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IOP Publishing
doi:10.1088/1757-899X/1066/1/012011
1
Duc wo k P essu e Loss De e mina ion U ilizing Building
In o ma ion Model
Michal No áček 1, Jose Remeš 1
1 Ins i u e o Compu e Aided Enginee ing and Compu e Science, Facul y o Ci il
Enginee ing, B no Uni e si y o Technology, Ve eří 95, 602 00 B no, Czech
Republic
xpno ac03@ u b .cz
Abs ac . Building design c ea ed as an in o ma ion model con ains no only in o ma ion
o ma ed du ing building geome y c ea ion bu also addi ional in o ma ion illed in by a
designe . The da a can be used u he as well as applied in building geome y analyses. One o
hese a e analyses o p essu e loss in ai -handling uni s. Such analyses ake he ad an age o
bo h c ea ed geome ic pa ame e s, and basic physical a iable. These analyses can be ca ied
ou di ec ly in BIM so wa e wi hou ex e nal calcula ions needed. The main aim o his a icle
is o desc ibe u iliza ion o in o ma ion in building model leading o ob ain p essu e loss in ai -
handling uni s.
1. In oduc ion
Building c ea ed as a building in o ma ion model p o ides plen y o oppo uni ies. In o ma ion
con ained in model a e as comp ehensi e as he designe is. The model con ains undamen al
geome ic in o ma ion which become he s anda d in ci il enginee ing. On he o he hand, building
in o ma ion model can con ain complemen a y in o ma ion. These complemen a y in o ma ion a e
especially physic o igin and can be u ilized o building analysing which is impo an o sus ainable
building design. P ojec design phase is a building li e cycle phase when he mos impo an decisions
a e made, and changes occu . The decisions a e impo an o u he ealiza ion and building using
phase especially because o expendi u e. O e ime decisions con e ge o an op imal solu ion.
In some cases, he building can be analysed di ec ly in o he modelling so wa e wi h no ex e nal
applica ions o o he me hods needed. Comme cial so wa e al eady p o ides analysing ools u ilizing
physical models. Howe e , mos o he analyses a e no possible o be u ilized di ec ly in modelling
so wa e and one o hem is en ila ion duc wo k p essu e loss analysis. The analysing ools a e
in luenced by building na ional s anda ds equi emen s. Al hough physical equa ions a e gene al, i s
in e p e a ion and u ilizing depends on na ional habi s and s anda ds. Tha is he eason why
inconsis ency is in he analysing ools be ween coun ies. The solu ion can be o de elop na ional
s anda d analysing ools wi h he use o BIM da a in building design phase. [1]
2. Ven ila ion duc wo k p essu e loss
One o he equi emen s o p ope en ila ion duc wo k design is a an powe su icien o supply ai
in o e e y oom. [2] Duc wo k p essu e loss is needed o be calcula ed o designing he an. P essu e
Building De ec s 2020
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IOP Publishing
doi:10.1088/1757-899X/1066/1/012011
2
losses a e caused by ai ic ion agains he duc walls [3]. The p essu e loss on s aigh duc sec ions is
e y small. On he o he hand, in places whe e low di ec ion is changed (elbows, educ ions, o he
en ila ion i ings), he p essu e loss is conside able. Fo p essu e losses in duc i ings (excluding
s aigh pieces o duc ) we use he e m local p essu e loss.
Local p essu e losses a e exp essed as a p essu e d op by he di e ence o s a ic p essu es a he
beginning o he i ing and a i s end. This is based on Be noulli’s equa ion
(1)
whe e ρ is he ai densi y, is he mean eloci y in a gi en c oss-sec ion, p is he s a ic p essu e, h is
he heigh di e ence be ween he measu ed c oss-sec ion and he e e ence plane and pz is he p essu e
loss caused by ic ion.
