Definition of Pump Specific Speed and Suction Specific Speed

Pump specific speed (Ns) as it is applied to centrifugal pumps is defined in U.S. units as:

Specificspeed is always calculated at the best efficiency point (BEP) with maximum impeller diameter and single stage only. As specific speed can be calculated in any consistent units, it is useful to convert the calculated number to some other system of units. See Table 2-1. The suction specific speed (Nss) is calculated by the same formula as pump specific speed (Ns) but uses NPSHR values in feet in place of head (H) in feet. To calculate pump specific speed (Ns) use full capacity (GPM) for either single- or double-suction pumps. To calculate suction specific speed (Nss) use one half of capacity (GPM) for double-suction pumps.

It is well known that specific speed is a reference number that describes the hydraulic features of a pump, whether radial, semi-axial (Francis type), or propeller type. The term, although widely used, is usually considered (except by designers) only as a characteristic number without any associated concrete reference or picture. This is partly due to its definition as the speed (RPM) of a geometrically similar pump which will deliver one gallon per minute against one foot of head.

To connect the term specific speed with a definite picture, and give it more concrete meaning such as GPM for rate of flow or RPM for rate of speed, two well known and important laws of centrifugal pump design must be borne in mind—the affinity law and the model law (the model law will be discussed later).

The Affinity Law

This is used to refigure the performance of a pump from one speed to another. This law states that for similar conditions of flow (i.e. substantially same efficiency) the capacity will vary directly with the ratio of speed and/or impeller diameter and the head with the square of this ratio at the point of best efficiency. Other points to the left or right of the best efficiency point will correspond similarly. The flow cut-off point is usually determined by the pump suction conditions. From this definition, the rules in Table 2-2 can be used to refigure pump performance with impeller diameter or speed change.

Specific Speed Charts

We have prepared a nomograph (Figure 2-2) relating pump specific speed and suction specific speed to capacity, speed, and head. The nomograph is very simple to use: Locate capacity at the bottom of the graph, go vertically to the rotating speed, horizontally to TDH, and vertically to the pump specific speed. To obtain suction specific speed continue from the rotating speed to NPSHR and vertically to the suction specific speed. Pump specific speed is the same for either single-suction or double-suction designs.

For estimating the expected pump efficiencies at the best efficiency points, many textbooks have plotted charts showing efficiency as a function of specific speed (Ns) and capacity (GPM). We have prepared similar charts, but ours are based on test results of many different types of pumps and many years of experience.

Figure 2-3 shows efficiencies vs. specific speed as applied to end-suction process pumps (API-types). Figure 2-4 shows them as applied to single-stage double-suction pumps, and Figure 2-5 shows them as applied to double-volute-type horizontally split multi-stage pumps.

Figure 2-5 is based on competitive data. It is interesting to note that although the specific speed of multi-stage pumps stays within a rather narrow range, the pump efficiencies are very high, equal almost to those of the double-suction pumps. The data shown are based on pumps having six stages or less and operating at 3,560 RPM. For additional stages or higher speed, horsepower requirements may dictate an increase in shaft size. This has a negative effect on pump performance and the efficiency shown will be reduced.

As can be seen, efficiency increases very rapidly up to Ns 2,000, stays reasonably constant up to Ns 3,500, and after that begins to fall off slowly. The drop at high specific speeds is explained by the fact that hydraulic friction and shock losses for high specific speed (low head) pumps contribute a greater percentage of total head than for low specific speed (high head) pumps. The drop at low specific speeds is explained by the fact that pump mechanical losses do not vary much over the range of specific speeds and are therefore a greater percentage of total power consumption at the lower specific speeds.

Correction for Impeller Trim

The affinity laws described earlier require correction when performance is being figured on an impeller diameter change. Test results have shown that there is a discrepancy between the calculated impeller diameter and the achieved performance. The larger the impeller cut, the larger the discrepancy as shown in Figure 2-6.

Model Law

Another index related to specific speed is the pump modeling law. The “model law” is not very well known and usually applies to very large pumps used in hydroelectric applications. It states that two geometrically similar pumps working against the same head will have similar flow conditions (same velocities in every pump section) if they run at speeds inversely proportional to their size, and in that case their capacity will vary with the square of their size. This is easily understood if we realize that the peripheral velocities, which are the product of impeller diameter and RPM, will be the same for the two pumps if the diameter increase is inversely proportional to the RPM increase. The head, being...