LOCAL HEAD LOSS IN PLASTIC PIPELINE JOINT WELDED BY ...

J. Hydrol. Hydromech., 54, 2006, 3, 299–308
LOCAL HEAD LOSS IN PLASTIC PIPELINE JOINT WELDED BY BUTT FUSION
JAN MELICHAR 1) , JAROSLAVA HÁKOVÁ 2) , JAROSLAV VESELSKÝ 3) , LUBOŠ MICHLÍK 4)
1)
Czech Technical University in Prague, Faculty of Mechanical Engineering, Technická 4, 166 07 Prague 6, Czech Republic;
mailto: Jan.Melichar@fs.cvut.cz
2)
Federation for Industrial′s Services CZ, s.r.o., Zelená 34, 160 00 Prague 6, Czech Republic; mailto: slavkah@volny.cz
3)
Czech Technical University in Prague, Faculty of Mechanical Engineering, Technická 4, 166 07 Prague 6, Czech Republic;
mailto: Jaroslav.Veselsky@email.cz
4)
Czech Technical University in Prague, Faculty of Mechanical Engineering, Technická 4, 166 07 Prague 6, Czech Republic;
mailto: Lubos.Michlik@email.cz
Introduction
The article deals with experimental determination of local head loss in straight polypropylene pipeline
(PP) joint connected by butt-welding. A local loss coefficient is introduced for turbulent flow of water in
plastic pipeline of circular cross-section. The value of local loss coefficient has not been experimentally
quantified so far and hence its determination is significant for designers of plastic pipeline systems.
KEY WORDS: Local Loss, Frictional Loss, Plastic Pipelines.
Jan Melichar, Jaroslava Háková, Jaroslav Veselský, Luboš Michlík: MÍSTNÍ ZTRÁTA VE SPOJI
PLASTOVÉHO POTRUBÍ SVAŘOVANÉHO NA TUPO. Vodohosp. Čas., 54, 2006, 3; 5 lit., 7 obr.
Článek pojednává o experimentálním stanovení místní ztráty ve spoji přímého potrubí z polypropylenu
(PP), zhotoveného svařováním na tupo. Je uvedena velikost součinitele místní ztráty spoje plastového
potrubí kruhového průřezu při turbulentním proudění čisté vody. Místní ztráta doposud nebyla
experimentálně kvantifikována, a proto je její stanovení pro projektanty potrubních systémů z plastů
významné.
KLÍČOVÁ SLOVA: místní ztráta, ztráta třením, plastové potrubí.
Pressure pipes for transport of water and other
fluids are used in many branches of industry.
Lately, the use of plastic pipes and fittings is more
frequent in various technological processes. This
results in a new quality for pipe works. It is possible
to substitute a standard steel pipe by plastic
pipe, in particular for a reconstruction of existing
technological equipments. The thermoplastic pipelines
hence become a standard pipeline material.
Polyethylene (PE) and polypropylene (PP) pipelines
are frequently used for pipeline conduits and
water supply networks, as well as for pipelines in
chemical and food processing industry. Using of
linear high-density polyethylene (PE-HD) for building
of long distance pipeline conduits in water supply
and distribution systems, for hydraulic transport
of solid wastes out from thermal power plants, for
transport of coal, ore substratum and gravel has
become common in the well-developed countries.
In the present days PE-HD pipelines of the third
generation enable to be used in severe working
conditions. PE-HD is partially crystalline thermoplastic
and belongs to a member of polyolefin
group. It is rigid and in comparison with PP has
greater hardness and compactness. The polypropylene-homopolymer
β modification pipes (βPP-H) are
used for example for the distribution of high temperature
mediums (lies, acids, thinners) and cold
water.
The knowledge of correct values of friction and
local loss coefficients is important for the designers
of pipeline systems that consist of straight plastic
pipes and constructional elements. Sufficient
amount of experimental data is important for correct
determination of losses. The precise evaluation
of losses enables to obtain the required fluid operation
parameters in the system (flow rate, pressure)
and can markedly affect the optimum operation in
long or complex pipeline conduits.
