CENTRIFUGAL PUMPS - Modern Design and Practices

Pump specific speed

Pump specific speed (Ns) is one of the most fundamental concepts in the study of centrifugal pumps. One must have a clear understanding of this concept to be able to work with pumps intelligently, yet many have misconceptions about this topic. This article discusses this concept and its applications in the design, selection, operation, upgrade, and hydraulic re-rates of centrifugal pumps.

Specific speed (Ns) is an index, or dimensionless number, that points to the hydraulic similarity of pumps. Pumps with same Ns, even of different make or size, are considered hydraulically similar - one pump being a hydraulic model or size-factor of the other.

An old definition defined Ns as the speed in RPM at which a pump, if sufficiently reduced in size, would deliver a flow rate of one gallon per minute, at one foot of differential head. The definition is useless, has no practical application, and simply a poor attempt at restating its equation. In fact, Ns is not a unit of speed and its equation has inconsistent units, and thus is considered dimensionless

The symbol Ns comes from the old practice of using N to designate speed in number of revolutions and the subscript stands for specific.

Pump specific speed (Ns) is calculated from the equation:

Ns = [N x Q^0.50] / [H^0.75]

where:

N = pump speed, in RPM

Q = capacity at best efficiency point (BEP) at maximum impeller diameter, in GPM

H = head at BEP at maximum impeller diameter, in FT; in multistage pump, the head is the head per stage

Example:

What is the specific speed of a two-stage pump whose capacity and total head at BEP is 400 GPM, and 200 FT, respectively at 1780 RPM?

Solution:

Ns = [1780 x (400)^0.50 / (200/2)^0.75] = 1126

Importance of pump specific speed

The concept of pump specific speed has several significant and practical applications: 

Specific speed identifies the type of pump according to its design and flow pattern. According to this criterion a pump can be classified as radial flow, mixed flow, or axial flow type. A radial flow  pump is one where the impeller discharges the liquid in the radial direction from the pump shaft centerline, an axial flow pump discharges the liquid in the axial direction and a mixed flow pump is one that is a cross between a radial and an axial flow pump design.

Specific speed identifies the approximate acceptable ratio of the impeller eye diameter (D1) to the impeller maximum diameter (D2) in designing a good impeller.

Ns: 500 4000

D1/D2 0.5   -  radial flow pumpNs:    4000 to   8000;   D1/D2 > 0.5   -  mixed  flow pumpNs:    8000 to 12000;   D1/D2 = 1      -  axial  flow pump

These figures for Ns and D1/D2 ratio are not restrictive, rather, there is a big amount of overlap in the figures as pump designers push the envelope of operating range of the different types of pumps.

These types of pumps are also indicative of the manner energy is imparted by the impeller into the liquid. 

In radial flow type, the pressure is developed by the centrifugal action of the impeller. In mixed flow type, the pressure is developed mainly by the centrifugal force in combination with the lifting action of the impeller. And in axial flow type, the pressure is developed solely by the lifting action of the impeller.

Specific speed is used in designing a new size pump by modeling, or size-factoring, a smaller pump with the same specific speed, or within the range of + or - 10% of the specific speed. The performance and construction of the smaller pump are used to predict the performance, and to model the construction, of the new pump.

The specific speed is also a good indicator of pump efficiency. Over the years charts have been developed showing plots of average pump efficiency versus pump specific speed. These charts are valuable tool in comparing pump efficiencies - whether a competitive pump is inferior, efficiency-wise, with another pump, or whether a particular pump shows an usually high efficiency whose accuracy might be doubtful.

Rule-of-Thumb: For similar pumps with about the same capacity at BEP, the pump with the higher specific speed will typically have a higher efficiency also. 

Discharge specific speed

Another term for specific speed is discharge specific speed.

Persons familiar with the term suction specific speed (Nss) know that Nss is affected by parameters on the suction side of a pump, such as the impeller eye area and eye diameter, the suction nozzle size, the suction area development of the casing, etc., hence the word suction in suction specific speed.

Similarly, the specific speed (Ns) of a pump is mainly affected by such factors as the impeller width (or impeller BA), the volute throat area, and by the discharge nozzle size.

To a lesser degree, Ns is also effected by the impeller discharge angle and number of vanes. In short, Ns is affected by parameters on the discharge side of the pump, hence those more familiar with pumps, including CENTRIFUGALPUMP.COM, prefer to call it as discharge specific speed to highlight its difference from suction specific speed.

There are many ways the concept of specific speed can be applied in pump selection.

Here is one example:

A chemical plant has a process requirement for 3,000 gallons per minute (GPM), and 900 feet head. It was estimated that a pump of this size, operating at 3560 RPM, will require a 1,000 HP motor driver based on an assumed pump efficiency of 80%. The plant has two spare 500 HP motors and control panels that they want to use so they would like to buy two smaller pumps. (Besides, the lead time for buying a new 1,000 HP motor is well beyond their start-up schedule.)How should one go about selecting the two pumps on the basis of these facts alone, assuming all other factors have equal weight and are to be ignored?

