*Tenth in a Series*_{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**

*Nomenclature*

## SYMBOL |
## DEFINITION |
## UNITS |
## EQUATION |

β_{1} |

The angle of the inlet edge of the impeller vane, at the point where the vane joins the front shroud, measured in a plane tangent to the shroud surface.

Degrees A_{e}

Eye area. The net flow area just upstream of the impeller vanes.

Square Inches

(π/4)( D12‑ Dh 2)

BEPBest efficiency point. The capacity (flow rate) at which pump efficiency is a maximum.

C_{m1}

The meridional component of the velocity of the liquid just upstream of the impeller vanes.

ft/sec 0.321 Q/A_{e}D

_{1}

Diameter of the circle prescribed by the inlet edge of the impeller vane, at the point where the vane joins the front shroud (Typically equal to the diameter of the impeller eye)

Inches D_{h}

Diameter of impeller hub, shaft or fastener, in the plane defined by the outer points of the leading edges of the impeller vanes.

Inches g Acceleration of gravity 32.2 ft.sec^{2}N Rotative speed of impeller rev/min (rpm) NPSH

_{3}

The NPSH available to the pump coincident with a 3 percent pump head loss

Feet NPSH_{40k}

As defined by Vlaming (3), the NPSH required by a pump, with a stainless steel impeller, pumping cool water, to obtain an impeller life of 40,000 hours

Feet P_{1}

The meridional velocity through the impeller eye required to obtain a right triangle with U_{1} and W_{1}
ft/sec
U_{1 }tan β_{1}
Q_{e}

Capacity (flow rate) through each impeller eye

GPM Q_{bep}

Capacity (flow rate) of the pump when pump efficiency is at its peak

GPM Q_{np}

Capacity (flow rate) through each impeller eye, when C_{m1} = P_{1} (no prerotation, shockless entry)

_{1}A

_{e}S

_{3}

Suction specific speed with cavitation sufficient to cause a 3 percent loss of pump head

RPM-GPM-FEET N Q_{e}

^{0.5}NPSH

_{3}

^{0.75}S

_{3/10}

Approximate suction specific speed with cavitation sufficient to cause a 3 percent loss of pump head, for β_{1} = 10^{0}
RPM-GPM-FEET
S_{40K}

Suction specific speed required to obtain 40,000 hour life, as defined by Vlaming

RPM-GPM-FEET N Q_{e}

^{0.5}/NPSH

_{40K}

^{0.75}U

_{1}

Peripheral velocity of the inlet edge of the impeller vane, at the point where the vane joins the front shroud

ft/sec D_{1}N/229 W

_{1}

Velocity of liquid, relative to the impeller, just upstream of the impeller vanes

ft/sec## References

1. Stepanoff, A. J., Centrifugal and Axial Flow Pumps, John Wiley & Sons, Inc., 1948.

2. Grist, Edward, B.Sc., "Nett Positive Suction Head Requirements for Avoidance of Unacceptable Cavitation Erosion in Centrifugal Pumps," Paper No. C163174, 1974.

3. Vlaming, D. J., "Analysis of Cavitation Provides Advanced NPSH Estimates for Centrifugal Pumps," Oil & Gas Journal, November 19, 1984

4. Ross, Robert R., "Theoretical Prediction of NPSHR for Cavitation Free Operation of Centrifugal Pumps," United Centrifugal Pumps, about 1982.

5. Yedidiah, S., "Factor Pump Size into NPSH Comparisons," Power, June 1973.

6. Henshaw, Terry, "NPSHA-How Much is Enough?", Hydrocarbon Processing, Oct. 2004.

7. Deeprose, W.M. and McNulty, P.J., "Cavitation Noise in Pumps," Proc. 4th Conference of Fluid Machinery, Hungarian Academy of Sciences, Budapest, 1972.

8. Deeprose, W.M., King, N.W., McNulty, F.J., and Pearsall, I.A., "Cavitation Noise, Flow Noise and Erosion," National Engineering Laboratory, Department of Industry, East Kilbride, Glasgow, 1974.

9. Henshaw, Terry L., Advanced NPSH Workshop, PumpUsers EXPO 99, Nashville, TN, Sept. 1999.

10. Gongwer, Calvin A., "A Theory of Cavitating Flow in Centrifugal-Pump Impellers," ASME Hydraulic Div. Semi-Annual Meeting, Milwaukee, WI, June 1940.