299

J. Melichar, J. Háková, J. Veselský, L. Michlík
In case of long pipelines like important water
supply pipeline or penstock into hydroelectric
power plants the way of connecting single plastic
tubes is from the mechanical and economical point
of view important. Besides classical and standard
connecting components for tube connections (e.g.
flanged connection, screwed fitting) in particular
glue connecting (eventually chemical welding
while cold) and thermal welding methods are used.
In general, butt-welding is the most common,
most simple and most reliable way of connecting
pipes for long pipeline conduits from PE and PP
materials. During this process of connecting, which
consists of warming-up and melting the ends of
elements prepared for the connection and following
their pressing down, the inner roughness – the emanation
of the material inside pipeline (see Fig. 1) is
created.
Fig. 1. The thermoplastic pipeline joint welded by the buttwelding
method; PE left, PP right.
Obr. 1. Spoj trubek z termoplastů svařovaných metodou na
tupo; PE vlevo, PP vpravo.
The size of a butt weld joint is for certain material
and wall thickness dependent on the welding
process. The exact welding techniques are recommended
for example by instructions of DVS
(Deutscher Verband für Schweisstechnik). The
inner butt weld in the tube represents the specific
kind of inner resistance and results in additional
losses of the fluid flow. The effect of local losses
caused by butt welds on total energy balance for
long pipelines is important. However, in design
practice it is often underestimated or neglected. The
adverse influence of the butt welds on head losses
for fluid flow in a pipeline and a possibility of creation
of cavitation in the jointing point under high
flow velocity is possible to eliminate by using the
300
apparatus for elimination of inner projections, alternatively
by more expensive connecting technology.
However, in design practise it is paradoxically
preferred the use of least expensive connecting
technology over a possibility to eliminate the local
losses and reduce the operating costs.
Insufficient amount of information for the determination
of a local loss coefficient ζ for the butt
weld with a projection is the main problem in design
practice. A certain simplification, for example
approximate analogy between butt weld projections
and an orifice, was considered. However, these
values of the local loss coefficient were only rough
estimates, anticipated parameters of designed systems
were often largely different from real parameters
that were determined after the construction.
Experimental works in the Czech Technical University
Prague, Faculty of Mechanical Engineering
were carried out in order to obtain quantitative values
that provide more accurate assessment of the
local losses for butt welds in jointing point of plastic
pipe from PP and PE materials. The main aim of
this research was to determine the fundamental data
on the local losses that should be usable in design
practice.
The experimental assessment of the local loss
coefficient of the butt weld in jointing point
in PP pipeline
Fig. 2 shows the pipe test that was constructed in
order to determine the local losses for the butt
welds.
The hydrodynamic pump powered by an asynchronous
electric motor provides flow of water
through pipeline. The flow rate through measuring
part of the pipe is possible to change by alternation
of the pump rotation speed through frequency converter
with full open regulation valve situated in the
end of the test loop or by closing and/or opening of
the valve at constant pump speed. The test section
of the test loop (see Fig. 3) was made of straight
polypropylene tube 90 x 8.2 βPP-H S5/SDR11
(equivalent 90 DN80/PN16), which was commercially
available from the manufacturer Georg
Fischer +GF+. These plastic tubes are supplied at
5 m sections. Allowed manufacturing tolerance of
external diameter and wall thickness is prescribed
by the DIN 8077 standard and corresponds also
with ISO 4065 standard. The average value of inner
tube diameter in joints d = 72.5 mm was ascertained
by metering.

Local head loss in plastic pipeline joint welded by butt fusion
Fig. 2. Straight pipe for local pressure loss measurement at βPP-H plastics tube joint. Experimental test loop (above): 1 – hydrodynamic
pump, 2 – electromotor with frequency converter, 3 – βPP-H pipeline, 4 – flow regulation valve, 5 – magnetic flow-meter, 6
– butt welded joint, 7 – pressure taps for static pressure, 8 – differential pressure sensors, 9 – A/D conversion unit, 10 – PC.
