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Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public.

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“Knowledge is such a treasure which cannot be stolen”

“Invent a New India Using Knowledge”

है”ह”ह

IS 2951-1 (1965): Recommendation for Estimation of Flow ofLiquids in Closed Conduits, Part I: Head Loss in StraightPipes Due to Frictional Resistance [WRD 1: Hydrometry]

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D lol, 5

IS : 2951 ( Part J.) • 1965

Indian StandardRE.COMMENDATION FOR

ESTIMATION OF FLOW OF LIQUIDSIN CLOSED CONDUITS

PART I HEAD LOSS IN STRAIGHT PIPES DUE TOFRICTIONAL RESISTANCE

Fluid F10w Measurement Sectional Committee, BDC 17

CluJirmtl1lDB. A. N.KHoSLA

R,prlSlntintIn personal capacity ( GoVmlM./ Orissa, Bluib••IIS111. )

In penonal capacity ( 140 SUM'" Nagar, New Dllhi)

Andhra Pradesh. Engineering Research Laboratories,Hyderabad

River Research Institute, West Bengal, Calcutta

Central Board of Irription & PowerIn personal capacity ~ c/o ECAFE, BatfrH)In penonal capacity (B-32 Kai/"." c.u"", KnitD.uti)

( e:.tirewtl",,.2 )

Vi&,·ClulinnanSmu N. D. GULHATI

Ml11IbnsDR. B. K. AOARWALA. National Physical Laboratory (CSIR), New DelhiSHBi: R. S. AGRAWAL.&. The Scientific Instrument Co. Ltd •• Allahabad

SHBI S. R. CHA=E1\JEE (AlUrnall)SaRI P. R. AHUJA Ministry of Irrigation & Power. SilRI V. N. NAGARAJA ( Ai'ema'e)S'HI\I BALESHWAR'NATH Committee on Plan Projects, Planninl CommiasieDSHBI K. L. BHATIA Central Board of Irrigation & PowerCHIEF ENGINEER, IBRIGATION Public Works Department, Mysore

PBOJECTSSHBI D. DODDIAH ( Allemale)

SHB.I R. D. DHIR Central Water & Power CommissionSHBI R. C. SHENOY ( AIUrnate)

DIRECT<.>R (BBIDGJt8 & FLOODS ),Railway Board ( Ministry of Railways)RDSQ

DIRECTOR

DIRECTORDEPUTY DIRECTOR ( Alternatl)

. SaRI K. K, FR4l\1JI In personal capacity ( 11 GymkhanaClub, Ne. Delhi)SHRI C. V. GOLE Central Water & Power Research Station, Poo••

:SHBIS. V. CHi1:UE (Allemate)hoI'. N. S; GOVIND4 RAo Indian Institute of Science. BanploreSHRIS. N. GunA Irrigation Departmeat, U.P.HYDRAULIO ENGINEER IIGmbay Municipal Corporation

Smu V. D. DESAI ( AlUrnate)Smu D. V.JOGLB][ARSHBI K4NWAR SAINSJDUK. N. K4TUALIA

IND IAN STANDARDS INSTITUTIONMANAK BHAVAN, 9 RAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

IS : 2951 ( Part 1) • 1965

(Conti_dfrtml /NIt' I)

Mem6mMEKBBB ( DESIGN & RESEARCH)SB:RI M. P. NAGAllSHETHSB:RI A. N. SENSUfEBINTENDING _EN GIN E E B

(DESIGNS)ExECU-TVB ENG IN E E B

( RESEABCH) (Altll7JQt4)OJ!,. H. L. UPl'AI.

DB. H. C. VISVESVABAYA,Deputy Director (£:ivil Eng)

RepresentingCentral Water & Power CommissionRoads Wing, Ministry of TransportNational Instrument ( Private) Ltd., CalcuttaPublic Works Department, Madras

Land Reclamation, Irrigation & Power ResearchInstitute, Punjab; and Institution of Engineers( India ), Calcutta

Director, lSI (Ex-officio Member)

SecretarySHRI K. RAGHAVENJ>RAN

Extra Assistant Director (Civil Eng), lSI

Fluid Flow Measurement in Closed Conduits Subcommittee,BDC 17: 3 .

