Specific speed (Ns) is a dimensionless number, or index, that identifies the
hydraulic similarity of pumps. Pumps with practically the same Ns, even of
different make or size, are considered hydraulically similar - one pump being a
hydraulic size-factor or model of the other.
[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, 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
The symbol Ns comes from the old practice of using N to designate speed in
number of revolutions and the subscript s stands for "specific".
Pump specific speed (Ns) is calculated from the equation:
Ns = [N x Q^0.50] / [H^0.75]
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
For simplicity the U.S. customary units are used in this article.
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?
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
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
Ns: 500 to 4000; D1/D2 < 0.5 - radial flow pump
Ns: 4000 to 8000; D1/D2 > 0.5 - mixed flow pump
Ns: 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 - 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
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
To a lesser degree, Ns is also effected by the number of impeller vanes and
their discharge angle. In short, Ns is affected by parameters on the discharge
side of the pump, hence CENTRIFUGALPUMP.COM and The EMA Project refers
to it as discharge specific speed to highlight its difference from suction
Application of specific speed in pump selection
There are many ways the concept of specific speed can be applied in pump
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] = 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, CENTRIFUGALPUMP.COM 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
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
D = [ (3,377,200 x H) / (N)^2 ]^0.50
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
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,
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,
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
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
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.
[This is a raw article that is undergoing revision. Please bookmark this page and come back
later to read the latest update.]
Pump Specific Speed
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