cm) discharge pipe diameter. Minimum losses and hence maximum efficiencies are seen to be in the vicinity of ns ^ 2500 (0.91), which agrees with Figure 6.

Effects of Pump Speed Increasing the impeller speed increases the efficiency of centrifugal pumps. Figure 7 shows a gain of about 15% for an increase in speed from 15,000 to 30,000 rpm. The increases are less dramatic at lower speeds. For example, Ippen9 reported about 1% increase in the efficiency of a small pump, D = 8 in (20.3 cm) and hs = 1992 (0.73), at best efficiency, for an increase in speed from 1240 to 1880 rpm. Within limits, the cost of the pump and driver usually decreases with increasing speed. Abrasion

FLOW RATE q = Q/Q„ FIGURE 8 Head curves for several specific speeds, as defined in Table 2 (Reference 12)

FIGURE 9 Power curves for several specific speeds, as defined in Table 2 (Reference 12)

FIGURE 10 Efficiency curves for several specific speeds, as defined in Table 2 (Reference 12).

FIGURE 10 Efficiency curves for several specific speeds, as defined in Table 2 (Reference 12).

TABLE 2 Characteristic curves as a function of specific speed (Figures 8, 9, and 10)
Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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