Obr. 2. Experimentální trasa pro měření místní tlakové ztráty ve spoji plastových trub z βPP-H. Schéma zařízení (nahoře): 1 –
hydrodynamické čerpadlo, 2 – elektromotor s frekvenčním měničem, 3 – βPP-H potrubí, 4 – regulační armatura, 5 – indukční
průtokoměr, 6 – spoj svařením na tupo, 7 – odběry statického tlaku, 8 – diferenční snímače tlaku, 9 – A/D převodník, 10 – PC.
301

J. Melichar, J. Háková, J. Veselský, L. Michlík
Fig. 3. Test section of the test loop, location of pressure taps and pressure-difference sensors; S – pipe jointing point, 1, 2, 3 – pressure
taps.
Obr. 3. Experimentální úsek potrubní trasy, umístění odběrů tlaků a snímačů tlakové diference; S – spoj potrubí, 1, 2, 3 – odběry
statického tlaku.
The horizontal test section of the test loop is
composed of the proper metering pipe length (pipeline
joint between pressure taps 2 and 3) with sufficient
straight pipeline length before (l2S ≈ 5.1d) and
behind the jointing point (lS3 ≈ 10.13d), where the
influence of jointing point on flow pattern is anticipated.
In front of this measuring section there is a
straight pipeline with the corresponding length (l12
= l2S + lS3 = l23 – b = 15.23d). The inner projection
of the butt weld with length b ≈ 0.08d in the pipeline
joint affects the flow in particular behind the
jointing point, where the head loss occurs at relatively
long pipeline length. The losses in a pipeline
before and behind the butt weld or more precisely
the lengths, which we can assume to have significant
influence on flow pattern, depend on the type
of element, its geometric parameters, pipeline wall
roughness and the Reynolds number value. Skalička
(1985) showed that the flow pattern could be sometimes
affected on the distance of 50d behind the
element projection that evokes the head loss. However,
for location of static pressure taps in relation
to measured element there are no any universal
recommendations. With reference to the butt weld
302
geometry and used pipeline material (βPP-H is nontransparent)
the above-mentioned distances between
static pressure taps and examined jointing
point were used. Static pressure taps at a pipeline
cross-section (metering locations) in the experimental
pipeline were made of four pipeline side inlets
that were evenly placed. Fig. 4 shows the detailed
arrangement.
The static pressure differences, ∆p12, between the
cross-section 1 and 2 and ∆p23 between the crosssection
2 and 3 were measured with the use of calibrated
differential pressure sensors with range 0 –
–16 kPa/4 – 20 mA. The estimated accuracy of
pressure difference measurements is up to 0.25 % of
a measuring range. The flow rate, Q, was measured
using magnetic flow meter of type MQI 99
SMART. The accuracy 0.5 % of measured flow rate
was guaranteed within the range of 10 to 100 %
of Qmax. The mercury thermometer was used to
measure the water temperature. The analogue output
signals from the magnetic flow meter and the
differential manometers were compiled by A/D
converter UDAQ – 1208 and transmitted and stored
into PC using program for UDAQ – 1208 proces-

Fig. 4. Annular arrangement of pressure taps.
Obr. 4. Kruhové odběry statického tlaku.
sing unit. The volumetric flow rate and the pressure
differences average values were shown in a graphical
form and then computed as the arithmetic average
of respective values recorded fifteen times
within interval of 2 seconds. The βPP-H tube jointing
point which is single constructional pipeline
element was made by engine plant according to
DVS 2208/1 in compliance with the requested production
process (direction DVS 2207/1), specifying
the exact warming-up time, the adherence pressure
size and the cooling time for a given material and
wall thickness. Dimensions of this etalon jointing
point are shown in Fig 5. The etalon size is proportional
to the tube inner diameter d = 72.5 mm.