Regional-Engineering College, WarangalMahindra Engineering Co. Ltd., CalcuttaDirectorate General of Health Services, Ministry of

fuallh .

Indian Institute of Science, Bangalore

SBJn J. S. JAIN ( Alt4rnat4)PBOJ'.S.NAGARATNAMSKaI M. PANIKK-ARSUBI S. RAJAGOPALAN

Qmvener-PBOJ'. N. S. GOVINJ>A RAO

MembersSHRl K. SEETHARAMIAH( Alllrnsl, to

Prof. N. S. Govinda Rao)ADDITIONAL CHID ENGINEER P.W.D. Health, Rajasthan

HEALTHSHBI P. S. RAJVANSHI (Alt4rnate)

DR. B. X. AGARWALA. National Physical Laboratory (CSIR), New DelhiSIlBI BALWANT SINGH Municipal Corporation of Delhi .SlfRl K. K. FBAIIJI In personal capacity ( 1J Gymkhana Club, NI/II Delhi;HYDRAULIC ENGINEER Bombay Municipal Corporation

SHRI V. D. DESAI (Altemate)DB. INDERJIT SINGH Oil -& Natural Gas Commission

SHBI H. P. ABAIUlA (Alternate)SHm S. K. KABAIU Corporation of CalcuttaSJfl\.1 A. N. KRISHNASWAMY W.H. Brady & Co. Ltd., BombaySJfl\.1 I. N. MEHTA P.W.D. Public Health Branch, Punjab

SJfl\.1 D. R. SINGAI. (Alternate)SB:RI R. S. MEHTA Central Public Health Engineering Researc:bIDsU.

tute (CSIR), Nagpur -

'SJlRI T. DuBAIRAJ (AlI,mau)D.. V. RAMAKBISHNAN P.S.G. College of Technology, Coimbatore

DB. S. BALAKRISHNAN (Alt4rnau)RE....NTATIVB Central Water & Power Research StatioD, PoonaSVJ'&BU'T_DINO ENG IN B B R Public Works Department, Madra.

{DUIGNB)hBCllTlVP E:N G I :N B B :B

( R_JI.U42) (Alt4mall)

2

18 I 2951 ( Part I ) • 1965

I ndian StandardRECOMMENDATION FOR

ESTIMATION OF FLOW OF LIQUIDSIN CLOSED CONDUITS

PART' HEAD LOSS IN STRAIGHT PIPES DUE TOFRICTIONAL RESISTANCE

o. FOREWORD

0.1 This Indian Standard was adopted by the Indian Standards Institutionon 24 March 1965,- after the draft finalized by the Fluid Flow Measure­ment Sectional Committee had been approved by the Building DivisionCouncil.

0.2 An important effect of fluid friction is experienced in the resistance tothe Bow of liquids through pipe lines. This resistance can only be over­come by a gradual fall of pressure in the liquid, in the direction of motion.A back-ground of the nature and magnitude of the frictional resistance tothe flow; experienced under different conditions occurring in practice,

-would be essential for proper designing of pipe lines.

0.3 The classical equation for the resistance to the flow of liquids inlong, straight, uniform pipes, as proposed by Darcy is followed widely.However, in this equation proper choice has to be made for the dimension­less friction. factor in order to arrive at the correct .assessment of losses.Several empirical formulre based on experiments carried out during thelast 100 years are available with their limited applicability. Later analysesare based on the roughness factor and Reynolds number of flow. Forexample, Hydraulic Institute at New York has made systematic work forthe revision of pipe friction data. This standard, therefore, recommendsthe values for friction factor fer a wide range of temperature, velocity anddiameter of pipe. It is hoped rhat the universal pipe friction diagram with,its nomograms, suggested in this standard would be useful in obtaining acomplete solution rapidly without lengthy calculations.

0." One more salient feature which affects the friction factor is the dete­rioration of pipes with age. The internal fouling of pipes due to corrosionor tuberculation which in turn is due to factors like chemical characteris..tics of the liquid, iron bacteria, will increase the friction factor with timeand reduce the available area for flow. _Approximate curves for different~wth rat~s of absolute r~\lghness and their effect on discharge in cast ironplpe5carrymg water are given as an example.

