EN 17038-1:2019
(Main)Pumps - Methods of qualification and verification of the Energy Efficiency Index for rotodynamic pump units - Part 1: General requirements and procedures for testing and calculation of Energy Efficiency Index (EEI)
Pumps - Methods of qualification and verification of the Energy Efficiency Index for rotodynamic pump units - Part 1: General requirements and procedures for testing and calculation of Energy Efficiency Index (EEI)
This document describes a methodology to evaluate energy efficiency performance of pump units based on a non-dimensional numerical value called Energy Efficiency Index (EEI).
This document covers pump units consisting of:
- one single or several rotodynamic water pump(s), including where integrated in other products, and driven by a motor system, consisting of an electrical motor, and either:
- a terminal box which only enables to operate the pump unit at constant motor stator frequency and thereby (nearly) constant rotational speed, or
- a CDM (Complete Drive Module) which enables to operate the pump unit at variable rotational speed depending on a varying demand of flow rate and/or discharge or differential pressure.
NOTE A CDM is also often called VSD (Variable Speed Drive).
Pump units as defined above are treated as extended products in respect to their energy efficiency.
Pumpen - Methoden zur Qualifikation und Verifikation des Energieeffizienzindexes für Kreiselpumpen - Teil 1: Allgemeine Anforderungen und Vorgehensweisen zur Prüfung und Berechnung des Energieeffizienzindexes (EEI)
Dieses Dokument beschreibt die Methodik, die Energie-Effizienz Leistung von Pumpenaggregaten auf der Basis einer dimensionslosen, numerischen Größe zu bewerten, die Energieeffizienzindex (EEI) genannt wird.
Dieses Dokument behandelt Pumpenaggregate, bestehend aus:
- einer einzelnen oder mehreren Kreiselpumpe(n) für Wasser, auch wenn sie in andere Produkte integriert sind, angetrieben von einem Motorsystem aus einem Elektromotor und
- entweder einem Kabelabschlusskasten, der nur den Betrieb des Pumpenaggregats bei konstanter Frequenz des Stators und daher (nahezu) konstanter Drehzahl ermöglicht,
- oder einem vollständigen Antriebsmodul (CDM, en: Complete Drive Module), das den Betrieb des Pumpenaggregats bei variabler Drehzahl entsprechend des schwankenden Bedarfsvolumenstroms und/oder der Entnahme bzw. des Differenzdrucks erlaubt.
ANMERKUNG Ein CDM wird oftmals auch drehzahlgeregelter Antrieb (VSD, en: Variable Speed Drive) genannt.
Pumpenaggregate entsprechend der obenstehenden Definition werden hinsichtlich ihrer Energieeffizienz als erweiterte Produkte behandelt.
Pompes - Méthodes de qualification et de vérification de l'indice de rendement énergétique des groupes motopompes rotodynamiques - Partie 1 : Exigences générales et procédures d'essai et de calcul de l'indice de rendement énergétique (EEI)
Le présent document décrit une méthode pour évaluer la performance énergétique des groupes motopompes qui se base sur une valeur numérique sans dimension appelée l’indice de rendement énergétique (EEI).
Le présent document s'applique aux groupes motopompes constitués des éléments suivants :
- une ou plusieurs pompe(s) à eau rotodynamique(s), intégrée(s) ou non dans d'autres produits et entraînée(e) par un système motorisé comprenant un moteur électrique ; et soit
- une boîte à bornes permettant simplement de faire fonctionner le groupe motopompe à une fréquence constante du stator de moteur et donc à une vitesse de rotation (quasi-)constante ; soit
- un CDM (module d'entraînement complet) permettant de faire fonctionner le groupe motopompe à une vitesse de rotation variable en fonction des différents besoins de débit et/ou de décharge ou de pression différentielle.
NOTE 1 Un CDM est également appelé souvent « entraînement à vitesse variable » (VSD).
Les groupes motopompes, tels qu'ils sont définis ci-dessus, sont considérés comme des produits globaux au regard de leur rendement énergétique.
