Specific Speed and Suction Specific Speed

Specific speed (N_s) is a design index primarily used by pump engineers to describe the geometry of pump impellers and to classify them as to their type. It is referred to as a “dimensionless” index, but the term is used loosely, as described below. An understanding of how to calculate and interpret the specific speed for a particular pump provides greater insight into the rea-sons why pump impellers are shaped so differently, why different impel-lers have such a range of flow and head capability, why impelimpel-lers have such differently shaped performance curves, and why there is such wide varia-tion in the value of efficiency at the BEP for different pumps. Furthermore, Chapter 6, Section II, shows how it is possible to use specific speed to select pumps for maximum efficiency.

The formula for pump specific speed N_s, in USCS units, is

N  = N  Q

s H3/4

× (2.23)

where N is the pump speed, rpm; Q is the capacity at BEP, full diameter, gpm; and H is the pump head per stage at BEP, full diameter, ft.

In the U.S. pump industry, the definition of Q in Equation 2.23 when it comes to double suction impellers (covered in Chapter 4, Section II.B) is not treated consistently. For the majority of U.S. pump designers, Q is taken as the full pump capacity. However, a few designers have employed an alterna-tive calculation using one half of the capacity, and U.S. pump standards do allow for this alternative calculation When working with manufacturers of double suction pump impellers, it’s best to clarify this point if specific speed is being discussed.

Note that the above inconsistency in defining Q does not exist in defining Q when It comes to calculating suction specific speed (discussed later in this section), where the value of Q in Equation 2.24 for a double suction impeller

is one half the total pump capacity. European practice uses one half of total pump capacity for both terms with a double suction impeller.

An analysis of the units in Equation 2.23 reveals that the term N_s is not truly dimensionless, although it would become so with the addition of g, the acceler-ation of gravity, into the equacceler-ation’s denominator (taken to the 3/4 power), and with appropriate conversion of the terms of the equation into other equivalent terms. The convention in the centrifugal pump industry is to omit the g term but still treat N_s as dimensionless. However, this creates the unfortunate con-sequence of having a different value for specific speed if SI units are employed in the calculation instead of USCS units. In SI units, the specific speed is desig-nated N_sm and is usually based on capacity expressed in cubic meters per hour and head in meters. Therefore, N_s = 0.8609 N_sm. If capacity is expressed in cubic meters per second and head in meters, then N_s = 51.65 N_sm.

The specific speed of a particular pump can be calculated from the pump curve; picking N, Q, and H off the curve at full diameter, best efficiency point; and applying Equation 2.23. Once N_s for a particular pump has been calculated, its value will not change, even if the pump is run at a different speed. Obviously, if the pump is run at a different speed, the pump’s total head and capacity do change but the specific speed does not change, because it is defined by the equation above. In fact, it is the fact that the specific speed will not change that is the basis for the derivation of the pump affinity laws (Section VIII), which allow the pump performance to be predicted for changes in pump speed or impeller diameter.

Table 2.4 shows the calculated value of specific speed based on Equation 2.23 for some arbitrarily selected pump BEP, full diameter conditions. The data are arranged in order of increasing N_s, the last column in the table. The data are not, however, arranged strictly in order of increasing Q or decreas-ing H (although that is the general trend). This is because the formula for N_s depends on all three variables, rather than on any one variable. For example, the fourth entry in Table 2.4 has the smallest Q value of all the entries. Yet because the value of H is so small for that pump, the value of N_s is higher than the others above it in the table.

Figure 2.19 illustrates typical impeller profiles for the range of specific speeds found for rotodynamic pumps. At the low end of the range, impellers

TABLE 2.4

Specific Speed Ns for Selected Pumps

Q H N N_s

120 300 3550 540

350 300 3550 1250

1000 100 1780 1780

70 20 3550 3140

9000 40 1180 7040

50,000 20 590 13,960

Values of specific speeds

Impeller shrouds Impeller shrouds

Impeller shrouds Impeller shrouds

Impeller hub

Axis of rotation

VanesVanesVanes Vanes Vanes Hub Radial-vane area Francis-vane area Mixed-flow area Axial-flow area

Hub US units US units MetricMetric

Hub Hub

500 10

20 40 60 80 100 150 200 300 400

600 700 800 900 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 15,000 20,000

1500

FIGURE 2.19 Impeller profile vs. Ns. (Courtesy of the Hydraulic Institute, Parsippany, NJ; www.pumps.org.)

develop head by moving the liquid radially from the shaft centerline. These low specific speed pumps are called radial flow pumps. Radial flow pumps have the characteristic of relatively low flow and high head. At the opposite end of Figure 2.19, impellers develop head through axial forces, and so these high specific speed pumps are referred to as axial flow pumps, or propeller pumps. Axial flow pumps have the characteristic of relatively high flow and low head. As N_s increases, the ratio of the impeller outlet diameter to inlet diameter decreases. This ratio becomes 1.0 for a true axial flow impeller.

