154 Re is a de la Facul ad de Ciencias Ag a ias
C. E. Schila di Sícoli e al.
Op imal design o d ip i iga ion submains:
p esu e-compensa ing emi e s
Diseño óp imo de sec o es de iego po go eo:
emiso es au ocompensados
Ca los E. Schila di Sícoli 1 *, Rica do Aliod 2, Fe nando Zo illa 2, José An onio Mo ábi o 1, 3
O iginales: Recepción: 26/03/2018 - Acep ación: 18/05/2019
Abs ac
Fo a d ip i iga ion sys em o be success ul, i mus be well designed, p ope ly
ins alled, managed and main ained. In plo s wi h s eep slopes and i egula opog aphy
ha ha e li le land le eling capaci y and/o ha equi e e y e icien ag icul u al
machine y, d ip i iga ion designs gene ally use p essu e-compensa ing emi e s.
This wo k de elops a me hodology and implemen s i in a compu e ool ha makes
i possible o op imally de e mine in d ip-i iga ed plo s wi h p essu e-compensa ing
emi e s: a) elescopic sizing o he submain mani old pipe, b) supply al e p essu e
and c) subuni ’s in ake al e loca ion, when conside ing all hyd aulic-economic aspec s
in he design phase. Techniques o op imal sizing o pipe ne wo ks and simula ion o
hyd aulic ne wo ks unde p essu e a e linked o economic analyzes o o al annualized
cos s. Finally, he p ac ical use ulness o he p oposed me hodology is shown wi h h ee
examples o complex eal cases whe e pipe design cos s a e educed by 16-34% and
ene gy cos s by 37-51%.
Keywo ds
d ip i iga ion • design • submain • p essu e-compensa ing emi e s
1 Uni e sidad Nacional de Cuyo. Facul ad de Ciencias Ag a ias. Almi an e B own
500. Luján. C. P. M5528AHB. Mendoza. A gen ina. * cschila di@ ca.uncu.edu.a
2 Uni e sidad de Za agoza. Escuela Poli écnica Supe io de Huesca (EPSH).
Ca e e a de Cua e S/N. C. P. 22071. Huesca. España.
3 Cen o Regional Andino. Ins i u o Nacional del Agua. Belg ano 210 Oes e
(M55500FIF). Mendoza. A gen ina.
Re . FCA UNCUYO. 2019. 51(2): 154-166. ISSN (en línea) 1853-8665.
155
Tomo 51 • N° 2 • 2019
Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s
Resumen
Pa a que un sis ema de iego po go eo enga éxi o, debe es a bien diseñado, adecua-
damen e ins alado, ap opiadamen e manejado y man enido. En pa celas con g andes
pendien es, opog a ía i egula , con poca capacidad de ni elación y/o en si uaciones
donde se p e ende ene una al a e iciencia de la maquina ia ag ícola, los diseños de
iego po go eo gene almen e ecu en a la u ilización de emiso es au ocompensan es.
El p esen e abajo desa olla una me odología y ealiza su implemen ación en una
he amien a in o má ica que pe mi e en sec o es de iego po go eo con emiso es
au ocompensan es de e mina de mane a óp ima: a) el dimensionado elescópico de la
ube ía secunda ia (po a-la e ales), b) la p esión en ál ula de alimen ación del sec o
y c) el pun o de alimen ación del sec o (ubicación de dicha ál ula); conside ando
odos los aspec os hid áulicos-económicos in oluc ados en la ase de diseño. Pa a ello,
se inculan écnicas de dimensionado óp imo de conducciones y simulación hid áulica
de edes a p esión con análisis económicos de cos os o ales anualizados. Finalmen e,
se demues a la u ilidad p ác ica de la me odología desa ollada median e ejemplos
eales de aplicación, donde los cos os de diseño se educen en e 16-34% y los cos os de
ene gía en e 37-51%.
