wa e
Technical No e
Simpli ied Indi ec Es ima ion o Pump Flow Discha ge:
An Example om Se bia
Milica Raši´c Amon 1,2 , Milan Radi´c 1, Zo an S aji´c 1,2, Dejan B ki´c 1,2,3,* and Pa el P aks 3


Ci a ion: Raši´c Amon, M.; Radi´c, M.;
S aji´c, Z.; B ki´c, D.; P aks, P.
Simpli ied Indi ec Es ima ion o
Pump Flow Discha ge: An Example
om Se bia. Wa e 2021,13, 796.
h ps://doi.o g/10.3390/w13060796
Academic Edi o s: S e ano Al isi and
Helena M. Ramos
Recei ed: 17 Decembe 2020
Accep ed: 10 Ma ch 2021
Published: 14 Ma ch 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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dis ibu ed unde he e ms and
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A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1Facul y o Elec onic Enginee ing, Uni e si y o Niš, 18000 Niš, Se bia; [email p o ec ed] (M.R.A.);
[email p o ec ed] (M.R.); [email p o ec ed] (Z.S.)
2Resea ch and De elopmen Cen e “IRC Al a ec”, 18000 Niš, Se bia
3
IT4Inno a ions, VSB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic; [email p o ec ed]
*Co espondence: [email p o ec ed] o [email p o ec ed]
Abs ac :
In he absence o a lowme e o due o i s inaccu acy, he low a e a he discha ge
sec ion o he pipeline ollowing he obse ed pump can be oughly es ima ed i he p essu e can be
measu ed ins ead. To use he p oposed p ocedu e wo main condi ions should be achie ed: (1) a
manome e should be ins alled a he discha ge pipeline be ween he pump and he low egula ion
al e, and (2) he ac ual cu e ha ela es p essu e and low o he obse ed pump uni should be
known in ad ance. The desc ibed example is om Se bia, bu i is o in e es o any wa e pumping
s a ion wi h a subme sible pump (ins alled in wells o anks) whe e a limi ed numbe o adequa e
places o he measu ing o low a e a ailable (i any a e a ailable a all), bu whe e he p essu e a he
discha ge pipe o he obse ed pump can be measu ed. This simpli ied me hod can ind applicabili y
in ins alla ions in emo e u al egions whe e limi ed esou ces a e a ailable. The esul s show ha
he calcula ed alues o he low ob ained by he p esen ed me hod de ia e g ea ly in ela ion o he
measu ed alues p o ided by he po able ul asonic lowme e , up o 60% a one o he measu ing
poin s. Howe e , in ela ion o he measu ed alues p o ided by he pe manen ly ins alled lowme e
he disc epancy is signi ican ly lowe (0.6–6.8%).
Keywo ds:
pumps; p essu e d op; low es ima ion; accu a e measu emen ; pipelines; wa e -
wo ks; lowme e
1. In oduc ion
In he absence o a lowme e o due o i s inaccu acy, he low a e a he discha ge
sec ion o he pipeline ollowing he obse ed pump can be oughly es ima ed i he wa e
p essu e can be measu ed ins ead. Ve y o en, i is p ac ically impossible o selec an
adequa e place o a lowme e due o he p esence o many elemen s in a wa e pumping
s a ion, such as al es and elbows whe e he pipeline changes i s di ec ion. The p oblem
o inco ec measu emen s o he discha ge low a e in wa e wo ks can be easily sol ed
i a sec ion o he pipe wi h an adequa e leng h wi h no low dis u bances is o eseen a
he discha ge side o he obse ed pump. To sol e he p oblem, in his p ac ical echnical
no e an al e na i e, simpli ied app oach is gi en o a ough es ima ion o he low a e
a he discha ge sec ion o he pipeline o hose pumps whe e he lowme e is absen o
when he eading om an exis ing lowme e is un eliable due o an un a o able pipeline
con igu a ion o due o any o he eason [
1
–
7
]. A pump is a machine ha is used o ans e
quan i ies o liquids om one place o ano he , and he e i s low-p essu e cha ac e is ic
is used o es ima e wa e low a e a he discha ge side o wa e pumping s a ions. The
p esen ed simpli ied app oach can be adap ed o any o he liquid, including c ude oil
whe e a special applica ion can be ound in o sho e ins alla ions wi h limi ed places
a ailable o measu emen .
In p ac ice, he e a e si ua ions when he e a e no lowme e s ins alled in pumping
s a ions (especially in emo e low-income egions), which is especially common when i
Wa e 2021,13, 796. h ps://doi.o g/10.3390/w13060796 h ps://www.mdpi.com/jou nal/wa e
Wa e 2021,13, 796 2 o 15
comes o pumping s a ions o smalle capaci y. In such cases, po able lowme e s a e used
o es ima e he low a e, i.e., he amoun o liquid pumped in a ce ain pe iod o ime, bu
choosing he place o hei ins alla ion is no easy.