The joint is placed between the straight pipeline
sections, which were possible to be considered as
hydraulically smooth. Absolute roughness of
k ≈ 0.003 mm was found from the manufacturers’
recommendations. Kolář and Vinopal (1963) indicate
that the pipeline is possible to be considered as
hydraulically smooth if it has uniform pipeline wall
roughness and if the following condition 17.85
Re -0.875 ≥ k.d -1 is guaranteed. This condition was
fulfilled for all Reynolds numbers during the experimental
measurements. The flow rate was chosen
with reference to recommended mean velocity
of fluid in order to prevent flow from high flow
velocities that could result in cavitation. For flow
velocities c > 4.3 m s -1 in pipeline with the inner
diameter d = 72.5 mm and with the corresponding
Reynolds numbers Re > 3.4 . 10 5 the cavitation was
indicated at least acoustically. With regard to inner
butt weld geometry the cavitation occurrence
should be considered as another significant restric-
Local head loss in plastic pipeline joint welded by butt fusion
tive factor for velocity selection in the case when
the tube joint method by butt-welding will be selected
and the inner weld projections will not be
removed.
Fig. 5. The inner butt weld geometry of plastic pipe joint 90 x
8.2 βPP-H S5/SDR11 welded by butt method; d 0 ≈ 0.87 d,
b ≈ 0.08 d, b′ ≈ h ≈ 0.04 d.
Obr. 5. Geometrie vnitřního svalku spoje plastových trubek
90 x 8,2 βPP-H S5/SDR11 svařených metodou na tupo;
d0 ≈ 0,87 d, b ≈ 0,08 d, b′ ≈ h ≈ 0,04 d.
303

J. Melichar, J. Háková, J. Veselský, L. Michlík
The head loss generated at the joint of straight
pipeline (local loss) is given by an increase of the
loss at the straight pipeline section with given local
loss against frictional loss at the same system without
local loss. The head losses can be expressed in
terms of fluid specific energy Yz (J kg -1 ), which is
consumed in a given pipeline section. The concrete
values of Yz are determined by computation from
the measured values of pressure difference, ∆p12
and ∆p23.
Along the straight pipeline length between cross
sections 1 and 2 the pressure drop through the frictional
losses can be computed from the Darcy-
Weisbach equation:
304
2
∆ p12 l12 c
Yzf
= = λ.
. . (1)
ρ d 2
The friction factor λ in the case of turbulent flow
in hydraulically smooth straight pipeline depends
only on Reynolds number. For this type of flow it is
possible to use a number of formulas, see for example
at Kolář and Vinopal (1963). Usually, the
Blasius formula is used:
−0.25
λ = 0.3164 . Re
(2)
or formula given by Advani:
−0.237
λ = 0.0032 + 0.221. Re , (3)
where Reynolds number is:
Re =
cd .
. (4)
ν
The validity of formula 2 is usually given in
literature for the range of Reynolds numbers
2 300 < Re

very good agreement between measured values of
the friction factor, λ, and computed ones from Eq.
(3). The results in Fig. 7 show practically constant
value of the local loss coefficient ζ = 0.6 for measured
values of the Reynolds number within a range
of 6.10 4 < Re < 5.10 5 and/or flow velocity 0.77
m s -1 < c < 6.39 m s -1 . According to Kolář and Vinopal,
(1963) value of the local loss coefficient for
a sharp-edged normalised orifice with the same
ratio d0/d = 0.87 is around 1.0, which is by 67 %
greater than the actual measured values of the tube
joints with butt welds. However, according to Idelčik
(1960) this value is only 0.6. It must be pointed
out that the sharp-edged normalised orifice and the
tube joints are quite different pipeline elements and
hence using of more accurate measured value is
justified.
In design practice it may be much easier to work
with equivalent pipe length, le. This is the length of
straight pipeline of the same diameter as the fitting,
which would have the same pressure drop as the
fitting, in our case the pipeline joint with the inner
butt weld. Considering the condition Yz f = Yz l from
Eqs. (1) and (8) the equivalent pipeline length can
be computed as follows:
ζ
le = . d.