Palab as cla e
iego po go eo • diseño • subunidades • emiso es au ocompensan es
In oduc ion
The success o a d ip i iga ion sys em
depends essen ially on p ope design,
selec ion and ins alla ion (25) and co ec
managemen and main enance (12). In
o de o ensu e i s inancial sus ainabili y,
he bene i o he i iga ed c op mus
co e he high capi al cos s which his
me hod en ails (17). Op imal design o
d ip i iga ion is impo an o inc ease he
in es men s in and bene i s de i ed om
i iga ion (16). Such design should aim a
minimizing o al annualized piping and
ene gy cos s (32, 33) and ensu ing wa e
dis ibu ion uni o mi y (4, 6, 17, 19)
In s eep slope plo s (20) wi h i egula
opog aphy and li le land le eling capaci y
and/o ha equi e highly e icien ag icul-
u al machine y, d ip i iga ion sys ems
gene ally use p essu e-compensa ing
emi e s. They deli e a p ac ically cons an
discha ge o e a wide ange o p essu es
(20, 21, 35), called e ec i e p essu e
compensa ion ange, be ween 5 and 35 m,
and can lowe he limi s by ± 2 o aise hem
by ± 5 m (3), depending on each manu ac-
u e . P essu e egula ion is achie ed by
means o an elas ic memb ane ha co e s
he low pa h (36). A p essu e-compen-
sa ing emi e can be desc ibed by he
ollowing p essu e-discha ge unc ion (26):
(1)
whe e:
q = low o he emi e [L] 3 [T] -1
K = cha ac e is ic discha ge coe icien
o he emi e [L] 3-x [T] -1
h = emi e p essu e [L]
x = emi e discha ge exponen
q0 = cons an discha ge o he compen-
sa ion ange [L] 3 [T] -1
0
0 0 max
,0
,
x
kh h h
qq h h h

〈 ≤
〈 〈

156 Re is a de la Facul ad de Ciencias Ag a ias
C. E. Schila di Sícoli e al.
h0 = minimum p essu e o he compen-
sa ion ange [L]; his is de ined as:
(2)
Fo a good p essu e compensa ing
emi e , mos designe s will y o keep he
p essu es h oughou he ield in a ange
be ween 7-24.5 m (5). Mon al o (2005)
ecommends o sa e y easons a minimum
p essu e alue o he emi e ha is a
leas 2 m highe han he lowe limi o
he compensa ion ange and a maximum
p essu e o 25 m. I is necessa y o keep
p essu es wi hin ha ange o a oid: a)
disconnec ion o he d ip la e als o he
mani old, b) b eakage o he d ip i iga ion
la e al o exhaus ion o hei se ice li e,
and c) high ene gy consump ion.
Se e al au ho s add ess he hyd aulic-
economic op imiza ion o design i iga ion
subuni s. Saad and Ma iño (2002) de eloped
a linea op imiza ion model o ec angula
subuni s, wi h elescopic pipes placed in
he di ec ion o he slope g adien which
minimizes he annualized equi alen
i iga ion and pumping cos s and maximizes
dis ibu ion uni o mi y. Valian zas (2003)
and Valian zas e al. (2007) de i ed a
simple equa ion o calcula e he leng h and
a ailable diame e s o pipes wi hin a subuni
ha minimizes o al annualized pipe and
ene gy cos s. De cas and Valian zas (2012)
p esen ed wo simple analy ical me hods o
calcula e he adequa e diame e s o he main
pipes based on hyd aulic-economic analyzes.
In I icad so wa e (2013), he pipe
sizing is ca ied ou using a Linea
P og amming op imiza ion (LP) in
conjunc ion wi h hyd aulic g ade lines
analysis me hod. Pipe sizes a e op imized
based on he annualized cos o pipes and
ene gy (18). In ake al e posi ion and
p essu e a e de ined by he use wi hou
op imiza ion c i e ia.
 
1/
0
0
x
q
hK
 
 
Ca ión e al. (2013) and Ca ión
e al. (2014) de ised a me hodology
and compu e ool (PRESUD-P esu ized
Submain Design) applied o u bulen
d ippe s o he op imal design o
submains. The c i e ion used o op imize
he design was o educe he o al
annualized cos s o wa e pe i iga ed uni
a ea (CT). They adop ed a double i e a i e
p ocess o he design o he submain
mani old pipe and he in ake al e
p essu e simila o he ones in oduced in
he p esen a icle. Thei app oach is alid
only o ec angula plo s, does no inco -
po a e he elescopic design o submain
mani old pipes and does no iden i y he
op imum in ake al e loca ion.
Mo eno e al. (2016) expands he
PRESUD ool as PRESUD-IR o op imize he
design o iangula o apezoidal plo s. I
inco po a es an ex ension o he algo i hm
abo e men ioned by Ca ión e al. (2013
and 2014); a a hi d i e a ion in ake al e
loca ion is de e mined by conside ing
he loca ion o each emi e as a possible
eeding poin o he submain. The
op imum in ake al e loca ion is he one
ha maximizes dis ibu ion uni o mi y
and minimizes he CT. This upda e does
no inco po a e he elescopic design o
submain mani old pipe and is no sui able
o i egula ly shaped subuni s.