In ce ain ins alla ions wi h pumps, o make measu emen s, i is easie and less cos ly
o ins all only a manome e (in al eady exis ing ins alla ions, his will p e en addi ional
cu ing o he pipeline o ins all a lowme e ). I he place a which a low me e should be
ins alled is no p ope ly chosen in he design phase p ope ly chosen in he design phase,
he p oblem can be sol ed by a adical app oach, which in ol es he exca a ion o a pa
o he pipeline ha is o he wise unde g ound. Howe e , his adical app oach in ol es
signi ican cos s and ca ies he isk o acciden s.
The p oposed app oach o low a e es ima ion has a gene al cha ac e and can be
applied in any pumping s a ion wi h a subme ged pump (in a ank o a well)
p o ided ha
:
1.
I has a pump uni wi h an in-ad ance known ac ual
H(Q)
cu e gained om lab-
o a o y es ing (possible disc epancy be ween he design sys em cu es a ailable
om manu ac u e s and he on-si e one is equen and he e o e such cu es om
ca alogues should be e-e alua ed i possible), and,
2. The p essu e can be measu ed a he discha geside o he obse ed pump.
Res ic ions include a lack o equipmen o egula e he speed o he o o s, and he
use o wo o mo e pumps in a pa allel con igu a ion, which means ha hei pe o mance
canno always be de e mined (especially ue when he non- e u n al es a he pumps
a e no ully igh ened). Such a si ua ion o en occu s in small emo e pumping s a ions
whe e he ope a ing egime is no ully espec ed ( he diame e o he suc ion pipe is no
always he same as he discha ge pipe diame e when, due o he isk o ca i a ion, a la ge
diame e o he suc ion pipe is usually used).
In he absence o pe manen measu emen s o low in wa e wo ks, o whe e accu acy
is doub ul, he mos commonly used p ac ice is o compa e he esul s ha can be ob ained
om se e al di e en po able con ol me e s ( hese a e, as a ule, po able ul asonic
me e s) [
8
–
16
]. We will also es ou app oach in his manne . As i will be p esen ed, he
esul s es ima ed ollowing he ecommenda ion om his p ac ical echnical no e a e mo e
eliable compa ed o hose ob ained using po able lowme e s in sys ems wi h a complex
geome y o pipeline ollowing he pump [17–21].
Based on one p ac ical example om Se bia, he heo e ical backg ound will be p e-
sen ed u he in he ex . This simpli ied me hod can ind applica ion in ins alla ions in
emo e, low-income egions whe e limi ed places o measu emen a e a ailable (i any a e
a ailable a all).
Simila ough app oxima e me hods o es ima ion o wa e low using local p essu e
loss measu emen s a e no known o he au ho s, bu inaccu acies o lowme e s a e no
a e [22,23].
2. The Desc ip ion o he P oposed App oach
To apply he simpli ied app oach p oposed in his wo k o low- a e es ima ion,
i is necessa y o ha e a pump wi h in-ad ance p ecisely de e mined
H(Q)
cu e and
o ha e a manome e ins alled a he discha ge side o he pump be o e he al e o
low egula ion [
24
,
25
]. I is no ad isable o ely on he ca alogued cha ac e is ics o he
pump, especially o olde pump models. E en wi h he pump uni s o he same ype
and manu ac u ed in he same yea , he ope a ing cha ac e is ics will no be he same
and will depend on hei eal condi ion such as he numbe o ope a ing hou s, he wea
o impelle s, he condi ion o bea ings, he numbe o o e hauls and losses in elec ic
mo o s, e c.
Figu e 1shows a gene al a angemen o elemen s equi ed o he applica ion o
he p oposed indi ec low a e es ima ion in a pump s a ion wi h subme sible pumps
( he lowme e s depic ed in ed a e no p esen a all o a e possibly inaccu a e due o
he unsui able place o placemen in a complex pipeline con igu a ion). The example
o he placemen o a po able lowme e shown in Figu e 1is a ypical example o an
Wa e 2021,13, 796 3 o 15
inapp op ia e posi ion in which a signi ican e o in low measu emen occu s (high
measu emen unce ain y).
Wa e 2021, 13, x FOR PEER REVIEW 3 o 16
lowme e s depic ed in ed a e no p esen a all o a e possibly inaccu a e due o he
unsui able place o placemen in a complex pipeline con igu a ion). The example o he
placemen o a po able lowme e shown in Figu e 1 is a ypical example o an inapp o-
p ia e posi ion in which a signi ican e o in low measu emen occu s (high measu e-
men unce ain y).
