centrifugal pumps sterling cap_6
TRANSCRIPT
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6 Head losses in pipework and fittings
6.1 Head losses HJ in straight pipework
6.1.1 General
For pipes with circular cross-section, and which are completely filled, the head lossHJ can be calculated according to DARCY-WEISBACH as follows:
l UHJ =
D 2g
where = coefficient of friction l= length of pipe
D = diameter of pipe U= mean flow velocity
The coefficient if friction is dependent on and determined by, the similarity law onthe dimensionless Reynolds number:
D URe =
ForRe < 2320, i.e. laminar flow, the HAGEN-POISSEULLE law applies, regardlessof the roughness of the pipe bore:
64 =
Re
ForRe > 2320, i.e. turbulent flow, which is generally the case in most conditions, thevalue of the coefficient of friction
for the extreme case of a hydraulically smooth pipe, where is only dependent onRe and can be determined from:
1 Re = 2 lg ()
2.51The internal surface roughness of the pipe is within the boundary layer and has noinfluence.
for the extreme case of a hydraulically rough pipe, where is only dependent onthe internal roughness and diameter of the pipe and can be determined from:
1 k = 1.14 2.0 lg
Dwhere k= internal surface roughness of the pipe
The surface roughness of the pipe penetrates the boundary layer to some extentand affects the main flow.
For the usual pipe materials, diameters and flow velocities, there is a relationshipbetween hydraulically smooth and hydraulically rough. For this transition range, thecoefficient of friction has the following equation according to PRANDTL-COLEBROOK:
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1 2.51 k 1 = 2 lg ( ) Re D 3.71
In this range, the Reynolds numberRe and the condition of the pipe expressed asabsolute roughness k or relative roughness k/D, will affect the magnitude of thecoefficient of friction .
For pipes with non-circular cross section, the diameter of an equivalent circular pipewhich would have the same head losses for the same flow velocity, roughness andlength can be calculated from:
4ADequivalent = in mm
U
where A = cross sectional area in mm
U= wetted circumference in mm
This equivalent formula is also valid for open channels, on the assumption that thefree surface of the liquid does not affect the resistance, (which is not entirely correct).This diameter can also be used for calculating the Reynolds numberRe.
6.1.2 Determination of head loss HJ
6.1.2.1 Reynolds number Re
The determination of the Reynolds number in order to establish whether laminar or
turbulent flow is present is only necessary for viscous liquids. In all other casesturbulent flow can be assumed.
Given:
D = diameter of the pipe in mm
(the nominal bore DN can be used)
U= mean flow velocity in m/s
Q = flowrate in m/h
= kinematic viscosity in mm/s
the Reynolds numberRe can be calculated from
D U 354 QRe = 10 or Re = 10
D
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6.1.2.2 Head loss HJ for laminar flow (Re < 2320)
l UHJ = 10 in m
D 2g
64where =
Re
L = length of pipe in m
D = diameter of pipe in mm (= DN)
U = mean flow velocity in m/s
6.1.2.3 Head loss HJ for turbulent flow (Re > 2320)
The determination of using the PRANDTL-COLEBROOK equation is very timeconsuming. It is therefore more expedient to calculate the head lossHJ with the helpof table 6.03 derived from PRANDTL-COLEBROOK.
Table 6.03 was established using the following parameters
an absolute inner surface roughness k = 0.1 mm (new cast pipe with internalbitumen coating)
a kinematic viscosity = 1.236 mm/s. This is the value for pure water at 12C.The values obtained are sufficiently accurate for water and other liquids of similarviscosities at normal ambient temperature.
a pipe length ofl= 100 m
If the absolute inner surface roughness of the pipe kdiffers greatly from the 0.1 mm(guideline values see table 6.01), then the head loss value obtained from table 6.03must be multiplied by a correction factor f as follows:
HJ = HJ (k = 0.1) f HJ (k = 0.1) established from table 6.03
f established from table 6.02
The correction factors in table 6.02 also enable an estimate of the change in head lossHJ which might be expected in a pipe after several years in service.
It should be noted that if the inner surface of a pipe becomes encrusted, then the
reduced diameter resulting from this, is important.If the kinematic viscosity of the liquid differs greatly from 1.236 mm/s, then thehead loss valueHJ obtained from table 6.03 must be corrected as described in section6.1.3.