Fo de e mining he op imum in ake
al e loca ion in he submain, p e ious
wo ks (20) s a ed ha he loca ion mus
be aligned o he slope and p essu e loss
in mani old pipes o a single diame e so
as o balance he minimum p essu es
on bo h sides o he al e. Fo elescopic
mani old pipes, his depends on he
selec ed diame e s and leng hs. Finally,
in o de o op imize he eeding poin o
an i iga ion subumain i is necessa y
o imp o e i iga ion uni o mi y and
conside ably educe he cos o pipes.
157
Tomo 51 • N° 2 • 2019
Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s
Rod igo López e al. (1992) said ha
when he a e age slope o he land in he
di ec ion o mani old pipes is less han
3%, i is usually mo e economical o eed
he subuni h ough an in e media e poin
so as o ensu e ha p essu e a ia ion is
almos he same in he mani old pipe o he
ups eam and downs eam eeding poin .
Al hough he e a e some gene al
ecommenda ions and c i e ia o he
op imal design o i iga ion submains
wi h p essu e-compensa ing emi e s,
he e is no me hodology o de ine, bo h
in opog aphies and/o a bi a y geome-
ies, he p essu e and he al e’s in ake
poin and he elescopic sizing o he
submain mani old pipe ha will lead o he
bes possible hyd aulic-economic design.
Objec i e
To de elop a me hodology o subuni s
wi h p essu e-compensa ing emi e s
o op imize: a) elescopic sizing o he
submain mani old pipe; b) he in ake
al e's inpu p essu e o he subuni ; c) he
in ake al e loca ion, by conside ing all
hyd aulic-economic aspec s in ol ed in
he design phase so as o minimize o al
annualized cos s pe i iga ed uni a ea. The
esul ing me hodology is applied wi hin
he design module in d ip i iga ion plo s
in he GESTAR compu e package (2), hus
p o iding a new ad anced unc ionali y.
Ma e ials and Me hods
Fo i iga ion submains wi h p essu e-
compensa ing emi e s, he me hodology
uses as ini ial design condi ion an admis-
sible ange o design p essu es based on
he c i e ia p oposed by Bu and S yles
(2007) and Mon al o (2005). Howe e ,
he use will be able o modi y he
minimum and maximum al e's p essu e
o he design (admissible ange o design
p essu es) acco ding o he cha ac e is ics
and knowledge o he submain.
The Da cy-Weisbach o mula is used
o calcula e p essu e losses in pipes and
la e als whe e: 1) he ic ion ac o ( ) is
de e mined by app oxima ion o he Basius
equa ion (in he case o la e als) and o he
Coleb ook's equa ion o mani old pipes;
and 2) he Ch is iansen educ ion coe i-
cien is used o calcula e p essu e losses in
pipes o la e al acco ding o he numbe o
ou le s as p essu e-compensa ing d ippe s
con o m o his model.
Fo op imal sizing o elescopic
submain mani old pipe, he me hod
de eloped by González and Aliod (2003),
and González (2006) is applied. I is an
op imiza ion algo i hm (LMM/KPH -LM)
ha uses an imp o ed Lag ange Mul i-
plie s Me hod (LMM) (27) in condi-
ions o Know P essu e Head (KPH), in
combina ion o a Labye- ype Me hod
(LM) (22) o s anda diza ion o he
con inous diame e s ob ained in LMM.
A each connec ion poin o e e y la e al
o he submain mani old pipe, he
op imiza ion algo i hm mus supply a
minimum equi ed p essu e so ha he
mos un a o able p essu e-compensa ing
d ippe o he espec i e la e al eaches
i s minimum ope a ing p essu e.
The Nodal Analysis me hod
(1, 9, 10, 11) is used o hyd aulic
simula ion o he i iga ion submain, once
i is al eady designed, which includes a se
o ma ix analysis echniques, ex ended
o conside he speci i ies o p essu e
i iga ion sys ems, ha inco po a es he
in eg al-di e en ial hyd aulic modeling
o d ip la e als whe e he emi e s
discha ge low can depend on he local
p essu e (10, 15, 34). I makes i possible
o pe o m a de ailed quasi-s a iona y
hyd aulic-ene gy simula ion ei he o
u bulen o sel compensa ing d ippe s.