Figu e 1. The layou o he elemen s equi ed o low a e es ima ion.
Rega ding he scheme om Figu e 1, one should no o ge abou he p essu e loss
in he e ical sec ion o he pipeline— he p essu e measu ed a i s op is lowe han a
he pump head.
Taking in o accoun he complexi y o he pipeline, he equi alen cha ac e is ics o
he pump should be e alua ed h ough he analysis o he indi idual sys em o pipes on
which he pump is ins alled. In such a case, i is di icul o alk abou he compliance o
noncompliance o he measu ed cha ac e is ics o hose gi en by he pump manu ac u e .
In p ac ice, he e a e si ua ions whe e lowme e s a e no ins alled in pumping s a-
ions, which is especially common when i comes o pumping s a ions o smalle capaci y
(usually wi h wo pump uni s ha do no wo k in a pa allel con igu a ion, bu whe e one
o hem is used as a backup pump). In such cases, po able lowme e s a e used o es ima e
he low a e, i.e., he amoun o liquid pumped in a ce ain pe iod, while he choice o he
posi ion o hei ins alla ion is no easy. I he e a e no manholes p epa ed in ad ance, i
is necessa y o exca a e he g ound a ound he pipeline. In such si ua ions, his is no a
common p ac ice, bu a he he lowme e is placed in any accessible place.
Fo he low- a e es ima ion, he p essu e can be exp essed in [Pa] (in [ba ], whe e 1
ba = 105 Pa) o as a p essu e head in a uni o leng h [m], whe e hese wo o ms a e ela ed
as 𝑝 =𝜌·𝑔·𝐻, whe e 𝑝 is p essu e [Pa] measu ed by he manome e a he dis-
cha ge side (exac ly abo e he pump), 𝜌 is he densi y o he wa e ~1000 kg/m3, g is g a -
i a ional cons an ~9.81 m/sec2, while 𝐻 is p essu e head [m]. 𝐻 is he co ec ion in [m],
which depends on he heigh di e ence be ween he posi ion o he manome e and he
wa e le el in he ank. I he wa e le el in he ank is cons an du ing he expe imen , he
eloci y a he suc ion side is 𝑉 =0 [m/s]. The eloci y a he discha ge side 𝑉 de-
pends on he pipeline diame e and he low a e, which a e unknown a iables a he
beginning. This p oblem can be sol ed ei he by he implemen a ion o i e a i e analysis,
o by p ope choice o he posi ion o he manome e (as i is shown in Sec ion 3.2.1). Ne-
glec ing local losses om he poin o luid suc ion o he poin o p essu e measu emen ,
o al head H in [m] can be es ima ed using Equa ion (1):
Figu e 1. The layou o he elemen s equi ed o low a e es ima ion.
Rega ding he scheme om Figu e 1, one should no o ge abou he p essu e loss in
he e ical sec ion o he pipeline— he p essu e measu ed a i s op is lowe han a he
pump head.
Taking in o accoun he complexi y o he pipeline, he equi alen cha ac e is ics o
he pump should be e alua ed h ough he analysis o he indi idual sys em o pipes on
which he pump is ins alled. In such a case, i is di icul o alk abou he compliance o
noncompliance o he measu ed cha ac e is ics o hose gi en by he pump manu ac u e .
In p ac ice, he e a e si ua ions whe e lowme e s a e no ins alled in pumping s a ions,
which is especially common when i comes o pumping s a ions o smalle capaci y (usually
wi h wo pump uni s ha do no wo k in a pa allel con igu a ion, bu whe e one o hem
is used as a backup pump). In such cases, po able lowme e s a e used o es ima e he
low a e, i.e., he amoun o liquid pumped in a ce ain pe iod, while he choice o he
posi ion o hei ins alla ion is no easy. I he e a e no manholes p epa ed in ad ance, i
is necessa y o exca a e he g ound a ound he pipeline. In such si ua ions, his is no a
common p ac ice, bu a he he lowme e is placed in any accessible place.
Fo he low- a e es ima ion, he p essu e can be exp essed in [Pa] (in [ba ], whe e
1 ba = 10
5
Pa) o as a p essu e head in a uni o leng h [m], whe e hese wo o ms a e
ela ed as
pdis =ρ·g·H
, whe e
pdis
is p essu e [Pa] measu ed by he manome e a he
discha ge side (exac ly abo e he pump),
ρ
is he densi y o he wa e ~1000 kg/m
3
,gis
g a i a ional cons an ~9.81 m/sec
2
, while
H
is p essu e head [m].
