By Esteban Araza
Pump Specific Speed (NS) is a fundamental concept in the study of pumps. One must have a clear and updated understanding of this concept to be able to work with pumps successfully – particularly when dealing with centrifugal pumps.
In pump terminology, Specific Speed (Ns) is an index or dimensionless number that identifies its hydraulic similarity with other pumps. Pumps with the same Ns, or within +/– 3%, even if they were of different size, are considered to be hydraulically similar – the performance curve of one pump being a hydraulic model, or size-factor, of the other.
The pumps must have the same number of stages to be hydraulically similar. For example, a single stage pump with Ns of 1500 is not similar, or size-factor, of a two-stage pump with same Ns of 1500. Additionally, the impeller (or the 1st stage impeller in instances of multistage pumps) must of the same suction design – either they are both single suction impellers, or both are double suction impellers.
[An old approach 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 and has no practical application. It was a poor attempt of defining Ns based on its equation. Ns is not a unit of speed; in fact, its equation has inconsistent units, and is considered dimensionless.]
The symbol Ns comes from the old practice of using N to designate speed in number of revolutions per minute, and the subscript s stands for "specific".
Pump specific speed (Ns) is calculated from the equation: Where:
N = pump speed, in RPMQ = capacity at best efficiency point (BEP) at maximum impeller diameter, in GPMH = head, per stage, at BEP at maximum impeller diameter, in FT
If the flow and head are taken from a pump curve at cut impeller diameter, those values shall first be corrected to their equivalent values at maximum diameter by applying Affinity Laws.
For simplicity the U.S. customary units are used in this article and elsewhere in this site.
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?
Importance of pump specific speed
Specific speed has many important 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 to 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
Francis vane impellers are of the radial flow type.
The figures for Ns and D1/D2 ratio are not restrictive and there can be a big amount of overlap in the numbers as pump designers push the operating range envelope of the different types of pumps.
The 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 - 5% 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.
Specific Speed should be called as Discharge Specific Speed
Persons familiar with the term Suction Specific Speed (Nss) know that Nss is determined by the suction side parameters of a pump, such as the impeller eye area, eye diameter and suction angle; by the suction bay area development of the casing, the suction nozzle size, etc. - hence the word suction in Suction Specific Speed.
Similarly, the Specific Speed (Ns) of a pump is determined by the discharge side parameters of a pump - mainly by the impeller width (or impeller “BA”), volute throat area, and the discharge nozzle size. To a lesser degree, Ns is also affected by the impeller number of vanes and its discharge vane angle. Hence this author aptly refers to this concept as Discharge Specific Speed.
Five things to remember about specific speed:
1. Changing the pump speed does not change its specific speed.2. Specific speed is changed by altering the discharge parameters of a pump – its impeller and volute.3. In calculating specific speed, it is acceptable to use the average head per stage in pumps with 2-stage, or multiple stage, design.4. Specific speed is used in correlation with other hydraulic parameters to perform other calculations such as:
A. determining the recommended volute B-gap of pumpsB. the empirical K factor in radial thrust calculations, etc.
Specific speed is a powerful tool in optimizing pump selection, hydraulic rerate, or designing a new pump. These are discussed in the second part of this article.
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 plant has 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 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?
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
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 obtained by request.
Application of specific speed in hydraulic rerates
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 there-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 layouts on something whose result is 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
D = required impeller diameter, in inchesH = developed head, in feetN = pump speed, in RPM
The derivation of this equation is available on request.
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: 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%
Application of specific speed in new pump design
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.
TYPICAL PUMP CHARACTERESTICS BASED ON SPECIFIC SPEED
Ns range 500 to 4000 4000 to 8000 8000 to 12000
Impeller type Radial flow Mixed flow Axial flow
D1/D2 ratio < 0.5 > 0.5 1.0
Impeller inlet flow axial direction axial direction axial direction
Impeller exit flow radial direction at slant angle axial direction
Flow range low to medium medium to high high to very high
Head range high to medium medium to low low to very low
Efficiency low to high high high to very high
Pump speed high to medium medium to low low to very low
Head developed by centrifugal force centrifugal force axial force or lifting . plus lifting action action of impeller
Minimum impeller 80% 85% 90% diameter, % of D2
Maximum BHP is at end-of-curve at mid of curve at shut-off
Pump starts with close valve close or open open valve
1. D1 - impeller eye diameter.2. D2 - impeller maximum diameter.3. Values given above are estimates - overlaps or variations are to be expected.
Data by Esteban Araza, February 2022