158 Re is a de la Facul ad de Ciencias Ag a ias
C. E. Schila di Sícoli e al.
The baseline da a o be selec ed
includes: a) o he hyd aulic calcula ion o
he subuni , he inne diame e (DI; mm),
leng h (Ll; m), slope (So; m/m), sepa a ion
(dis ance be ween ows; Sl; m) and la e als
pe c op ow (N°la / ow); low (qo; L h-1)
and emi e spacing (Se; m), maximum
(PVmax; m) and minimum design p essu e
(PVmin; m) o he subuni , as well as he
design p essu e s ep ange (PV S ep; m);
b) o he economic calcula ion o he
subuni , g oss c op wa e equi emen s
(Nb; m3 ha-1 yea -1) pe yea , pumping
equipmen e iciency (Ep; %/100), ans-
mission a io (T , his ep esen s he
addi ional amoun o wa e ha mus
be applied du ing he highes demand
pe iod aking in o accoun he ine i able
deep pe cola ion, wi h alues anging
be ween 1.0 and 1.1 (20)), cos o ene gy
(Ce; € kwh-1); wa e p ice (Cw; € m-3); in e es
a e (i; %/100), se ice li e (N); main e-
nance cos as a pe cen age o he i iga ion
sys em pu chase cos (Cm; %/100). Figu e
1 (page 159), shows he low diag am o
he design op imiza ion p ocess.
The p oposed algo i hm i s de e -
mines i he la e al should be ed om
one end o h ough an in e media e
poin by checking i Pmin = minimum
design p essu e o he submain is highe
han Pminobj = minimum a ge design
p essu e. I also e alua es he in e me-
dia e eeding poin o he la e al using
he me hodology de ined by Kelle and
Bliesne (1990) acco ding o he p oce-
du es men ioned in Schila di e al. (2017).
Figu e 1 (page 159), shows a nes ed
i e a ion p ocess o op imally de e mine
he al e p essu e (P op) and op imal
in ake al e loca ion (Nop). The calcu-
la ion sequence begins a he i s possible
in ake poin (N1) wi h an ou e i e a i e
p ocess (posi ion i e a ion), whe e op imal
elescopic sizing o he submain mani old
pipe is ca ied ou a di e en in akes
p essu es which a e s ablished in a second
inne i e a i e p ocess (p essu e i e a ion).
Thus, o each possible in ake posi ion and
o each possible al e p essu e head, om
he minimum (P min) o he maximum
design p essu e (P max) in an inc emen al
ange de ined by he use (PV S ep - Ex:
1 m), he op imal sizing o he submain
mani old pipe is ca ied ou wi h he abo e
men ioned p ocess (LMM-LM/KPH).
A a ian o he LMM me hod o
unknown p essu e head (LMM /UPH)
was no used o ind in a single sequence
pipe sizing and op imal al e p essu e,
a oiding he p essu e i e a ion cycle, since
i depends on he a p io i iden i ica ion o
he mos un a o able poin o he ne wo k,
which is subjec o unce ain y.
As addi ional condi ions o he design
o he i iga ion submain, he speed in
mani old pipes is es ic ed o a ange
o maximum and minimum admissible
alues, which a e de e mined by he use ,
usually be ween 2.5 and 0.5 m s-1.
Fo each p essu e and posi ion i e a ion
( igu e 1, page 159) an op imal design o
he submain mani old pipe is ob ained
and i s annualized o al cos s pe uni o
i iga ed a ea (CT; € ha-1 yea -1), li e-cycle,
o al in es men cos (Ca, € ha-1 yea -1),
main enance cos s (Cm - 5% o Ca; € ha-1
yea -1), ene gy cos s; i pumping is equi ed
(Ce; € ha-1 yea -1) and wa e cos (Cw; € ha-1
yea -1) associa ed o he subuni a e calcu-
la ed as shown in he ollowing equa ion
(Ca ión e al. 2013) which s a es:
(3)
(4)
1.05
a e w
CT C C C  
CT P
9.81
(1 ) (1 ) 3600
(1 ) 1 (1 ) 1
1.05
N N OS O n c
N N OS n w
Q H R
i i i i En
Ep Q eA R T
i i i i
S S S EU
 
−−
   

159
Tomo 51 • N° 2 • 2019
Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s
whe e:
Ci = o al in es men cos (€)
S = i iga ed a ea (ha)
i = in e es a e
N = se ice li e (yea s)
Qos= design low (m3 s-1)
Ho = subuni in ake p essu e (m)
Ep = pumping e iciency (0.65 on a e age)
Rn = annual ne c op wa e equi emen
(m3 ha-1 yea -1)
Enc = a e age cos o ene gy consumed,
(€ kwh-1)
Ea = gene al applica ion e iciency o he
i iga ion sys em (%/100)
T = ansmission a io o maximum
demand pe iod (20)
Pw = p ice o wa e , excluding ene gy
cos s o p essu e supply (€ m-3).