Hg
is he co ec ion in
[m], which depends on he heigh di e ence be ween he posi ion o he manome e and
he wa e le el in he ank. I he wa e le el in he ank is cons an du ing he expe imen ,
he eloci y a he suc ion side is
Vsuc =
0 [m/s]. The eloci y a he discha ge side
Vdis
depends on he pipeline diame e and he low a e, which a e unknown a iables a he
beginning. This p oblem can be sol ed ei he by he implemen a ion o i e a i e analysis,
o by p ope choice o he posi ion o he manome e (as i is shown in Sec ion 3.2.1).
Neglec ing local losses om he poin o luid suc ion o he poin o p essu e measu emen ,
o al head H in [m] can be es ima ed using Equa ion (1):
H =pdis
ρ·g+Hg+V2
dis
2·g(1)
Wa e 2021,13, 796 4 o 15
To es he app oach o indi ec es ima ion o pump low discha ge p oposed he e, he
al e a he discha ge side o he pump should be ully open. Fu he , he al e needs o be
g adually closed in disc e e s eps, which changes he alues o he low and subsequen ly
o he p essu e. The e o e, o each achie ed s a iona y ope a ing poin , he alues o
he p essu e
pdis
om he manome e should be eco ded. Based on Equa ion (1) and
g aph in Figu e 2, i is possible o es ima e he low a e
Qes
a he discha ge side o he
obse ed pump. The cu e in Figu e 2 ela es he o al head
H
and he low a e
Q
and
has o be ob ained om he manu ac u e ’s ca alogue o p e e ably om a labo a o y
es in ad ance. The possibili y o disc epancy be ween he labo a o y cha ac e is ics and
cha ac e is ics om he ca alogue is some hing ha exis s in eali y, especially o an olde
pump, which has been in se ice o a long pe iod o ime and has been de ined by alid
echnical s anda ds (such as [
26
]). Depending on he ype o pump equi ed, mino o majo
de ia ions om he ac o y cha ac e is ic a e pe mi ed. The echnical s anda d, EN ISO
9906:2012 [
26
], allows ela i ely la ge disc epancies be ween he ope a ing cha ac e is ics
o he pumps he ca alogue cha ac e is ics.
Wa e 2021, 13, x FOR PEER REVIEW 4 o 16
𝐻=𝑝
𝜌·𝑔+𝐻+𝑉

2·𝑔 (1)
To es he app oach o indi ec es ima ion o pump low discha ge p oposed he e,
he al e a he discha ge side o he pump should be ully open. Fu he , he al e needs
o be g adually closed in disc e e s eps, which changes he alues o he low and subse-
quen ly o he p essu e. The e o e, o each achie ed s a iona y ope a ing poin , he al-
ues o he p essu e 𝑝 om he manome e should be eco ded. Based on Equa ion (1)
and g aph in Figu e 2, i is possible o es ima e he low a e 𝑄 a he discha ge side o
he obse ed pump. The cu e in Figu e 2 ela es he o al head 𝐻 and he low a e 𝑄
and has o be ob ained om he manu ac u e ’s ca alogue o p e e ably om a labo a o y
es in ad ance. The possibili y o disc epancy be ween he labo a o y cha ac e is ics and
cha ac e is ics om he ca alogue is some hing ha exis s in eali y, especially o an olde
pump, which has been in se ice o a long pe iod o ime and has been de ined by alid
echnical s anda ds (such as [26]). Depending on he ype o pump equi ed, mino o
majo de ia ions om he ac o y cha ac e is ic a e pe mi ed. The echnical s anda d, EN
ISO 9906:2012 [26], allows ela i ely la ge disc epancies be ween he ope a ing cha ac e -
is ics o he pumps he ca alogue cha ac e is ics.
Figu e 2. Indi ec de e mina ion o low 𝑄 a he measu ing poin based on he cu e, which
ela es o al head 𝐻 and low 𝑄.
The e o e, he co esponding low 𝑄 can be de e mined indi ec ly o each meas-
u ing poin om he known 𝐻(𝑄) cu e, (wi h sa is ac o y measu emen unce ain y) o
each measu ing poin o he p essu e 𝑝 ob ained om he manome e , as shown in
Figu e 2 ( ecalcula ed o 𝐻).
Figu e 2.
Indi ec de e mina ion o low
Qes
a he measu ing poin based on he cu e, which ela es o al head
H
and
low Q.
The e o e, he co esponding low
Qes
can be de e mined indi ec ly o each mea-
su ing poin om he known
H(Q)
cu e, (wi h sa is ac o y measu emen unce ain y)
o each measu ing poin o he p essu e
pdis
ob ained om he manome e , as shown in
Figu e 2( ecalcula ed o H).