Črpalke - Metode za kvalifikacijo in verifikacijo indeksa energijske učinkovitosti centrifugalnih črpalk - 1. del: Splošne zahteve in postopki za preskušanje in izračun indeksa energijske učinkovitosti (EEI)
Ta dokument zajema črpalke, sestavljene iz:
– ene ali več centrifugalnih vodnih črpalk, vključno z vgrajenimi črpalkami v ostalih proizvodih, pri čemer jih poganja motorni sistem, ki je sestavljen iz električnega motorja in
– priključne omarice, ki samo omogoča obratovanje črpalke s stalno statorsko frekvenco motorja in posledično (skoraj) stalno vrtilno hitrostjo,
– ali celovitega pogonskega modula (CDM), ki omogoča obratovanje črpalke pri spremenljivi vrtilni hitrosti glede na spreminjajoče se zahteve pretoka in/ali praznjenja ali diferenčnega tlaka.
OPOMBA 1: Motorni sistem, ki je sestavljen iz električnega motorja in celovitega pogonskega modula, se imenuje tudi pogonski sistem (PDS).
OPOMBA 2: Celovit pogonski modul se pogosto imenuje tudi pogon s spremenljivo hitrostjo (VSD).
Črpalke, kot so opredeljene zgoraj, se v zvezi z energetsko učinkovitostjo obravnavajo kot razširjeni proizvodi.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-julij-2019
Črpalke - Metode za kvalifikacijo in verifikacijo indeksa energijske učinkovitosti
centrifugalnih črpalk - 1. del: Splošne zahteve in postopki za preskušanje in
izračun indeksa energijske učinkovitosti (EEI)
Pumps - Methods of qualification and verification of the Energy Efficiency Index for
rotodynamic pumps units - Part 1: General requirements and procedures for testing and
calculation of energy efficiency index (EEI)
Pumpen - Methoden zur Qualifikation und Verifikation des Energieeffizienzindexes für
Kreiselpumpen - Teil 1: Allgemeine Anforderungen und Vorgehensweisen zur Prüfung
und Berechnung des Energieeffizienzindexes (EEI)
Pompes - Méthodes de qualification et de vérification de l'indice de rendement
énergétique des groupes motopompes rotodynamiques - Partie 1 : Exigences générales
et procédures d'essai et de calcul de l'indice de rendement énergétique (EEI)
Ta slovenski standard je istoveten z: EN 17038-1:2019
ICS:
23.080 Črpalke Pumps
27.015 Energijska učinkovitost. Energy efficiency. Energy
Ohranjanje energije na conservation in general
splošno
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN 17038-1
EUROPEAN STANDARD
NORME EUROPÉENNE
May 2019
EUROPÄISCHE NORM
ICS 23.080
English Version
Pumps - Methods of qualification and verification of the
Energy Efficiency Index for rotodynamic pump units - Part
1: General requirements and procedures for testing and
calculation of Energy Efficiency Index (EEI)
Pompes - Méthodes de qualification et de vérification Pumpen - Methoden zur Qualifikation und Verifikation
de l'indice de rendement énergétique des groupes des Energieeffizienzindexes für Kreiselpumpen - Teil 1:
motopompes rotodynamiques - Partie 1 : Exigences Allgemeine Anforderungen und Vorgehensweisen zur
générales et procédures d'essai et de calcul de l'indice Prüfung und Berechnung des Energieeffizienzindexes
de rendement énergétique (EEI) (EEI)
This European Standard was approved by CEN on 15 July 2018.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 17038-1:2019 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
Introduction . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions, symbols and subscripts . 5
4 Energy Efficiency Index (EEI) calculations . 9
4.1 General information and explanation on EEI . 9
4.2 Weighted-average value of the electric power input . 9
4.3 The reference electric power input P . 10
1, ref
5 Qualification of pump unit types in respect to their Energy Efficiency Index . 10
5.1 General remarks . 10
5.2 Qualification methods . 11
6 Verification of the Energy Efficiency Index for pump units . 12
6.1 General remarks . 12
6.2 Procedure and decision . 12
Annex A (informative) Mean value and confidence interval of the Energy Efficiency Index EEI . 14
Annex B (informative) Methods recommended for the qualification of a pump unit type by
test . 19
B.1 General remarks . 19
B.2 Determination of the mean value of EEI of a pump unit type population from a test
on only one test pump unit . 19
B.3 Determination of the mean value of EEI of a pump unit type population from a
sample test of M pump units . 20
Annex C (informative) Application of mathematical statistics on tests . 23
C.1 Purposes of applying statistics in the frame of qualification and verification . 23
C.2 Normal or Gaussian distribution . 23
C.3 Confidence interval . 24
C.4 Outlier test . 25
Annex D (informative) Measurement uncertainties . 27
Annex E (informative) The probability of the result of the verification procedure . 30
E.1 General . 30
E.2 Probability that the conformity to law is confirmed by verification tests . 32