Pumps that are neither pure radial flow nor pure axial flow are called mixed flow, and represent some combination of radial flow and axial flow. Actually, because the total specific speed range for centrifugal pumps is a continu-ous spectrum from several hundred to about 20,000, pumps with N_s rang-ing from several hundred to about 2000 are often referred to as radial flow, pumps with N_s greater than about 8000 are called axial flow, and pumps with N_s between these two ranges are called mixed flow.

One of the characteristics of specific speed is its effect on the shape and slope of the pump head–capacity and BHP curves. This is illustrated in Figure 2.20. Radial flow pumps have the flattest H–Q curves, with the head at zero flow (called the shutoff head) often no more than about 120% of the head at BEP. The lower the specific speed, the flatter the pump H–Q curve. Note that the slope of the H–Q curve is also affected by certain design parameters in the impeller design such as the number of vanes and the vane angles.

Low specific speed pumps sometimes exhibit a drooping characteristic at shutoff, as illustrated in Figure 2.21. This may lead to unstable operation in certain systems, although it may be perfectly acceptable for use in other circumstances. The dashed lines shown as A and B in Figure 2.21, and the conditions that might lead to instability with a drooping H–Q curve such as shown in this figure, are discussed in Section IX on system head curves.

BHPTotal head

Flow rate

Axial flow head Axial flow BHP Mixed flow head Mixed flow BHP Radial flow head Radial flow BHP

FIGURE 2.20

Slope of H–Q and BHP curves varies with specific speed.

Mixed flow pumps have steeper H–Q curves than radial flow pumps, as illustrated in Figure 2.20. The head at shutoff for mixed flow pumps is on the order of 160% of the head at BEP. Axial flow pumps have the steepest H–Q curves of all, with shutoff head being in the range of 300% of head at BEP.

Another characteristic of some mixed flow pumps is a dip in the H–Q curve (Figure 2.22). This may or may not be a problem, depending on the shape of the system head curve (see Section IX). Some manufacturers simply do not show the dip on their published curves, but stop the H–Q curve short of going back to zero flow, with a notation that the pump should not be run in the unstable region.

The BHP curve shape is also affected by specific speed, as shown in Figure 2.20. Radial flow pumps exhibit increasing horsepower with increas-ing pump flow, with the maximum BHP occurrincreas-ing at the maximum flow at which the pump can operate (called runout). Because most process and transfer pumps are in the radial flow specific speed range, this is the shape of the horsepower curve with which the majority of pump engineers and users are most familiar. Mixed flow pumps have a flatter horsepower curve, and axial flow pumps have their horsepower curve shaped just the opposite of radial flow pumps, with the highest horsepower at the lowest flow. The BHP at shutoff for an axial flow pump is in the range of twice the BHP at BEP. Axial flow pumps are generally not run at low flows, in part because of this higher horsepower at lower flows. Furthermore, if it has a BHP curve that rises toward shutoff, the pump is started with the pump discharge valve open rather than closed or nearly closed, which is the usual valve position when the pump is started. In most cases, the motor for axial flow pumps is not sized to handle the higher horsepower at lower flows. Attempting to start the pump with the valve closed would cause the motor to overload.

(ft)H

Q (gpm)

1 2

3

A

B

FIGURE 2.21 Drooping H–Q curve.

Suction specific speed is a design index used to describe the geometry of the suction side of an impeller, or its NPSH_r characteristics. The term “suction specific speed” is designated N_ss or S, and its formula, very similar to the formula for specific speed, is

S    N  Q NPSHr

= ×

3 4/ (2.24)

As with specific speed, the terms in the equation above are taken at BEP, full diameter. The value of Q in Equation 2.24 for a double suction impeller (see Chapter 4, Section II.B) is taken as one half the total pump capacity.

Typical values of S for most standard designed impellers are in the range of 8000 to 9000. Although there are special impeller designs available from some manufacturers having higher S values (Section VI.C and Chapter 4, Section II.C), various sources recommend that, except in special circum-stances, pumps be chose with S values below a maximum value. A maxi-mum value of S that is often specified is 10,000. Using higher values of S as an impeller design criteria will result in lower NPSH_r, but could introduce problems of recirculation (discussed in Chapter 8, Section III.B.5) if the pump operates at flows less than the BEP flow.

4000 m³/h

0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 18,000 gpm

Feet Meters

Dip in H–Q curve. (Courtesy of Goulds Pumps, Inc., a subsidiary of ITT Corporation.)