The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he
low a e using he p oposed app oach.
Wa e 2021,13, 796 5 o 15
Wa e 2021, 13, x FOR PEER REVIEW 5 o 16
The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he
low a e using he p oposed app oach.
Figu e 3. A simple algo i hm o es ima ion o discha ge low.
3. A P ac ical Example
The pumping s a ion obse ed in which he me hod has been es ed has had a long
his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline
wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am
o he measu ing pump s a ion is shown in Figu e 4 ( he op iew).
Figu e 4. Simpli ied diag am o he pump s a ion.
Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline
made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows
a sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he
loo o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing
he mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps
we e aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G).
Figu e 3. A simple algo i hm o es ima ion o discha ge low.
3. A P ac ical Example
The pumping s a ion obse ed in which he me hod has been es ed has had a long
his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline
wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am
o he measu ing pump s a ion is shown in Figu e 4( he op iew).
Wa e 2021, 13, x FOR PEER REVIEW 5 o 16
The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he
low a e using he p oposed app oach.
Figu e 3. A simple algo i hm o es ima ion o discha ge low.
3. A P ac ical Example
The pumping s a ion obse ed in which he me hod has been es ed has had a long
his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline
wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am
o he measu ing pump s a ion is shown in Figu e 4 ( he op iew).
Figu e 4. Simpli ied diag am o he pump s a ion.
Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline
made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows
a sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he
loo o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing
he mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps
we e aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G).
Figu e 4. Simpli ied diag am o he pump s a ion.
Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline
made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows a
sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he loo
o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing he
mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps we e
aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G). Be o e
he ins alla ion, one o he new pumps, ma ked as P1 in Figu e 4, had been addi ionally
es ed by he manu ac u e ’s labo a o y.

Wa e 2021,13, 796 6 o 15
To e i y he accu acy o he simpli ied app oach p oposed he e in p ac ice, low
measu emen s in he obse ed pumping s a ion using lowme e s we e pe o med (in
u he ex
Qmes
) and hen hose measu ed alues we e compa ed o he es ima ed alues
(in u he ex
Qes
). Besides, he exac cu e o he obse ed G und os SP 270-3A G, which
ela es o al head
H
and low
Q
was de e mined in he manu ac u e ’s labo a o y ( he
es ing o he pump in he manu ac u e ’s acili y is shown in Figu e 5, while he esul s a e
shown in Table 1). In he speci ic si ua ion p esen ed in his pape , he eal cha ac e is ics o
he pump eco ded in he labo a o y di e om hose om he manu ac u e ’s ca alogue.
Fu he mo e, some imes i is no possible o ha e a s able equency o 50 Hz, so he
ac ual cu e om he labo a o y, which ela es he o al head
H
and he low
Q
should be
ecalcula ed o he ac ual condi ions in he obse ed wa e pumping s a ion [
27
]. As we
will show in he ollowing case, he ope a ing equency was se o 49 Hz, o show how o
ecalcula e a cu e designed o 50 Hz.
Wa e 2021, 13, x FOR PEER REVIEW 6 o 16
Be o e he ins alla ion, one o he new pumps, ma ked as P1 in Figu e 4, had been addi-
ionally es ed by he manu ac u e ’s labo a o y.
To e i y he accu acy o he simpli ied app oach p oposed he e in p ac ice, low
measu emen s in he obse ed pumping s a ion using lowme e s we e pe o med (in u -
he ex 𝑄) and hen hose measu ed alues we e compa ed o he es ima ed alues
(in u he ex 𝑄). Besides, he exac cu e o he obse ed G und os SP 270-3A G,
which ela es o al head 𝐻 and low 𝑄 was de e mined in he manu ac u e ’s labo a o y
( he es ing o he pump in he manu ac u e ’s acili y is shown in Figu e 5, while he
esul s a e shown in Table 1). In he speci ic si ua ion p esen ed in his pape , he eal
cha ac e is ics o he pump eco ded in he labo a o y di e om hose om he manu-
ac u e ’s ca alogue. Fu he mo e, some imes i is no possible o ha e a s able equency
o 50 Hz, so he ac ual cu e om he labo a o y, which ela es he o al head 𝐻 and he
low 𝑄 should be ecalcula ed o he ac ual condi ions in he obse ed wa e pumping
s a ion [27]. As we will show in he ollowing case, he ope a ing equency was se o 49
Hz, o show how o ecalcula e a cu e designed o 50 Hz.
Figu e 5. Tes ing o SP 270-3A G pump in he labo a o y.