E.3 Probability that a numerical value of indicated by the responsible company is
confirmed by verification tests . 33
Bibliography . 34
European foreword
This document (EN 17038-1:2019) has been prepared by Technical Committee CEN/TC 197 “Pumps”,
the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by November 2019, and conflicting national standards
shall be withdrawn at the latest by November 2019.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Introduction
This document is the first part of a series of standards describing a methodology to evaluate energy
efficiency performance of pump units, comprising the pump, the motor with or without frequency
converter, based on a non-dimensional numerical value called Energy Efficiency Index (EEI). An EEI
allows the comparison of different pump sizes and types with one common indicator. Physical
influences such as pump size, specific speed, pump unit part-load operation, motor-efficiency
characteristic and frequency converter influence are implemented into this indicator.
This standard series covers pump units which component wise can be placed on the market and
assembled into a pump unit or are placed on the market as one single product. To cover these two cases
a semi-analytical model has been developed in order to derive the EEI based on nominal data of the
components only. This case happens for example when an assembler of the components builds the
pump unit on site and consequently a product test cannot be done by for this assembler or when a
manufacturer is quoting a pump-unit which uses a combination of components not previously built.
This particular standard gives an overview of the basic concept of EEI (Clause 4), basic concepts of flow-
time profiles and reference pressure control curves, the qualification (Clause 5) of a pump unit type
regarding an EEI and the verification of EEI values (Clause 6) given for a pump unit type either by
measurement or calculation.
Specific requirements for testing, a calculation method for an EEI, the so called semi-analytical model of
a complete pump unit, specific flow-time profiles and reference control curves are given in the
subsequent parts of this standard series.
1 Scope
This document describes a methodology to evaluate energy efficiency performance of pump units based
on a non-dimensional numerical value called Energy Efficiency Index (EEI).
This document covers pump units consisting of:
— one single or several rotodynamic water pump(s), including where integrated in other products,
and driven by a motor system, consisting of an electrical motor, and either:
— a terminal box which only enables to operate the pump unit at constant motor stator frequency
and thereby (nearly) constant rotational speed, or
— a CDM (Complete Drive Module) which enables to operate the pump unit at variable rotational
speed depending on a varying demand of flow rate and/or discharge or differential pressure.
NOTE A CDM is also often called VSD (Variable Speed Drive).
Pump units as defined above are treated as extended products in respect to their energy efficiency.
2 Normative references
There are no normative references in this document.
3 Terms and definitions, symbols and subscripts
For the purpose of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
fixed speed
constant motor stator frequency
3.2
variable speed
varying motor stator frequency
3.3
Energy Efficiency Index
EEI
ratio between P and P
1, avg 1, ref
3.4
reference electrical power input P
1, ref
calculated power input of the pump unit at the best efficiency point
3.5
average electrical power input P
1, avg
power input weighted by the load profile
3.6
pump unit
pump driven by a motor system
3.7
motor system
combination of an electric motor and either a terminal box or a CDM
3.8
pump unit type
identical pump units of the same configuration
3.9
pressure control curve
functional dependency of the demanded head H vs. the delivered flow rate Q in the form of a non-
dimensional correlation H/H = f (Q/Q )
100% 100%
3.10
reference pressure control curve
pre-defined functional dependency H/H = f (Q/Q ) for standardized measurements and
100% 100%
calculations of average power input P
1, avg
3.11
Complete Drive Module
CDM
electronic power converter connected between the electric supply and a motor as well as extensions
such as protection devices, transformers and auxiliaries
[SOURCE: EN 61800-2]
3.12
Power Drive System
PDS
combination of CDM and motor
Table 1 — List of basic letters and subscripts
Symbol Quantity Unit
C Constant dimensionless number
D Diameter m
e Measurement uncertainty, relative value dimensionless number
E Overall measurement uncertainty dimensionless number
−1
f Frequency
s , Hz
...