3

IS:2HI (Part 1)-1965

1.5 The Sectional Committee responsible for the preparation of:diis:standani has taken into consideration the views of users and technql()gis~

and has related the standard to the practices followed in the cou~try in'this field. Due weightage has also been given to the need for internationalco-ordination' 'among standards prevailing in different countriea-of-tbeworld. These considerations led the Sectional Committee to cl.eriveassiSC',tance from the following publications: . . . . .

ISO Draft Recommendation No. 532 Measurement of fluid flow bymeans of orifice plates and nozzles

Pipe Friction Manual 1954 Hydraulic Institute, New York

I.i This standard is one of a series of Indian Standards covering fluid Bowin closed conduits. Other standards in the series are:

IS: 2951 (Part II )-1965 Recommendation for estimation of flowof liquids in closed conduits, Part II Head loss in valves andfi~~ "

IS: 2952 (Part I )-1964 Measurement of fluid flow by means oforifice plates and nozzles, Part I Incompressible fluids

'.7 For the purpose of deciding whether a particular requirement of thisstandard is complied with, the final value, observed or calculated, express­ing the result of a test or analysis, shall be rounded off in accordance withIS: 2-1960*. The number of significant places retained in the rounded offvalue should be the same as that of the specified value in this standard.

1. SCOPE

1.1 This standard recommends a method for estimating the loss of headdue to friction in straight pipes having uniform flow of liquids. .

2. TERMINOLOGY

2.1 For the purpose of this standard, the following definitionsshall apply.

2.1 LaJDiaar Flow - The flow of liquid in which stream Jines 01' streamsurfaces of the flowing liquid appear to divide the entire region of flow intoan orderly series of liquid laminae or layers, conforming generally to theboundary configuration.

NOTE - Generally, pipe flow is assumed to be laminar for values of the Reynoldsnumber (s" 2.6) below-2000.

2.2 Crideal ZOlie - The zone where the flow characteristics vary fromlaminar to turbulent and is therefore unstable.

• Rulea for rounding off numerical values (MfiutI)•

..

IS: 2951 (Part.l) -1965

2.~. n.rbaleDt now- A state of flow of liquid in which irregularfluc,;t~ions (mixing or eddying motion) are superimposed on the main$tream;·Jt is an irregular motion in which time-average quantities can bedefined only in a statistical sense.

• :. - l

NOTE,,""" Generally, pipe Sow IS assumed to be turbulent for values of Reynoldsnu~\l~~ceedingS 000.

2.4 ~uihPiPe. - Pipes in which the roughness protrusion on the pipewalls are not completely submerged in the laminar sub-layer, which is the'Very . thin layer at the pipe wall in which only laminar friction exists(Stt 2.5). The value of Roughness Reynolds number ( R.r ) shall be 3 ormore, where Rer is as defined in 2.9.

NOTE - Genelllllly for commercial pipes, I?r is between 3 and 60, unless the Sow ishighly turbulent in which case the value"would exceed 60.

2.5 Smooth Pipes - Hydraulically smooth pipes are those in which. theRoughness Reynolds number ( Rer ) is less than 3, where R.r is as defined.in 2.9.

NOTE - Generally, smooth-drawn non-ferrous pipes of aluminium, brass, copper, lead,plastic, glass, asbestos cement, and spun concrete or bitumen lined pipes free from slimeare considered tobe hydraulically smooth.

2.6 lleYl'Olu NaiIlber (R.)-A dimensionless number, given by vD.u

where v is the mean velocity, D is the diameter and u is the kinematicviscosity at the given temperature. all. these being expressed in consistentunits.

2.7A_olute ll.......... ( K.) - The maximum height of the l'9ughnelaprotrusion measured inmillimetres•

. ~TII-Table 1 &iva the~ed desip values of Ablolute llouP--

2.' Relative It.......... (c) - The ratio oC the absolute roughness to theinternal diameter .of the pipe expeaed in the same unit, that isK./D(see Fig.·l ).

2.9 ROueJuaH. Reyaoau N....... (R.r)'- A number which is a func­tion of Reynolds number, relative roughness and "friction factor and iagiven by the foDowing Cormula:

. Rer - Re cv]78where

Re::;: Reynolds number of the flaw.c == relative roughncss{ lei 2.8 ) j andf = Criction factor.