Table 1. Values o he cu e ha ela es o al head and low o he SP 270-3A G pump measu ed
in he labo a o y a 50 Hz and ecalcula ed o 49 Hz.
50 Hz
𝑄 [dm3/s] 0 11.67 59.88 75.84 90.08
𝐻 [m] 145.38 138.89 97.47 86.2 71.96
49 Hz
𝑄 [dm3/s] 0 11.44 58.68 74.32 88.28
𝐻 [m] 139.62 133.39 93.61 82.79 69.11
The ollowing equipmen was used o he es in he pumping s a ion:
1. A subme sible pumping uni G und os SP 270-3A G wi h a a ed powe o 110 kW,
Figu e 5. Tes ing o SP 270-3A G pump in he labo a o y.
Table 1.
Values o he cu e ha ela es o al head and low o he SP 270-3A G pump measu ed in
he labo a o y a 50 Hz and ecalcula ed o 49 Hz.
50 Hz
Q[dm3/s] 0 11.67 59.88 75.84 90.08
H[m] 145.38 138.89 97.47 86.2 71.96
49 Hz
Q[dm3/s] 0 11.44 58.68 74.32 88.28
H[m] 139.62 133.39 93.61 82.79 69.11
The ollowing equipmen was used o he es in he pumping s a ion:
1. A subme sible pumping uni G und os SP 270-3A G wi h a a ed powe o 110 kW,
2.
The low was measu ed using a pe manen ly ins alled ul asonic lowme e Siemens
SITRANS F a he main discha ge pipeline a he obse ed pump s a ion (addi ionally
a po able ul asonic lowme e TDSH100 was used),
Wa e 2021,13, 796 7 o 15
3.
The p essu e was measu ed using an IDROSCAN digi al manome e which was
ins alled on he discha ge side o he pump (addi ionally, an analogue manome e
was ins alled),
4.
The equency o he powe supply o he d i e mo o was egula ed using a Mi subishi
F740 egula o , and
5.
The low was egula ed using he al e ins alled a he s eel discha ge pipe DN 200
a e he pump P1.
All equipmen used in ou expe imen s has been p ope ly es ed using all common
echnical no ms and s anda ds equi ed o such de ices [28].
3.1. De e mina ion o Subs i u e Cha ac e is ics
The pu pose o his subsec ion is o show how he accu a e
H(Q)
cu e o he obse ed
G und os SP 270-3A G was de e mined.
3.1.1. Measu ing in he Manu ac u e ’s Labo a o y and he Recalcula ion o he Ac ual
F equency o Powe Supply
The measu ing in he manu ac u e ’s labo a o y:
The ac ual
H(Q)
cu e o he ob-
se ed pump SP 270-3A G was de e mined expe imen ally in he manu ac u e ’s labo a o y
and he esul s a e alid o powe supply equency o 50 Hz ( ela ed lows and he p es-
su e ob ained in disc e e s eps, which ha e been used o cons uc he cu e a e gi en in
Table 1).
Labo a o y es s a e expensi e, bu hey a e no manda o y and do no ep esen
wha he au ho s sugges in e e y si ua ion. In ce ain si ua ions, especially when i
comes o pumping uni s o highe powe , he p ice o such es s may be negligible when
compa ed o he possibili ies ha he use can ge wi h he help o such es s. The ac
is ha pump manu ac u e s usually do no ag ee o p o e he pe o mance o pumping
uni s a he ins alla ion si es o such pumps, because hey canno gua an ee he accu acy o
he measu ing equipmen in he pumping s a ions whe e he obse ed pumps ha e been
ins alled. Ins ead, hey p e e es ing in an independen o he manu ac u e ’s labo a o y.
Also, he cha ac e is ics o pump uni s change du ing se ice li e. In si ua ions whe e he e
a e lowme e s ins alled in pumping s a ions, i is no complica ed o pe iodically pe o m
measu emen s a he ins alla ion si e o check and/o co ec he ope a ing cha ac e is ics
o pumping uni s. This can usually be done as a pa o planned main enance ac i i ies in
he pumping s a ions so ha i does no inc ease unning cos s. This way, he deg ee o
de e io a ion o he ope a ing cha ac e is ics o he pumping uni s can be moni o ed. This
is pa icula ly impo an because hei e iciency can be educed o such an ex en ha i
would be necessa y o epai and/o o eplace hem.
The obse ed pumping s a ion in which he me hod was es ed has had a long his o y
o ques ionable measu ing o low due o he complex geome y o he pipeline wi h
insu icien leng h o pipe whe e a lowme e could be ins alled. The ins alled pumps a e
old and due o ha d exploi a ion, hei cha ac e is ics we e al e ed compa ed o hose om
he ca alogue. The e o e, he old pumps we e aken ou and eplaced wi h new pumps
which ha e been addi ionally es ed by he manu ac u e ’s labo a o y ( es ing o he pump
in he manu ac u e ’s acili y is shown in Figu e 5, while he esul s a e shown in Table 1).