I is assumed ha he sys em is ai igh , and he mass low is he e o e cons an . I he duc c oss-
sec ional a ea is cons an , he mean low eloci ies in di e en pa s o he duc a e equal. In he case
o ai duc s, he e ec o g a i y on he low is o en neglec ed. Wi h his simpli ica ion, he p essu e
d op o he duc i ing can hen be exp essed as equa ion
(2)
This p essu e d op can also be exp essed in e ms o mean eloci y as
(3)
whe e ρ is he ai densi y, is he low mean eloci y and ξ is he p essu e loss coe icien .
The p essu e loss coe icien is based on he duc i ing ype and depends especially on he na u e
o he low (Reynolds numbe ) and he i ing geome y. The p essu e loss coe icien alues can be
ound in ables [3-5] o (less o en) in he o m o ma hema ical equa ions [3, 6-7].
Fo p essu e loss calcula ion on s aigh duc s sec ions is used equa ion
(4)
whe e λ is he ic ion ac o , l is he leng h o he s aigh duc sec ion, D is he duc hyd aulic
diame e , ρ is he ai densi y, is he low mean eloci y.
The Coleb ook-Whi e equa ion is o en used o he ic ion ac o calcula ion
(5)
whe e ε is he absolu e oughness o he duc ma e ial, D is he duc inne diame e and Re is he
Reynolds numbe . In addi ion o he Coleb ook-Whi e equa ion, i s app oxima ion equa ions a e also
o en used. These equa ions exp ess he ic ion ac o explici ly [6].
To selec he su icien an powe , i is necessa y o calcula e he o al duc wo k p essu e loss. Tha
means o sum he p essu e losses o all i ing ypes and s aigh duc sec ions on he duc wo k. The
designe is o ced o conside a ious geome ic pa ame e s and ypes o indi idual i ings o selec
𝜌𝑣1
2
2+ 𝑝1+ ρgℎ = 𝜌 𝑣2
2
2+ 𝑝2+ ρgℎ + 𝑝𝑧,
𝑝𝑧= 𝑝2− 𝑝1
∆𝑝 = 𝜉𝜌 𝑣2
2,
∆𝑝 = $𝜆 ∙ 𝑙
𝐷∙𝜌𝑣 2
2,
1
√𝜆=%−2log+2,51
𝑅𝑒√𝜆+𝜀
3,7%𝐷5,
Building De ec s 2020
IOP Con . Se ies: Ma e ials Science and Enginee ing 1066 (2021) 012011
IOP Publishing
doi:10.1088/1757-899X/1066/1/012011
3
he app op ia e p essu e loss coe icien . Howe e , his p ocess can be au oma ed u ilized a duc wo k
model in building in o ma ion model.
3. Building in o ma ion model
Plen y o so wa e ha p o ides modelling buildings as BIM, also allows o model building se ices.
The me e geome y o a gi en duc sec ion exp essed by pa ame ic alues can se e as an inpu
a iable in he calcula ion o he p essu e loss.
Some so wa e, such as Au odesk Re i , allow o analyse en ila ion duc s di ec ly in he
applica ion’s use in e ace. Using men ioned so wa e, i is possible o analyse he en ila ion duc s
o p essu e loss by means o se e al me hods. Fo s aigh duc sec ions i is possible o choose om a
couple o app oxima ion equa ions (speci ically he Haaland equa ion and he Al shul-Tsaal equa ion)
and he Coleb ook-Whi e equa ion (5) o ob ain he ic ion ac o . The in e nal calcula ion also
conside s he na u e o he low acco ding o he alue o Reynolds numbe (so wa e dis inguishes
be ween lamina and u bulen low). The o al s aigh duc sec ions p essu e loss is de e mined using
he modelled geome y and speci ied amoun o supplied ai .
The duc i ing p essu e loss is calcula ed acco ding o equa ion (3) u ilizing he mass low and he
p essu e loss coe icien . The p essu e loss coe icien is ob ained in se e al possible ways: by he
inpu o use -en e ed coe icien alue o each en i y (each duc i ing) o by he use duc i ing
p essu e loss inpu di ec ly o each en i y and o by ob aining he coe icien alue om ASHRAE
able [8] which is au oma ically assigned o each en i y acco ding o he i ing ype.