5

IS : 2951 (Part I ) • 1965

TABLE 1 RECOMMENDED DESIGN VALUES OP ABSOLUTEROUGIINESS (Ie.)

(Clau 2.1)

MATERIAL

81'1'11, copper, aluminium,plastics and glass

Steel

Cut iron

Asbestos cement

CoNDITION

Smooth, without sediments

New, seamless cold drawnNew, seamless warm drawn }New, seamless rolledNew, welded 10ngitudiDallyNew, welded spirallySlightly rustedRustyEncrustedWith heavy incrustationsBituminized, newBitu"linized, normalZincedNewRustyEncrustedBituminized, newInsulated and not insulated, newNot insulated. normal

K. INmm

<0·03

<0·03

0.()5 to 0·10

0·100·10 to 0·20().20 to 0·30

().50 to 2>2

0·003 to 0·05 .0·10 to 0;20

0·130·25

1·0 to 1·5>1·5

0·1 to 0·15<0·03

0·05

3. GENERAL FOR.MULA FOR. CALCULATING FR.IcnONALRESISTANCE

3.1 Frietioual Resistaace - The resistance to the flow of any liquid inany pipe may be computed from the equation: .

L jlht=l- ­D 2g

where

ht = loss of head due to fFiction in m of liquid.f = friction factor.L = length of pipe in m,D = average internal diameter of the pipe in m,ii - average velocity in m/s. andg = acceleration due to gravity m/s'.

NOTB I-The equation" mentioned ahove may be lJSed for regtdar Sections likesq~oval, triangular and similar types which are non-circular by replac:ingthe term Dby:.4R". where R" is hydraulic radius giveD by A./P, where A. and Pare area and wetted ..perimeter respectively, to yield satisfactory results by this approach.

6

lSI 2951 {Part 1)-1965 '

This may be usedfor square ducts, rectangular ducts where the ratio of the ,idesdoes not exceed about 8, equilateral triangular ducts and for annular ducts for ratiosof inner to outer diameter less than about 0'3.

The above assumption cannot be expected to hold good for odd-shaped sections.

NOTB 2 - The actual average internal diameter D of a pipe can be determinedgravimetrically from the following equation:

nD'w='YI~

where-w... weight of water, .y = specific weight of water (note the temperature of water to determine

the specific weight ), andI = length of pipe.

One end of the pipe shall be closed by u,ing a screw cap and the pipe shall befilled with water, in a vertical position such that it is completely full. The contentsshall then be emptied and the weight of water determined. Since w, y and I areknown, D can be determined.

3.2 Calculation of Friction Factor

3.2.1 Laminar Flow3.2.1.1 When theftow is laminar, the friction factor for any liquid in

any pipe shall be calculated from the equation:Friction factor, f = 64/R.

whereR. = Reynolds number.

3.2.2 Turbulent Flow3.2.2.1 When the flow is turbulent and in the range of Reynolds num­

ber between 3 000 and lOO000 friction factor f for any liquid shall becalculated from the following equation:

, For smooth pipes

f= 0'316R.l

Far rough pipesI

---2'0vJ -I

IOg102c- + 1'74

wheref = friction factor I

R. = Reynolds number, andc -relative roughness.

7

IS a2951 ( Part J) • 1965

o ,.._,,-...;.'

,.....+,9

" .~

.- ~">.~

RIVETED "STEEL

CONCRET ~

WOOD '':;.I~.t~AVE ~.

..... 1', ..... I '" ~

0·000005 30 40 \) Kl 80 1 0 oo 30( 1500 1Joe400

PIPE DIAMETER IN mm

00

FIG. 1 ·RELATIVE ROUGHNESS I'OB NEW CL!:AN PIPE8

8

IS : 2951 ( Part I) - 1965

.. 3.2.2.2 When the Reynolds number of the flow exceeds 100 000 thefriction factor f for any liquid shall be calculated from the followingequations:

For smooth pipes

J.-- = 2'0 10glO R.vf - 0'8

For rough pipesI IvI- = 2'0 loglo 2& + 1'74

where

f = friction factor,R. =:=.•Reynolds number, and

e = relati~~ughness.