Recalcula ion o he ac ual equency o he powe supply:
Fo an illus a ion o
he p oposed es ima ion o he low in gene al condi ions, du ing he es in he wa e
pumping s a ion whe e he pump has been ins alled, he equency has been se o 49 Hz
using a Mi subishi F740 egula o and consequen ly, he cu e, which ela es o al head
H
and low
Q
o such condi ions has been ecalcula ed. The co ec ed alues ha e been
calcula ed using Equa ion (2) and a e also p esen ed g aphically in Figu e 6(based on he
da a poin s om Table 1).
H49 =49
50 2·H50
Q49 =49
50 ·Q50 ), (2)
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Wa e 2021, 13, x FOR PEER REVIEW 8 o 16
calcula ed using Equa ion (2) and a e also p esen ed g aphically in Figu e 6 (based on he
da a poin s om Table 1).
𝐻 =49
50·𝐻
𝑄 =49
50·𝑄 ⎭
⎬
⎫
, (2)
S a is ical calcula ions in he shown case a e based on a limi ed numbe o measu e-
men poin s om Table 1. Al hough his may be insu icien o a ho ough analysis whe e
he numbe o hese poin s should be inc eased, o p ac ical analyses, i e poin s can be
su icien especially in cases whe e mo e da a is no a ailable such as in his case.
Figu e 6. The expe imen ally de e mined cu e which ela es p essu e head and low o he SP
270-3A G pump ecalcula ed o 49 Hz.
3.1.2. Reg ession Model and S a is ical Analysis
To acili a e he use o he da a om Table 1, he o al head and he low o he pump
SP 270-3A G in ou expe imen can be p esen ed g aphically as gi en in Figu e 6. The
co ec ed g aph o 49 Hz is also gi en in Figu e 6, while he ela ed cu e based on e-
g ession analysis is gi en in Equa ion (3).
To a oid eading om he cu e p esen ed in Figu e 6, i is be e o use he eg es-
sion o mula as gi en in Equa ion (3), which gi es he low as he unc ion o he o al
head o he obse ed pump; he da a om he labo a o y o 50 Hz and ecalcula ed al-
ues o 49 Hz a e in Table 1.
𝑄 =−0.0018·𝐻−0.8643·𝐻+156.77 (3)
The da a om he measu emen ha was used o p oducing o Equa ion (3) is gi en
in Table 1. The ela ion based on he inpu da a o Table 1 was i ed by eg ession analysis
using S a g aphics Cen u ion, a s a is ical s a is ics package ha pe o ms and explains,
in plain language, bo h basic and highly ad anced s a is ical unc ions. We ha e ied se -
e al eg ession models, and we es ed hem using Pea son co ela ion and R-Squa ed
alue coe icien o de e mina ion [29,30]:
Figu e 6.
The expe imen ally de e mined cu e which ela es p essu e head and low o he SP 270-3A G pump ecalcula ed
o 49 Hz.
S a is ical calcula ions in he shown case a e based on a limi ed numbe o measu e-
men poin s om Table 1. Al hough his may be insu icien o a ho ough analysis whe e
he numbe o hese poin s should be inc eased, o p ac ical analyses, i e poin s can be
su icien especially in cases whe e mo e da a is no a ailable such as in his case.
3.1.2. Reg ession Model and S a is ical Analysis
To acili a e he use o he da a om Table 1, he o al head and he low o he pump
SP 270-3A G in ou expe imen can be p esen ed g aphically as gi en in Figu e 6. The
co ec ed g aph o 49 Hz is also gi en in Figu e 6, while he ela ed cu e based on
eg ession analysis is gi en in Equa ion (3).
To a oid eading om he cu e p esen ed in Figu e 6, i is be e o use he eg ession
o mula as gi en in Equa ion (3), which gi es he low as he unc ion o he o al head o
he obse ed pump; he da a om he labo a o y o 50 Hz and ecalcula ed alues o 49
Hz a e in Table 1.