SLOVENSKI STANDARD
01-julij-2019
Črpalke - Metode za kvalifikacijo in verifikacijo indeksa energijske učinkovitosti
centrifugalnih črpalk - 1. del: Splošne zahteve in postopki za preskušanje in
izračun indeksa energijske učinkovitosti (EEI)
Pumps - Methods of qualification and verification of the Energy Efficiency Index for
rotodynamic pumps units - Part 1: General requirements and procedures for testing and
calculation of energy efficiency index (EEI)
Pumpen - Methoden zur Qualifikation und Verifikation des Energieeffizienzindexes für
Kreiselpumpen - Teil 1: Allgemeine Anforderungen und Vorgehensweisen zur Prüfung
und Berechnung des Energieeffizienzindexes (EEI)
Pompes - Méthodes de qualification et de vérification de l'indice de rendement
énergétique des groupes motopompes rotodynamiques - Partie 1 : Exigences générales
et procédures d'essai et de calcul de l'indice de rendement énergétique (EEI)
Ta slovenski standard je istoveten z: EN 17038-1:2019
ICS:
23.080 Črpalke Pumps
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN 17038-1
EUROPEAN STANDARD
NORME EUROPÉENNE
May 2019
EUROPÄISCHE NORM
ICS 23.080
English Version
Pumps - Methods of qualification and verification of the
Energy Efficiency Index for rotodynamic pump units - Part
1: General requirements and procedures for testing and
calculation of Energy Efficiency Index (EEI)
Pompes - Méthodes de qualification et de vérification Pumpen - Methoden zur Qualifikation und Verifikation
de l'indice de rendement énergétique des groupes des Energieeffizienzindexes für Kreiselpumpen - Teil 1:
motopompes rotodynamiques - Partie 1 : Exigences Allgemeine Anforderungen und Vorgehensweisen zur
générales et procédures d'essai et de calcul de l'indice Prüfung und Berechnung des Energieeffizienzindexes
de rendement énergétique (EEI) (EEI)
This European Standard was approved by CEN on 15 July 2018.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 17038-1:2019 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
Introduction . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions, symbols and subscripts . 5
4 Energy Efficiency Index (EEI) calculations . 9
4.1 General information and explanation on EEI . 9
4.2 Weighted-average value of the electric power input . 9
4.3 The reference electric power input P . 10
1, ref
5 Qualification of pump unit types in respect to their Energy Efficiency Index . 10
5.1 General remarks . 10
5.2 Qualification methods . 11
6 Verification of the Energy Efficiency Index for pump units . 12
6.1 General remarks . 12
6.2 Procedure and decision . 12
Annex A (informative) Mean value and confidence interval of the Energy Efficiency Index EEI . 14
Annex B (informative) Methods recommended for the qualification of a pump unit type by
test . 19
B.1 General remarks . 19
B.2 Determination of the mean value of EEI of a pump unit type population from a test
on only one test pump unit . 19
B.3 Determination of the mean value of EEI of a pump unit type population from a
sample test of M pump units . 20
Annex C (informative) Application of mathematical statistics on tests . 23
C.1 Purposes of applying statistics in the frame of qualification and verification . 23
C.2 Normal or Gaussian distribution . 23
C.3 Confidence interval . 24
C.4 Outlier test . 25
Annex D (informative) Measurement uncertainties . 27
Annex E (informative) The probability of the result of the verification procedure . 30
E.1 General . 30
E.2 Probability that the conformity to law is confirmed by verification tests . 32
E.3 Probability that a numerical value of indicated by the responsible company is
confirmed by verification tests . 33
Bibliography . 34
European foreword
This document (EN 17038-1:2019) has been prepared by Technical Committee CEN/TC 197 “Pumps”,
the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by November 2019, and conflicting national standards
shall be withdrawn at the latest by November 2019.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Introduction
This document is the first part of a series of standards describing a methodology to evaluate energy
efficiency performance of pump units, comprising the pump, the motor with or without frequency
converter, based on a non-dimensional numerical value called Energy Efficiency Index (EEI). An EEI
allows the comparison of different pump sizes and types with one common indicator. Physical
influences such as pump size, specific speed, pump unit part-load operation, motor-efficiency
characteristic and frequency converter influence are implemented into this indicator.
