Centrifugal Pumps Sterling CAP_6

8/9/2019 Centrifugal Pumps Sterling CAP_6

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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

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