Qes −49 =−0.0018·H2−0.8643·H+156.77 (3)
The da a om he measu emen ha was used o p oducing o Equa ion (3) is gi en
in Table 1. The ela ion based on he inpu da a o Table 1was i ed by eg ession analysis
using S a g aphics Cen u ion, a s a is ical s a is ics package ha pe o ms and explains, in
plain language, bo h basic and highly ad anced s a is ical unc ions. We ha e ied se e al
eg ession models, and we es ed hem using Pea son co ela ion and R-Squa ed alue
coe icien o de e mina ion [29,30]:
•
The coe icien o de e mina ion R-Squa ed alue deno ed as R
2
equals o 1.0 would
indica e a pe ec i , while an R-Squa ed alue o 0.0 would indica e he opposi e case;
•
The Pea son co ela ion coe icien is a s a is ic ha measu es he linea co ela ion
be ween wo a iables and has a alue be ween +1 and
−
1, whe e a alue o +1 is
a o al posi i e linea co ela ion, 0 is no linea co ela ion, and
−
1 is o al nega i e
linea co ela ion.
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In ou pa icula case, a linea model is sligh ly mo e sui able o he poin s om
Table 1, bu we use he squa ed model because i is mo e gene al and sui able o mos
cases. Fo example, he linea model
Qes −49 =
180.147
−
1.26628
·H
, shows he In e cep
180.147 and he Slope
−
1.26628 as p edic o s. These a iables a e s a is ically signi ican
because hei p- alues equal 0.000, which a e < 0.05. I also means ha he e is a s a is ically
signi ican co ela ion be ween
Qes −49
and
H
a he 95% con idence le el (de ails o he
s a is ical analysis a e gi en in Table 2).
Table 2.
Compa ison o al e na i e models ob ained by he S a g aphics Cen u ion so wa e using
Pea son co ela ion and R-Squa ed alue coe icien o de e mina ion.
Model Co ela ion R-Squa ed
Linea −0.9991 99.82%
Squa ed-H −0.9980 99.60%
Squa ed-Qes −49 ecip ocal-H 0.9978 99.56%
Squa e oo -H −0.9977 99.53%
Loga i hmic-H −0.9945 98.91%
Squa ed-Qes −49 loga i hmic-H −0.9920 98.41%
Squa ed-Qes −49 squa e oo -H −0.9866 97.34%
Recip ocal-H 0.9822 96.47%
Squa ed-Qes −49 −0.9799 96.03%
Squa e oo -Qes −49 squa ed-H −0.9760 95.26%
Squa e oo -Qes −49 −0.9663 93.37%
Double squa ed −0.9643 92.98%
Double squa e oo −0.9592 92.01%
Squa e oo -Qes −49 loga i hmic-H −0.9504 90.33%
Squa e oo -Qes −49 ecip ocal-H −0.9269 85.92%
Besides, i is possible o use he poin s om Figu e 6and Table 1 alid o he equency
o powe supply o 50 Hz o cons uc he cu e and he ela ed unc ion, while in ha case
he alues o he measu ed low and he p essu e om he nex wo subsec ions whe e he
equency was 49 Hz, should be ecalcula ed o 50 Hz, see Equa ion (2).
3.2. Measu emen in he Obse ed Pumping S a ion
The measu emen s in he obse ed pumping s a ion we e pe o med o compa ison
wi h he es ima ed alues ob ained using he shown simpli ied me hod. The p essu e mea-
su emen in his subsec ion is used as one o he inpu pa ame e s and is essen ial o he
me hod o low es ima ion desc ibed in his echnical no e. Howe e , low measu emen s
in his subsec ion a e used only o compa ison. The equency o he powe supply du ing
he measu emen a he wa e pumping s a ion was se o 49 Hz.
3.2.1. P essu e Measu emen
The p essu e change, in he sec ion be ween he pump and he al e o he egu-
la ion o low, was moni o ed by IDROSCAN digi al manome e wi h measu ing ange
0–50 ba
(wi h a eading esolu ion o 0.01 ba and wi h a decla ed nonlinea i y
±
0.2%).
The IDROSCAN digi al manome e was placed di ec ly on he discha ge side o he pump,
oge he wi h he analogue manome e (Figu e 7). Because o he posi ion o he manome-
e s, some undesi able a ia ion o low can occu which can in oduce a ce ain e o o
p essu e measu emen due o incomple ely s abilized low. Howe e , bo h manome e s
showed he iden ical alues o he measu ed p essu e. I should be men ioned ha due o
he speci ic placemen o he manome e (i is moun ed in a special socke on he elbow o
he discha ge pipeline, exac ly abo e he pump), he wa e eloci y a he poin o measu -
ing is locally conside ed o be
Vdis ≈
0 [m/s]. Thus, he measu ed p essu e is somewha
highe han he eal s a ic p essu e and includes he dynamic p essu e. Due o he heigh
di e ence be ween he posi ion o he manome e and he wa e le el in he ank du ing
ou expe imen , co ec ion
Hg
= 1.6 m ( ela ed o Figu e 1) is in oduced in o Equa ion (1).