Figu e 1. Subuni op imiza ion p ocess wi h p essu e-compensa ing emi e s (GESTAR).
Figu a 1. Diag ama de lujo del p oceso de op imización de sec o es con emiso es
au ocompensan es (GESTAR).
160 Re is a de la Facul ad de Ciencias Ag a ias
C. E. Schila di Sícoli e al.
Though in he case o p essu e-
compensa ing emi e s he alues o
Cw and Cm a e cons an , hey a e inco -
po a ed in o he calcula ion p ocess o
be compa ed wi h designs made wi h
o he so wa e and/o wi h designs ha
include u bulen emi e s. The a o e-
men ioned cos app oach does no
conside explici elly he ex ended leng h
o he main pipe necessa y o conec he
op imum in ake poin o plo ne wo k.
Ne e heless, his cos and all s o age
and in as uc u e ine es men s equi ed
o make he subuni ope a ional can be
included in Cw and, i i is app op ia e,
also he ene gy cos s asocia ed o head
losses in he plo ne wo k and collec i e
ne wo k ha d i e wa e o he subuni .
Once he double nes ed i e a i e
p ocess is comple ed, he op imal join
design ( elescopic sizing o he submain
mani old pipe, p essu e and al e in ake
loca ion) is de e mined as he al e na i e
ha minimizes he o al annualized cos
pe uni o i iga ed a ea. A soon as he
op imal design has been comple ed, i s
hyd aulic simula ion can be pe o med
o p edic he de ailed p essu e dis i-
bu ion and e i y he p ope hyd aulic
ope a ion o he submain. The desc ibed
me hodology was implemen ed wi hin
he d ip i iga ion design module, in
he GESTAR so wa e package, using he
Visual Basic 6.0 p og amming language,
p o iding a new ad anced unc ionali y.
Resul s
The me hodology is applied o h ee
examples o i iga ion submains wi h
p essu e-compensa ing emi e s o hei
op imal design, whe e he geome ical and
opog aphic con igu a ion is he e oge-
neous. The esul s ob ained a e compa ed
wi h p e ious designs de eloped wi h
ano he comme cial compu e ool
(I icad P o) as a easibili y es .
The submains i iga e ineya ds
ha sha e he ollowing cha ac e is ics:
a) dis ance be ween ows: 2 m, b) dis ance
be ween plan s: 1 m, c) emi e low: 1.60 L h-1,
d) emi e spacing: 0.60 m, e) emi e ange o
compensa ion: 4-40 m, ) ex e nal diame e s
o he la e al: 16 mm, g) in e nal diame e o
he la e al: 15.5 mm, h) numbe o la e als
pe ow: 1 la e al, i) emi e manu ac u ing
a ia ion coe icien : 4%. Fo each example,
he layou o he main pipe uns pa allel o
e e y mani old pipe; his gi es he possibili y
o connec ing he al e a any poin along he
submain mani old pipes.
Based on he ex e nal diame e s (mm),
able 1 shows he cos s pe linea me e
o he possible pipes ha a e used in he
LMM/KPH-LM algo i hm o he submain
mani old pipe op imiza ion.
Fo he hyd aulic-economic op imiza ion
o he submains, he ollowing a iables
ha e been conside ed: a) ene gy p ice:
0.06 € kwh-1, b) wa e p ice: 0.10 € m-3,
c) cos o he la e al: 0.33 € m-1, d) in e es
a e: 7%, e) se ice li e: 25 yea s, ) pump
e iciency: 65%, g) annual ne i iga ion
equi emen s: 6,000 m3 ha-1, h) ansmission
a io: 1.05, and i) main enance cos : 5% o
annualized ma e ial acquisi ion cos (Ca).
Table 1. Ex e nal diame e s o pipes and hei co esponding cos pe linea me e .