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Material and type of pipe Condition of pipe kin mm
new (ductile) cast iron bitumen coated
not bitumen coated
cement lined
0.1 to 0.15
0.25 to 0.15
0.025used (ductile) cast iron evenly corroded
slightly to heavily encrusted
cleaned after several years in service
1 to 1.5
1.5 to 3
1.5
new seamless steel rolled or drawn 0.02 to 0.05
new welded steel 0.04 to 0.1
new coated steel zinc plated
bitumen coated
cement lined
galvanised
0.1 to 0.15
0.05
0.025
0.01
used steel evenly corroded
slightly encrusted
medium encrusted
heavily encrusted
0.15
0.15 to 0.4
1.5
2 to 4
new concrete commercial grade smooth
commercial grade medium
commercial grade rough
0.3 to 0.8
1 to 2
2 to 3
used concrete after several years use 0.2 to 0.3
centrifugally spun concrete 0.25
drawn or extruded copper, brass, aluminium, plasticor glass
new
used
to 0.01
to 0.03
Table 6.01 Roughness values kfor various materials and conditions of pipe
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Table 6.02 Correction factor for roughness value k 0.1 mmFork= 0.05 to 3mm, the difference in the correction values due to flow
velocity are negligible, so average values are shown. However fork=
0.01mm, the effect of flow velocity must be taken into account.
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Table 6.03a Head loss per 100m of pipe using PRANDTL-COLEBROOK for
k= 0.1mm and turbulent flow = 1.236 mm/s.
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Table 6.03b Head loss per 100m of pipe using PRANDTL-COLEBROOK for
k= 0.1mm and turbulent flow = 1.236 mm/s.
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Example:
Given: pure water with t= 10 C ( = 1.30 mm/s), Q = 360 m/h
new steel pipe bitumen coated DN 200, l= 400 m
Reynolds number:
354 360Re = 10 = 4.9 105 i.e. turbulent flow
200 1.30
From table 6.03 is given:HJ = 4.5 m/100 m, U= 3.2 m/s
From table 6.01 a roughness value for new steel pipe, bitumen coated k= 0.05 mm isgiven and from table 6.02 a correction value f = 0.91 so the head loss is obtainedfrom:
HJ (k = 0.05) = 4.5 m 0.91 = 4.1 m/100 m
or for the entire pipe length l= 400 m:
400 mHJ = 4.1 m = 16.4 m
100 m
6.1.3 Correction of head loss HJ for liquids with a kinematic viscosity 1.236 mm/s
Assumption of turbulent flow withRe > 2320.
The correction is carried out in three steps a) to c). The subscript x denotes thevalues for the given kinematic viscosity.
1.236a) Q = Qx in m/h with Q in m/h and in mm/s
b) from table 6.03,HJ is evaluated as described in section 6.1.2 for the flowrate Qand the given nominal bore of pipe.
c) HJ x is then obtained from:
Example:
Given: Liquid with = 20 mm/s, Q = 150 m/h
New cast pipe, bitumen coated (k= 0.1 mm), DN 100, l= 50 m354 150
Re = 10 = 2.65 104 = turbulent flow100 20
HJx = HJ in m per 100 m pipe1.236
with HJ in m per 100 m pipe and in mm/s
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a): 1.236 mm/sQ = 150 m/h = 9.3 m/h
20 mm/s
from table 6.03
HJ
= 0.13 m per 100 m pipe
or for the entire pipe length l= 50 m:50 m
HJx = 34 m = 17 m100 m
The flow velocity is obtained from table 6.03 forQ = 150 m/h and DN100
as U= 5 m/s.
6.2 Head loss HJ in valves and fittingsU
HJ = in m2g
with U= average flow velocity across the reference section in m/s
= friction coefficient of the fittingU
or. HJ = in m,2g
if the friction coefficients of all the fittings are summed, which is only correct if allhave the same nominal bore.
The following tables summarise the friction coefficients of the most commonly usedvalves and fittings. Using known values for U and , the value HJ can easily beobtained from table 6.04.
Valves and fittings
Straight through valves - fully open
Globe valves vertical spindle
Cast body, DN 25 to 200 = 2.5
Forged body, DN 25 to 50 = 6.5
and the required value20 mm/s
HJx = 0.13 m = 34 m per 100 m pipe1.236 mm/s
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Inclined seat, full flow valve with inclined stem
DN 25 32 40 50 65 80 100 125 to 200
1.7 1.4 1.2 1.0 0.9 0.8 0.7 0.6
Angle valve - fully open DN 25 to 200: = 2.0Non-return valve
Flat seat valve, DN 25 to 200 = 3.5
Inclined seat valve, DN 50 to 200 = 2.0
Foot valve with strainer
DN 50 to 80 100 to 350
U= 1 m/s = 4.1 = 3
U= 2 m/s = 3.0 = 2.25
Combination of foot valves
DN 400 500 600 700 800 1000 1200
7.0 6.1 5.45 4.95 4.55 4.05 3.9
Butterfly and shut off valves - fully open
DN 400 600 800 1000 1200 1500
for PN 2.5 0.08 0.06 0.05 0.13
PN 6 0.16 0.30 0.25 0.22
PN 10 0.48 0.33 0.50 0.45 0.41 0.37
PN 16 1.20 0.85 0.73 0.63
Non-return valves, without lever and weight
DN 200 300 500 600 700 800 1000 1200
for U=1m/s 2.95 2.90 2.85 2.70 2.55 2.40 2.30 2.25
U=2m/s 1.30 1.20 1.15 1.05 0.95 0.85 0.80 0.75
U=3m/s 0.76 0.71 0.66 0.61 0.54 0.46 0.41 0.36
If the check valves are fitted with lever and weight, the loss coefficients can amountto a multiple of the values given. A rough estimate can be obtained by application ofthe following factors: forU= 1m/s f = 4, forU= 2m/s f = 3 and forU= 3m/sf = 2.