(10)
λ
Using Eqs. (10) and (3) for the friction factor λ
and considering pipe diameter and experimentally
0.04
0.03
λ (1) 0.02
Local head loss in plastic pipeline joint welded by butt fusion
determined value ζ = 0.6 the equivalent length of
pipe can be computed. For the above-mentioned
range of flow velocity c through pipeline 90 x 8.2
βPP-H S5/SDR11 the value of the equivalent pipe
length varied from le = 2.23 to 3.33 m. These values
show that the local losses represent important part
of the total losses. This is significant in particular
for long PP pipeline systems. For examples in pipeline
90 x 8,2 βPPH S5/SDR11 with the length of
100 m inner projections of nineteen butt-welded
joints may cause the increase of head losses from
42 to 63 % for the above-mentioned Reynolds
numbers in comparison with the same pipeline
without butt welds.
The geometry of inner projections of the buttwelding
joints in PE tube is rather different. The
ration of d/d0 is approximately the same as for PP
tube joints. The expected projection width b depends
on wall thickness and for the same inner
diameter and wall thickness is for PP tube and PE
tube approximately identical. However, the PE tube
projections have more rounded edge, which leads to
assumption of lower basic local loss coefficient
value in the PE tube joints. It should be pointed out
that correct values of the local loss coefficient ζ
could be determined only experimentally using the
PE tube etalon joints.
Experimental data
Advani Eq. 3
Blasius Eq. 2
5x10
Re (1)
4 5x105 105 0.01
Fig. 6. Measured and computed values of the friction factors in straight pipeline test section of length l 12 in dependence on the
Reynolds number.
Obr. 6. Porovnání naměřených a vypočtených hodnot součinitelů tření v přímém potrubí délky l 12 v závislosti na Reynoldsově čísle.
305

J. Melichar, J. Háková, J. Veselský, L. Michlík
306
ζ s (1)
0.8
0.6
0.4
0.2
5x10
Re (1)
4 5x105 105 0.0
Fig. 7. Values of basic local loss coefficient for the βPP-H tube joint ζ in dependence on Reynolds number.
Obr. 7. Hodnoty základního součinitele místní ztráty spoje βPP-H trub ζ v závislosti na Reynoldsově čísle.
Conclusions
The paper shows basic values of the local loss
coefficient for the βPP-H tube joints with butt
welds that were experimentally determined for turbulent
flow with Reynolds numbers within the
range of 60 000 < Re < 500 000. The local loss
basic coefficient at pipeline joints was for the
above-mentioned range of Reynolds numbers constant
with the average value of ζ = 0.6 . This value
was determined for PP tube diameter of 72.5 mm
and for the joint and diameter proportion
d0/d = 0.87 .
It is necessary to point out that in practice the local
loss value can be dependent on various butt
weld dimensions that depend on a technological
process of the assembly. However, taking into account
the exact size variability is practically impossible.
With regard to large pressure drops at buttwelded
PP tube joints that become significant in
particular for long pipelines it is possible to recommend
removing the butt welds projections
and/or using tube joint technology, which would
not result in this kind of local losses.
Acknowledgement. The authors are particularly
grateful to the companies FIS CZ s.r.o. Praha and
BHV sensory s.r.o. Praha. Thanks are expressed to
the Company FIS CZ for necessary material supply
and experimental pipeline assembly and to the
Company BHV for granting the techniques for experimental
measurements.
Received 15. December 2005
Review accepted 14. June 2006
List of symbols
b, b´ – width of inner butt weld projection at pipeline joint
[m], [mm],
c – mean flow velocity [m s -1 ],
d – inner pipeline diameter [m], [mm],
h – height of butt-welds projections [m], [mm],
I – electric current [A], [mA],
K – constant in Eq.(6),
k – hydraulic roughness of inner pipeline wall [mm], constant
in Eq.(9),
l – length of straight pipelines sections [m], [mm],
p – static pressure [Pa],
Q – flow rate [m 3 s -1 ],
Re – Reynolds number [–],
T – fluid temperature [ 0 C],
Y – specific fluid energy [J kg -1 ],
λ – friction factor [–],
ν – kinematic viscosity [m 2 s -1 ],
ρ – fluid density [kg m -3 ],
ζ – local loss coefficient [–],
∆ – difference.