Tabla 1. Diáme os ex e nos de ube ías y su co espondien e cos o po me o lineal.
DE (mm) 50 63 75 90 110 125 140 160 200
€/m 1.33 1.39 2.62 2.71 3.12 3.89 4.97 3.36 10.4
161
Tomo 51 • N° 2 • 2019
Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s
Figu e 2 and able 2 show he geome -
ical and opog aphic cha ac e is ics and
he esul s o he p e ious hyd aulic design
o he h ee submains, whe e he al e’s
p essu e (P ), submain low, leng h,
diame e and o al cos o seconda y pipes
a e shown.
Figu e 3 (page 162), shows he new
o m c ea ed wi h he GESTAR ool o
in oduce he necessa y da a o he
op imal hyd aulic-economic design o he
submains. Table 3 (page 162), summa-
izes he esul s o he hyd aulic design
op imiza ion o he submains and shows:
he numbe o hyd aulic designs (Designs
No.), he op imized design al e p essu e
(P ); he leng h, diame e and o al cos o
he mani olds op imized pipes.
While he cos o he la e al o each
design al e na i e (ini ial and op imized)
Table 2. Hyd aulic design cha ac e is ics o he i iga ion sec o acco ding o I icad P o.
Tabla 2. Ca ac e ís icas hid áulicas de diseño de los sec o es de iego ejemplo según
I icad P o.
Ej. S Flow P Diame e (mm) and
leng h (m) o pipes
To al
leng h
To al
Cos
ha m3h-1 m 90 75 63 50 m €
1 2.30 30.67 28 66 56 78 200 354.5
2 1.94 25.87 24 49 70 38 157 369.8
3 2.09 27.87 24 50 65 118 232 376.6
is he same, signi ican cos sa ings a e
achie ed by placing he al e a an in e -
media e poin o he submain mani old
pipe whe e he lows a e di ided and
design is op imized using he p oposed
algo ihm LMM/KPH-LM (13). Thus,
in Example 1 a 22% mani old pipe cos
educ ion is achie ed, while in Example
2 cos educ ion is in he o de o 34%
(because he pipe h oughou i s en i e
leng h is on an ascending slope) and in
Example 3 i is 16%.
Table 4 (page 162), summa izes he main
esul s o he hyd aulic-economic op imi-
za ion o he i iga ion submains and shows:
he in ake poin o he subuni (X/Lp), whe e
X is he dis ance downs eam o he submain
mani old pipe wi h espec o he connec ion
o he al e and Lp is he o al leng h o he
submain mani old pipe (20).
Figu e 2. Geome ic and opog aphic o m o submains (con ou lines e e y 1 m).
Figu a 2. Fo ma geomé ica y opog á ica de sec o es de iego (cu as de ni el cada 1 m).
162 Re is a de la Facul ad de Ciencias Ag a ias
C. E. Schila di Sícoli e al.
Figu e 3. GESTAR o m o da a en y o economic hyd aulic op imiza ion o submains
wi h p essu e-compensa ing emi e s.
Figu a 3. Fo mula io GESTAR de ing eso de da os pa a la op imización hid áulica y
económica de sec o es con emiso es au ocompensados.
Table 3. Op imized hyd aulic design ea u es o he i iga ion submains (Ges a ).
Tabla 3. Ca ac e ís icas de diseño hid áulicas op imizadas de los sec o es de iego (Ges a ).
Table 4. Main hyd aulic ope a ion cha ac e is ics o he op imized Ges a design o
he i iga ion submains (Ges a ).
Tabla 4. P incipales ca ac e ís icas de uncionamien o hid áulico del diseño
op imizado de los sec o es de iego (Ges a ).
Ej. A ea Designs PVop Diame e (mm) and Leng h (m) o pipes To al To al Cos
ha N° m 110 90 75 63 50 m €
1 2.30 1648 15 2 68 122 202 276.2
2 1.94 924 15 2 22.25 43.13 87.51 157 240.9
3 2.09 1648 15 2 72.31 157.59 232 315.4
Ej. X/Lp P (m) Pmax (m) Pmin (m) Vmax (m/s) Vmin (m/s) CeCeOp .
1 77 15 14.46 7.48 2.47 0.041 49.30 23.77
2 72 15 14.90 6.62 2.50 0.102 42.26 26.41
3 92 15 15.24 7.49 2.50 0.041 49.30 26.41