SOLUTION: The two pumps can be selected to operate either is series, or in parallel connection.

For pumps to operate in series, each pump will be rated for 3,000 GPM and 450 feet head. The pump specific speed is: Ns = [ 3,560 x (3,000)^0.50] / [ (450)^0.75] = 1996

For pumps to operate in parallel, each pump will be rated for 1,500 GPM and 900 feet head. The pump specific speed is: Ns = [ 3,560 x (1,500)^0.50] / [ (900)^0.75] = 839

For simplicity,  this article uses the U.S. system of units in the calculations through-out this web site. Many charts have been published for estimating the efficiency of pumps based on their flow rates and specific speed. It was observed that no matter how well-designed the pumps are their peak efficiency is still correlated to their hydraulic size. (Some would call it the hydrodynamic size.) Based on using one of those efficiency charts (*) , it is estimated that a pump with a flow rate of 3000 GPM and NS of 1996 would have an efficiency of 86%. In comparison, a pump with a flow rate of 1500 GPM and Ns of 839 would have an efficiency of 77% - a significant difference of 9 points. Expectedly, different efficiency charts will show different values of estimated efficiencies but the point to keep in mind is the significant relative difference in the efficiencies.(*) a copy of a typical efficiency chart can be requested from  the author .

Application of specific speed in pump selection

There are many ways the concept of specific speed can be applied in pump selection. Here is one example:

A chemical plant has a process requirement for 3,000 gallons per minute (GPM), and 900 feet head. It was estimated that a pump of this size, operating at 3560 RPM, will require a 1,000 HP motor driver based on an assumed pump efficiency of 80%. The plant has two spare 500 HP motors and control panels that they want to use so they would like to buy two smaller pumps. (Besides, the lead time for buying a new 1,000 HP motor is well beyond their start-up schedule.)How should one go about selecting the two pumps on the basis of these facts alone, assuming all other factors have equal weight and are to be ignored?

SOLUTION:

The two pumps can be selected to operate either is series, or in parallel connection. For pumps to operate in series, each pump will be rated for 3,000 GPM and 450 feet head. The pump specific speed is: Ns = [ 3,560 x (3,000)^0.50] / [ (450)^0.75] = 1996For pumps to operate in parallel, each pump will be rated for 1,500 GPM and 900 feet head. The pump specific speed is: Ns = [ 3,560 x (1,500)^0.50] / [ (900)^0.75] = 839

For simplicity, this article uses the U.S. system of units in the calculations. Many charts have been published for estimating the efficiency of pumps based on their flow rates and specific speed. It was observed that no matter how well-designed the pumps are their peak efficiency is still correlated to their hydraulic size. (Some would call it the hydrodynamic size.)Based on using one of those efficiency charts (*) , it is estimated that a pump with a flow rate of 3000 GPM and NS of 1996 would have an efficiency of 86%. In comparison, a pump with a flow rate of 1500 GPM and Ns of 839 would have an efficiency of 77% - a significant difference of 9 points. Expectedly, different efficiency charts will show different values of estimated efficiencies but the point to keep in mind is the significant relative difference in the efficiencies. A copy of a typical efficiency chart can be requested from the author.

Application of specific speed in hydraulic re-rates

There are many ways the concept of specific speed can be applied in hydraulic re-rates. Here is one example:

An engineering firm was doing a feasibility study on using a radial flow , 20x20x22 (*) pump, in a flood control system. The pump was originally rated for 20,000 gallons per minute (GPM), and 400 feet head, at 1780 RPM. The proposed new rated conditions are 40,000 GPM, 200 feet head, using some existing motors.(*) 20" suction nozzle  x 20" discharge nozzle x 22" maximum impeller diameter pump size. The firm contacted the original vendor (A) to study the feasibility of the hydraulic re-rate. Engineers from vendor A reviewed the operating conditions, pulled out some drawings, reviewed some test curves, and after two days came back with the conclusion that the re-rate is not feasible. Not satisfied with that answer, the firm contacted pump vendor B and made the same inquiry. Within 15 minutes of receiving the inquiry its engineer come back with the same conclusion that the re-rate is not doable.