Subscripts
e – equivalent,
f – frictional,
l – local loss,
s – pipeline joints,
z – loss-making,
0 – at pipe contraction,
12, 2S, S3 – at cross sections between marked locations,
eventually between pressure taps.
REFERENCES
HÁK V., 2002: Long force main projection speciality by pipeline
thermoplastic PE-HD application. (In Czech.) Heating,
ventilation, installation no. 4, p, 142–145.
IDELČIK I. E., 1960: Handbook of hydraulic. (In Russian.)
Moskva: Gosenergoizdat, p. 123.

KOLÁŘ V., VINOPAL S., 1963: Hydraulics of industrial
armature. (In Czech.) I. publication, Prague, SNTL, p. 64–
181.
MELICHAR J., BLÁHA J., HÁKOVÁ J., 2004: Contribution
to possibility of using plastics pipeline for fluid transport at
waterpower engineering. (In Czech.) Hydroturbo 2004 – International
conference of Water power engineering. Brno
2004, p. 243–252.
SKALIČKA J., 1985: Local hydraulic loss by stable pressure
flow. (In Czech.) Pumps, pipeline, armature no. 2-3, p. 10–
–15.
MÍSTNÍ ZTRÁTA VE SPOJI PLASTOVÉHO
POTRUBÍ SVAŘOVANÉHO NA TUPO
Jan Melichar, Jaroslava Háková,
Jaroslav Veselský, Luboš Michlík
Tlaková potrubí pro dopravu vody i jiných kapalin se
používají v mnoha odvětvích národního hospodářství.
V poslední době se v řadě technologických procesů stále
více uplatňují potrubí a armatury z plastů, které představují
novou kvalitu částí zařízení čerpací techniky. Standardní
ocelové potrubí může být v opodstatněných
případech nahrazeno potrubím z plastů, zejména při rekonstrukci
stávajících technologických zařízení. Termoplasty
se tak stávají standardním potrubním materiálem.
Často používanými plasty pro stavbu potrubních rozvodů
a sítí ve vodárenství, chemickém a potravinářském
průmyslu jsou polyetylény (PE) a polypropylény (PP).
Používání lineárních vysokohustotních polyetylenů (PE-
HD) při stavbě dlouhých potrubních řadů ve
vodárenských potrubních soustavách, v hydrodopravě
tuhých odpadů energetických centrál, uhelných
a rudných substrátů a štěrkopísků, je dnes již ve
vyspělých zemích běžné. V současnosti zaváděné
lineární PE-HD 3. generace umožňují aplikace do nejtěžších
provozních podmínek. Potrubí z polypropylenuhomopolymeru
β modifikace (βPP-H) se používají např.
pro rozvody médií s vysokou teplotou (louhy, kyseliny,
ředidla) a studené vody.
Pro projektanty potrubních systémů, složených
z přímých plastových trub a nezbytných konstrukčních
prvků, je důležitá znalost konkrétních hodnot součinitelů
třecích a místních ztrát. Pro spolehlivý návrh systému,
resp. pro co možná nejpřesnější výpočet velikosti hydraulických
ztrát, je důležitý dostatek experimentálně
ověřených podkladů. Správné určení velikosti hydraulických
ztrát rozhoduje o splnění požadovaných parametrů
kapaliny v systému (průtok, tlak) a výrazně
může ovlivnit hospodárnost provozu systému, zejména
u dlouhých nebo členitých potrubních řadů.