Au oma ic i ing de ec ion in Re i and inding he p essu e loss coe icien in he ASHRAE able
may seem like he bes choice o he designe . Bu his me hod has some disad an ages. The i s is
he inabili y o edi he able (inabili y o edi he coe icien alues and pa ame e s) [9] and he second
is he impe ec sea ching o duc i ing ype. The able consis s o geome ic pa ame e s o a de ined
duc i ing ype, acco ding o which Re i inds he app op ia e coe icien alue. The p oblem occu s
when he geome ic pa ame e s o he duc i ing do no co espond exac ly o he abula alues o
he geome ic pa ame e s. In Czechia, duc i ings a e o en made- o-measu e and ha is he eason
why he e is no app op ia e alue in ASHRAE able. In hese cases, he able is unable o in e pola e
in e media e pa ame e alues. The exac ype o i ing is o en di icul o de ec ( o example, he
di e ence be ween smoo h adius elbow and mi e ed elbow).
The solu ion o hese impe ec ions can be ee access o abula alues and he possibili y o
edi ing hem. The abili y o in e pola ion is also needed o he u ilizing o ma hema ical equa ions
exp essing coe icien alues depending on geome ic pa ame e s and mo e accu a e de ec ion o duc
i ing ype.
4. Complex p essu e loss solu ion in BIM
The da a use om he building in o ma ion model o he pu pose o de e mining he duc wo k
p essu e loss can be u ilized by se e al ways. When using comme cial so wa e, in o ma ion can o en
be accessed wi h an ex e nal applica ion using API (Applica ion P og amming In e ace). As a esul ,
plen y o pa ame e s ha a e pa o he so wa e in o ma ion model can be u ilized as inpu a iables
o he physical models c ea ed in he sou ce code o he ex e nal applica ion.
An al e na i e o c ea ing an ex e nal applica ion may be o p ocess IFC ile. IFC ile is an
in e changeable o ma con aining he undamen al pa ame e s o he in o ma ion model. This ile
con ains numbe o pa ame e s ha can be used o analyse duc i ing p essu e loss. The ad an age is
he e sa ili y o his ile. Comme cial BIM ools can wo k wi h his ype o ile. Howe e , he
Building De ec s 2020
IOP Con . Se ies: Ma e ials Science and Enginee ing 1066 (2021) 012011
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doi:10.1088/1757-899X/1066/1/012011
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disad an age is he limi a ion in he numbe o pa ame e s con ained in he ile. In pa icula , he
physical pa ame e s wi h he duc i ing ype a e missing.
In bo h cases, i is possible o use geome ic pa ame e s and p ocess hem u he . The main pa o
he analy ical ool is i s physical model (physical equa ions), acco ding o which he calcula ion uns.
In he case o p essu e loss, he key ac o is local p essu e loss, i s alues o en a y in he li e a u e.
They a e mos o en w i en in abula o m. These coe icien alues a e cu en ly o en ob ained by
nume ical me hods, bu wi h some simpli ica ions hey may di e om he ac ual measu ed alues on
a eal duc wo k. Tabula alues may be unsui able o use in au oma ed calcula ion, as hei alues
need o be in e pola ed and he e is a isk ha he en e ed pa ame e s will be ou o he ange o alues
in he able. In such a case, i seems mo e app op ia e o use app oxima ion equa ions desc ibing he
dependences o he magni ude o he coe icien o local p essu e losses on he geome ic pa ame e s
o he duc i ing. Fo many duc i ings, he app oxima ion equa ions ha e no ye been de e mined
o a e de e mined based on nume ical analyses, no eal duc wo k expe imen s.