Questions:

1. Why was the hydraulic re-rate not feasible?

2. Why did it take two days for vendor A, but only 15 minutes for vendor B, to arrive at that conclusion? 

The simple answers: specific speed! And, apparently, the engineer of vendor B knows how to use that concept to respond quickly to its customer inquiry. Let us analyze the situation and, for simplicity, let us assume that the pump should be operating close to its best efficiency point (BEP) at both original and proposed re-rate conditions. Based on its original rated conditions, the pump specific speed would have been: Ns = [1,780 x (20,000)^0.50] / [(400)^0.75] = 2,814^ is used here as an exponential symbol. This value of specific speed confirms that the pump is of radial flow design, even if the actual NS deviates slightly from this value depending on the actual location of its BEP..To meet the re-rate conditions, the pump specific speed (Ns) should be:

Ns = [1,780 x (40,000)^0.50] / [(200)^0.75] = 6,694

Even if a slight deviation from this Ns value is allowed to account for the actual location of its BEP, when re-rated, this Ns value indicates that it will require a pump of mixed flow design to meet the re-rate conditions. There is simply no way a radial flow pump can be modified to become one of a mixed-flow design. The engineer from vendor A failed to realize this and wasted valuable time to review and made some lay-outs on something whose result is quite obvious to the engineer from vendor B.

It is, of course, very simplistic to turn down a potential business opportunity on one factor alone so such conclusion should be validated in some other way. In this situation, one way of validating it is to estimate the impeller diameter required to meet both the original and the re-rate conditions. The impeller diameter required to develop a certain head can be estimated roughly from the equation:

D = [ (3,377,200 x H) / (N)^2 ]^0.50

Where:

D = required impeller diameter, in inches

H = developed head, in feet

N = pump speed, in RPM

The derivation of this equation is available on request from the author.

For the original rated condition, the impeller diameter required to develop 400 feet head is approximately:

D = [ (3,377,200 x 400) / (1,780)^2 ]^0.50 = 20.6

This is approximately 93.6% of the 22 maximum impeller diameter (or, 20.6/22=0.936)

For the re-rate condition, the impeller diameter required to develop 200 feet head is approximately:

D = [ (3,377,200 x 200) / (1,780)^2 ]^0.50 = 14.6

This is approximately 66.4% of the 22 maximum impeller diameter (or, 14.6/22=0.664).

The above figures indicate that, even assuming for the sake of discussion, the pump could be converted from being a radial flow type into a mixed flow type, still the impeller diameter required to meet the reduced head would fall below the acceptable minimum diameter for the pump.

Rule-of-thumb by the author: Typical acceptable minimum impeller diameter, as a percentage of maximum diameter, for various pump types are:radial flow = 80%, mixed flow = 85%, axial flow = 90%

There are many ways the concept of specific speed can be applied in new pump design. Here is one example:

A pump manufacturer was requested to submit a proposal for the design, manufacture, testing, and installation of four identical single stage pumps. Each pump will be rated for 95,000 gallons per minute (GPM) and 1500 feet of head, at 1780 RPM. The manufacturer has not yet built a pump of this size. Given the short time frame with which to submit a proposal, there was no sufficient time to do an initial design concept, predict and simulate a predicted performance, and do some CFD analysis to validate the hydraulic design. 

So how did it respond to the inquiry? By size-factoring, or modeling, an existing and proven pump design based on the concept of specific speed. The application calls for pumps with a specific speed (Ns) of:

Ns = [ 1,780 x (95,000)^0.50] / [ (1,500)^0.75] = 2,276

Next, the manufacturer checked its existing same type product line for the biggest pump it has ever built whose specific speed is within + or - minus 5% of the calculated Ns (or, Ns of 2160 to 2390.) It found a smaller but similar pump type, a 28x30x30 pump, with a specific speed of 2200. Using this pump size as a model, and applying the principles of size-factoring, it was able to offer a newly designed pump, a size 40x40x42, complete with predicted performance, preliminary linear dimensions, and estimated component weights. The procedures for size-factoring will not be discussed in this article but is available on request. The intent of this article is mainly to highlight the application of the specific speed concept in new pump design.

Text below in red color is omitted:

Some hydraulic considerations apply to the impeller and volute design based on specific speed.

On the impeller side, the specific speed dictates the D1/D2 ratio of the impeller, as does whether the impeller is going to be of radial, mixed flow, or axial flow design.

On the volute side, the specific speed dictates the recommended volute B-gap, as does the area ratio and diffusion angle at the diffusion chamber of the volute.

Text above in red color is omitted.

Other resource materials

Chart, Ns vs. typical pump efficiencies

Chart, Ns vs. impeller D1/D2 ratio

Chart, Ns vs. empirical radial thrust factors, K

Chart, Ns vs. volute B-gap

Chart, Ns vs. volute diffusion angle 

Chart, Ns vs. volute diffusion area ratio

Chart, Ns vs. recommended MCSF

Chart, Ns vs. hydrodynamic size and efficiency

Chart, Ns vs. pump losses

Chart, Ns vs. head rise and impeller vane count 

Chart, Ns vs. Nss and pump type

Figure, relative pump size based on hydrodynamic size (Z)

Nomograph, Ns vs. commercially available pump design