U dlouhých potrubních řadů, jako jsou např. vodovodní
potrubí nebo přivaděče vodních elektráren, je
z technicko-ekonomického hlediska významný způsob
spojování jednotlivých plastových trub. Při spojování
částí plastového potrubí se vedle klasických spojovacích
prvků (např. přírubové spoje, šroubení) uplatní hlavně
spojování lepením (popř. chemickým svařováním za
Local head loss in plastic pipeline joint welded by butt fusion
studena) a tepelným svařováním. Svařování na tupo je
v běžné praxi nejobvyklejším, nejjednodušším
a spolehlivým způsobem spojování trub v dlouhých
potrubních řadech z PE a PP. Při této technologii spojování,
sestávající z ohřevu a natavení konců spojovaných
dílů a jejich následného přítlaku, však v místě
spoje vznikají vnitřní nerovnosti – svalky v potrubí.
Vnitřní svalek v potrubí představuje specifický typ
místního odporu, způsobujícího ztráty mechanické energie
proudu při průtoku kapaliny. Vliv svalky způsobených
lokálních ztrát na celkovou energetickou bilanci
dlouhých potrubních řadů není zanedbatelný,
v projektové praxi však bývá často podceňován nebo
opomíjen. Nepříznivý vliv vnitřních svalků na velikost
ztrát při proudění kapaliny potrubím a možnost vzniku
kavitace v místě spoje při vysokých rychlostech
proudění lze eliminovat použitím zařízení k odstranění
vnitřního svalku, případně využitím nákladnější technologie
spojování. V praxi však někdy bývá paradoxně
upřednostňována nejméně nákladná technologie spojování
před možností snížení nákladů provozních, a to
vyloučením místních ztrát energie ve spojích trub.
Problémem v projekční činnosti je nedostatek dostupných
podkladů pro stanovení základní hodnoty součinitele
místní ztráty spoje ζ . Při stanovení výpočtových
hodnot součinitelů ζ spoje s vnitřním svalkem se dosud
vycházelo ze zjednodušení, jakým je například určitá
analogie mezi svalkem a potrubní clonou. Je ale zřejmé,
že svalek a normalizovaná potrubní clona jsou tvarově
odlišné prvky. Odhadované hodnoty součinitele místní
ztráty byly orientační, předpokládané parametry
navržených systémů se mnohdy lišily od parametrů skutečných,
zjištěných až po realizaci zařízení. K získání
kvantitativních hodnot, umožňujících přesnější stanovení
velikosti místních ztrát na vnitřním svalku ve spoji
plastových trub z PE a PP, byly proto provedeny na
Fakultě strojní ČVUT v Praze experimentální práce.
Cílem bylo získání základních údajů o velikosti výše
uvedené místní ztráty, které by byly využitelné
v projekční praxi.
Seznam použitých symbolů
b, b′ – šířka vnitřního svalku ve spoji potrubí [m], [mm],
c – rychlost proudění kapaliny [m s -1 ],
d – vnitřní průměr potrubí [m], [mm],
h – výška svalku [m], [mm],
I – proud [A], [mA],
K – konstanta ve vztahu (6) [kg m -6,25 s -0,25 ],
k – hydraulická drsnost vnitřní stěny potrubí [mm], konstanta
ve vztahu (9) [m 7 kg -1 ],
l – délka rovných úseků potrubí [m], [mm],
p – statický tlak [Pa],
Q – průtok [m 3 s -1 ],
Re – Reynoldsovo číslo [–],
T – teplota kapaliny [°C],
Y – měrná energie kapaliny [J kg -1 ],
λ – součinitel tření [–],
ν – kinematická viskozita [m 2 s -1 ],
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J. Melichar, J. Háková, J. Veselský, L. Michlík
ρ – měrná hmotnost kapaliny [kg m -3 ],
ζ – součinitel místní ztráty [–],
∆ – rozdíl.
Indexy
e – ekvivalentní,
f – třecí,
308
l – místní ztráty,
s – spoje potrubí,
z – ztrátová,
0 – v místě zúžení průtočného průřezu,
12, 2S, S3 – v úseku mezi vyznačenými místy, příp. mezi
odběry tlaku.