Swing type non-return valves, with lever and weight
U 1 m/s 1.5 m/s 2 m/s 2.5 m/s
8 3 1.3 0.7
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Flap valves
The coefficient of friction of flap valves depends on the flow velocity, the design andthe weight of the flap. For this reason reliable figures can only be given by themanufacturer. For rough approximation, the following values can be used: = 1.0 to
1.5.Back flow preventer (HYDRO - STOP)
DN 50 100 150 200 250 300 400
for U=2 m/s 5 6 8 7.5 6.5 6 7
U=3m/s 1.8 4 4.5 4 4 1.8 3.4
U=4m/s 0.9 3 3 2.5 2.5 1.2 2.2
Gate valve, flat type fully open
DN 100 200 300 400 500 600 to 800 900 to 1200
0.18 0.16 0.14 0.13 0.11 0.10 0.09
Gate valve, oval and round type fully open
DN 100 200 300 400 500 600 to 800 900 to 1200
0.22 0.18 0.16 0.15 0.13 0.12 0.11
Needle valve, fully open
with reference to the smallest cross section = 0.5 to 0.8
Fittings
The reference cross section for the flow velocity is always denoted by
Inlet, also the outlet from a container into a pipe
sharp edged very sharp = 0.5
slight chamfer = 0.25
full chamfer = 0.2
rounded entry smoothness = 0.06 to 0.05
normal = 0.05
45 60 75
0.8 0.7 0.6
sharp edged
with angle
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projecting sharp edged very sharp = 3
slight chamfer = 0.6
Pump intake
bell mouthed = 0.05
conical = 0.20
Outlet, outlet loss = 1
The flow velocity in the outlet cross section is the determining parameter
Changes in cross section
d1 /d2 0.5 0.6 0.7 0.8 0.9
0.56 0.46 0.24 0.13 0.04
d1 / d2 0.5 0.6 0.7 0.8 0.9
for =8 0.12 0.09 0.07 0.04 0.02
=16 0.19 0.14 0.09 0.05 0.02
=25 0.33 0.25 0.16 0.08 0.03
d1 /d2 1.2 1.4 1.6 1.8 2.0
0.10 0.22 0.29 0.33 0.35
d1 /d2 1.2 1.4 1.6 1.8 2.0
0.02 0.05 0.10 0.17 0.26
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Bends 45 60 90
swept surface smooth rough smooth rough smooth rough
for R=d 0.14 0.34 0.19 0.46 0.21 0.51
R=2d 0.09 0.19 0.12 0.26 0.14 0.30R5d 0.08 0.16 0.10 0.20 0.10 0.20
fabricated 45 60 90
Number of weld seams 2 3 3
0.15 0.2 0.25
90 bends in series
2 90 3 -90 4 90
Elbow bends 45 60 90surface smooth rough smooth rough smooth rough
0.25 0.35 0.50 0.70 1.15 1.30
Combination with 90 elbows
= 2.5 = 3 = 5
Expansion joints
Pipe expansion joints, with/without guide tube = 0.3 / 2.0
Lyra expansion section smooth = 0.7
Lyra expansion bellows = 1.4
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Tee-pieces, with flow separation
sharp edged rounded with
straight base
spherical with
concave neck
spherical
= 1;3 = 0.7 = 0.9 = 2.5 to 4.9
Branches, main line and branch of same nominal bore
Confluence
Qa = 0 Qa = 0.5 Q Qa =0.8 Q Qa = Q
=90 d 0.04 0.35 0.5 -
a - 0.3 0.7 0.9
=45 d 0.04 0.2 0.1 -
a - 0.15 0.35 0.4
Qa = 0 Qa = 0.5 Q Qa =0.8 Q Qa = Q
=90 d 0.04 0.01 0.2 -
a - 0.9 1.1 1.3
=45 d 0.04 0.02 0.2 -
a - 0.4 0.35 0.5
Divergence
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UTable 6.04 Determination of the head lossHJ =
2g