5. Resul s and discussions
Labo a o y expe imen o de e mine p essu e losses on he duc wo k is ime consuming bu
co esponds mos o he eal s a e o he duc wo k in he building. F om he alues measu ed in his
way, i is possible o compile equa ions, which can be used in he au oma ion o p essu e loss
calcula ions in he building in o ma ion model. An example o an au oma ic p essu e loss calcula ion
could be an ex e nal applica ion / add-on o Re i ha calcula es p essu e losses o undamen al duc
i ings, which a e elbows and ansi ions o ound and ec angula pipe c oss-sec ions. On he
in e ne , his applica ion called Re i Duc wo k P essu e Loss Calcula o is loca ed on he Gi Hub web
hos ing in he o m o an open-sou ce add-on o he Re i applica ion. I is an ex e nally accessing
applica ion ha uses he in e nal pa ame e s o he Re i so wa e o de e mine he ype o duc i ing
and hen assigns he app op ia e p essu e loss coe icien o each i ing u ilizing geome ic
pa ame e s. The coe icien is assigned om wo di e en sou ces. One sou ce is a abula alue
acco ding o he ASHRAE able om 2001 and he o he is ma hema ical equa ion e lec ing he
dependence o he coe icien on he geome y. Fo hese pu poses, he labo a o y expe imen esea ch
es ablished analy ical equa ions depending he coe icien o local p essu e losses on 45° and 90°
elbows geome y pa ame e s. The equa ions a e inco po a ed in o he applica ion and can be ound in
he Table 1.
The ad an age o he applica ion is he possibili y o i s use edi ing. Edi ing abula alues,
including he alues o hei pa ame e s, is use - iendly wi hou he need o in e ene in he sou ce
code, as hese alues a e s o ed in a ex ile. I is he e o e possible o adap he coe icien alues o
designe expe ience o p e e ences. The men ioned applica ion has he po en ial in Re i so wa e o
be de eloped in o an au oma ic ool o he analysis o p essu e losses o he Czech (and o
in e na ional) en i onmen . The applica ion de elopmen consis s mainly in adding o he duc i ings
o he sou ce code, which he algo i hm would conside and hus con ain a sa is ac o y numbe o
i ings o e ime. O he elemen s sui able o inclusion in he calcula ion could also be he e ec o
elbows ha a e placed downs eam nea ly each o he wi h small o no duc s aigh pa . This
ad anced analysis can lead o mo e accu a e esul s o p essu e losses. Fo wo consecu i e elbows,
he abula alues a e o en unsa is ac o y, and he analy ical exp ession o he coe icien -geome y
dependency is no common. Fo his pu pose, ec angula c oss-sec ion elbows wi h di e en aspec
a ios o c oss-sec ions and di e en alues o axial ounding and di e en sizes o he s aigh
in e media e pa be ween he elbows we e analysed. The esul is he equa ion ha can be
inco po a ed in o an analy ical ool ha u ilizes in o ma ion in a building model. The equa ions o
p essu e loss dependence a e gi en in he ollowing Table 1.
Building De ec s 2020
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doi:10.1088/1757-899X/1066/1/012011
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Table 1. Dependency o p essu e loss coe icien on he geome y (W is wid h o he ec angula duc
c oss-sec ion, H is heigh o he ec angula duc c oss-sec ion, L is leng h o in e media e s aigh
sec ion).
Duc wo k ype
Dependency o p essu e loss coe icien and duc i ing
geome y
Elbow 1 × 45°
Elbow 1 × 90°
Elbows 2 × 45°
Elbows 2 × 90°
Table 2. Measu emen e o s, equa ion alidi y in e als, esidual sum o squa es and le el o
signi icance (W is wid h o he ec angula duc c oss-sec ion, H is heigh o he ec angula duc c oss-
sec ion, L is leng h o in e media e s aigh sec ion).
Duc wo k ype
Absolu e e o
Validi y in e al
Residual sum
o squa es
(RSS)
Le el o
signi icance α
Elbow 1 × 45°
0,339
0,95
Elbow 1 × 90°
0,395
0,95
Elbows 2 × 45°
8,578
0,95
Elbows 2 × 90°
30,390
0,95
6. Conclusions
The building in o ma ion model s o es a subs an ial amoun o in o ma ion ha can po en ially be
used. The mo e in o ma ion he model con ains, he mo e p ac ical u ilizing ways he e a e. U ilizing
he BIM model o analy ical asks is an ad anced ea u e o design so wa e and o e s conside able
po en ial, which allows us o make compe en decisions based on analysis and da a a a ime when we
can in luence he shape o he building wi h a minimum o cos s. By simply using he al eady exis ing
pa ame e s and supplemen ing he physical calcula ing, i is possible o au oma e and o s eamline
building analysing. In his way, we can also maximize he use o a ailable in o ma ion in he model.