This standard series covers pump units which component wise can be placed on the market and
assembled into a pump unit or are placed on the market as one single product. To cover these two cases
a semi-analytical model has been developed in order to derive the EEI based on nominal data of the
components only. This case happens for example when an assembler of the components builds the
pump unit on site and consequently a product test cannot be done by for this assembler or when a
manufacturer is quoting a pump-unit which uses a combination of components not previously built.
This particular standard gives an overview of the basic concept of EEI (Clause 4), basic concepts of flow-
time profiles and reference pressure control curves, the qualification (Clause 5) of a pump unit type
regarding an EEI and the verification of EEI values (Clause 6) given for a pump unit type either by
measurement or calculation.
Specific requirements for testing, a calculation method for an EEI, the so called semi-analytical model of
a complete pump unit, specific flow-time profiles and reference control curves are given in the
subsequent parts of this standard series.
1 Scope
This document describes a methodology to evaluate energy efficiency performance of pump units based
on a non-dimensional numerical value called Energy Efficiency Index (EEI).
This document covers pump units consisting of:
— one single or several rotodynamic water pump(s), including where integrated in other products,
and driven by a motor system, consisting of an electrical motor, and either:
— a terminal box which only enables to operate the pump unit at constant motor stator frequency
and thereby (nearly) constant rotational speed, or
— a CDM (Complete Drive Module) which enables to operate the pump unit at variable rotational
speed depending on a varying demand of flow rate and/or discharge or differential pressure.
NOTE A CDM is also often called VSD (Variable Speed Drive).
Pump units as defined above are treated as extended products in respect to their energy efficiency.
2 Normative references
There are no normative references in this document.
3 Terms and definitions, symbols and subscripts
For the purpose of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
fixed speed
constant motor stator frequency
3.2
variable speed
varying motor stator frequency
3.3
Energy Efficiency Index
EEI
ratio between P and P
1, avg 1, ref
3.4
reference electrical power input P
1, ref
calculated power input of the pump unit at the best efficiency point
3.5
average electrical power input P
1, avg
power input weighted by the load profile
3.6
pump unit
pump driven by a motor system
3.7
motor system
combination of an electric motor and either a terminal box or a CDM
3.8
pump unit type
identical pump units of the same configuration
3.9
pressure control curve
functional dependency of the demanded head H vs. the delivered flow rate Q in the form of a non-
dimensional correlation H/H = f (Q/Q )
100% 100%
3.10
reference pressure control curve
pre-defined functional dependency H/H = f (Q/Q ) for standardized measurements and
100% 100%
calculations of average power input P
1, avg
3.11
Complete Drive Module
CDM
electronic power converter connected between the electric supply and a motor as well as extensions
such as protection devices, transformers and auxiliaries
[SOURCE: EN 61800-2]
3.12
Power Drive System
PDS
combination of CDM and motor
Table 1 — List of basic letters and subscripts
Symbol Quantity Unit
C Constant dimensionless number
D Diameter m
e Measurement uncertainty, relative value dimensionless number
E Overall measurement uncertainty dimensionless number
−1
f Frequency
s , Hz
g Acceleration due to gravity
m/s
H Pump total head m
k Number of sample pumps dimensionless
...
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