_{3}. Therefore, although providing additional NPSHA will increase pump head and efficiency, it will also push the NPSHA toward, or into, the range where maximum erosion rate occurs to the impeller.

Vlaming (3) concluded that it was not reasonable to eliminate all cavitation in an impeller, and settled on 40,000 hours (five years) as a reasonable life of an impeller. His NPSH recommendations for obtaining 40,000 hours with a properly designed, stainless steel impeller pumping cool water can be condensed to the following equation:

NPSHR_{40K} = 1.2 **(13‑8)**

This equation applies only to the capacity (flow rate), which results in non‑prerotating, shockless entry of the pumpage into the impeller vanes.* That capacity is normally about 20 percent higher than the best efficiency capacity, but can be even higher (1).

**Equation 13‑8** can be rewritten, in terms of U_{1} and β_{1}, as follows:

NPSHR_{40K} = **(13‑9)**

Converting to suction specific speed results in:

S_{40K} = 8150 ** (13-10)**

**Equation 13‑10** is plotted in **Figure 1**, for Dh = 0 and β_{1} = 17˚(which is the angle for which S_{40K} is maximum). Vlaming stated that his experience did not exceed a U_{1} of 220 ft/sec, so the S_{40K} values above 220 ft/sec must be recognized as extrapolated.

Conditions that apply to the 40,000 hour curve are:

1. Cool water

2. Stainless steel impeller

3. Impeller vanes properly twisted and tapered. (For plain vanes, S is lower.)

4. β_{1} = 17˚

5. No‑prerotation, shockless‑entry capacity

6. No hub, shaft or fastener blocking part of the eye. If the eye is partially blocked by a hub, shaft or fastener, multiply S from the figure by (1-(D_{h}/D_{1}) ^{2})^{0.5}

This author's work (9), supported by Yedidiah (5), demonstrated that, based on the 3 percent head drop, the approximate suction specific speed, calculated at Q_{bep}, varies with U_{1} as follows:

S_{3} = C U_{1}^{ 0.375} ** (13‑11)**

Gongwer's work (10) allowed this author to determine that S_{3} reaches its peak value when β_{1} = 10˚. With β_{1} = 10˚, **Equation 13‑11** becomes:

S_{3} = 2520 U_{1 }^{0.375} ** (13‑12)**

**Equation 13‑12** is also plotted in **Figure 1**.

Note that the 3 percent head drop curve is based on Q_{bep} and β_{1} = 10˚, and the 40,000 hour curve is based on Q_{np} and β_{1} = 17˚, so the two curves are not directly comparable. However, the figure does provide a general comparison, and it emphasizes the diversion of S values as U_{1} increases. Any S value selected from the top curve could result in a problematic pump.

^{*} Vlaming provided a set of curves for estimating NPSHR_{40K} for capacities above and below the non-prerotating shockless capacity, which showed that the NPSHR_{40K} is higher at all capacities other than shockless.

**Figure 1**