In addi ion o he bene i apid ans e o all c ea ed in o ma ion abou he building, BIM also o e s
he po en ial o applica ion in he physical cons uc ion ield.
The duc wo k p essu e losses de e mina ion is necessa y o he design o en ila ion sys em in a
building. This p ocess can be leng hy and complica ed. The undamen al a iables o he calcula ion,
which a e he coe icien s, o en di e and a e no uni o m o he Czech en i onmen . In his espec ,
𝜉 =−12,970*𝑊
𝑅-2+31,350𝑊
𝑅−18,490
𝜉 =−5,606(𝑊
𝑅+2+14,210𝑊
𝑅−8,470
𝜉 =0,043'𝐻
𝑊*−2,441 −0,015'𝐿
𝑊*3+0,072'𝐿
𝑊*2
𝜉 =0,432(𝐻
𝑊+−1,248 −0,007(𝐿
𝑊+3+0,032(𝐿
𝑊+2
𝑊
𝑅= (1,0244; 1,3548)
𝑊
𝑅= (1,0244; 1,3548)
𝐻
𝑊= (0,254; 1,000)
𝐿
𝑊= (1,476; 3,952)
𝐻
𝑊=(0,254; 1,000)
𝐿
𝑊= (1,476; 3,952)

Building De ec s 2020
IOP Con . Se ies: Ma e ials Science and Enginee ing 1066 (2021) 012011
IOP Publishing
doi:10.1088/1757-899X/1066/1/012011
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he uni ica ion o alues o ma hema ical dependencies can be a s ep owa ds s anda dizing his
analysis and a simpli ying, e ining, and speeding i up. Wi h simple au oma ion p ocesses, we can
sa e a conside able amoun o ime and hus design buildings e icien ly in he con ex o cu en
needs.
Re e ences
[1] P. Smi h, “BIM implemen a ion - global s a egies,” P ocedia enginee ing, pp. 482-492, 2014.
[2] P. Schild, and M. Mysen, “Recommenda ions on Speci ic Fan Powe (SFP) and Fan Sys em
E iciency –IV,” TZB-in o, P ague: Jícha, 2014.
[3] J. Chyský, and K. Hemzal, “Ven ila ion and ai condi ioning,” Thi d comple ely ewo ked
edi ion. P ague: B p ess, B no; 1993.
[4] I. Idelchik, D. G unae , and A. Ba ouch, “Handbook o Hyd aulic Resis ance,” X/5. Mosk a-
Lening ad: Gosuda s ennoe Ene ge icheskoe Izda el's o, 1960.
[5] K. Labou ka, and T. Suchánek, “Local p essu e loss coe icien alues – hea sou ces and
undamen al duc i ings,” TZB-in o, P aha, ©2001-2019.
[6] J. Schwa ze , and V. Zm hal, “De e mina ion o local p essu e loss coe icien s u ilizing,”
A icle. 2010.
[7] S. Genić, I. A andjelo ić, P. Kolendić, M. Ja ić, N. Budimi , and V. Genić, “A Re iew o
Explici App oxima ions o Coleb ook’s Equa ion,” Re iew, 2011.
[8] R. Howell, H. Saue , and W. Coad, “P inciples o Hea ing, Ven ila ing, and Ai Condi ioning,”
Ilus a ed edi ion, A lan a: Ame ican Socie y o Hea ing, Re ige a ing and Ai -Condi ioning
Enginee s, 2005.
[9] Au odesk. I 's no possible o modi y ASHRAE Table in Re i . Au odesk Knowledge Ne wo k,
Au odesk Inc.; 2017.