3.2.3 Flowin Critical Z~'n.

3.2.3.1 When the flow is in the criticat zone, that is, generally in therange of Reynolds number 2 000 to 3000, friction factor fis indeterminatedue to unstable conditions of flow. However, for commercial pipes, fric­tion factor f may be calculated from the following equation:

I [K,' 2'5 ]VI =-2'0Ioglo 3'7D + R. VTwhere

f = friction factor,R. = Reynolds number,K. = absolute roughness, andD = average internal diameter in m.

3.2•• Relative Roughness (e) of Pipes - The relative roughness &shall, asfar as possible, be determined by the actual measurement of the absoluteroughaess, Where, however, this is not possible, .values obtained fromTable i should be used. Figure I may be used to determine the relativeroughness for new clean pipes of any material. In the case of riveted steel,concrete and wood stave pipes, where ranges of relative roughness havebeen shown,suitable values may be assumed within the range .given inFig. 1.

3.2.5 Kinematic Viscosi!1(u)- Unless otherwise established, the value ofkinematic viscosity u at various temperatures shall be determined fromFig. 2.

9

IS : 2951 (Part I) • 1965

oo

0

B

\.

, IF'0 -V 1\

H~~K

00

0

0'" \

\\0

'l: \\~ ;~

108

6 p

"-4

r-,2

r./:!. Q \1-~ r-, ['. "1

T·8

·6 ,.\!r--.0·4

0'2

V

u-200 400

108

6

800

600

-10 -5 0 10 20 40 60 80 100

TEMPER,lTURE IN DEGREES CENTIGR,lDE

-20

400

A -Fuel oil sp gr == 0·968B - S.A.E. 70 Eastern lubricating oilC - Fuel oil sp gr = 0'940D - GlycerineE - S.A.E 30 Wes~rnF - S.A.E. 30 EasternG - S.A.E. 10 Western lubricating oil

R - S.A.E. 10 Eastern lubricating oilJ - Crude oil sp gr = 0·925K - 75% Glycerine - 25% water

L - 50% Glycerine - 50% waterM - Crude oil sp gr = 0·855N - 25% Glycerine - 75% waterp- Kerosene sp gr= 0·813Q- Brine 20% NamR·-WaterS - Gasoline sp gr = 0·748T - Gasoline sp gr = 0·716II - Gasoline sp gr = 0·680V-Mercury

FIG. 2 CHART FOR KINEMATIC VISCOSITY

10

IS: 2951 (Part I) ·1965

3.2.6 Universal Pipe Friction Diagram - The equations recommended forvarious types of flow may be used for any liquid over a very wide range ofdiameter, velocity and temperature. Although they are concise mathe­matically, the unknown quantity occurs frequently in two or more of theterms of the appropriate equation. This' difficulty has, however, beenovercome by representing the formule graphically. The universal pipefriction diagram given in Fig. 3 (su P 19) consists of a graph with threelinked nomograms, by means of which it is possible, not only to see at aglance the type ~f flow applicable to any particular problem, but to obtaina solution rapidly and without calculation.

NOTE - Although every carei s taken in the preparation of the nomogram to make Itsufficiently. accurate, it should be noted that the nomogram is not necessarily anaccurate answer for the quantities required. Therefore, it is recommended that nomo­gram may be readily used for checking performances and the final design should bebased on practical experience.

3.2.'7 Friction Factor Charts

Although the universal pipe friction diagram is quite sufficient for thecomplete solution of the problems relating to pipe friction, individualcharts are available for the determination of friction factor in more frequentmaterials of use and these charts are given in Fig. 4,5 and 6 (see P 21, 22and 23).

3.3 Ageing of Pipes

3.3.1 The deterioration of pipes with age depends upon the particularchemical properties of the liquid and the material with which it is incontact. The effects of deterioration with age on roughness are soinconsistent that it is not possible to prepare tables or charts to includethis factor. It is recommended that prior experience be considered andlocal authorities consulted where it is necessary to estimate the friction lossesin old pipes or to allow for the ageing of new pipes. In the absence ofexperimental data or other considerations which warrant the adoption ofother values, the effect of ageing of pipes for the purpose of design ( periodof 30 years) may be taken to decrease the discharges by 25 percent forcast iron and wrought iron pipes, 15 percent for galvanized iron and rivetedsteel pipes and 5 percent for asbestos cement and concrete pipes.

NOTE - Detailed data on ageing for cast iron pipes are, however, available -andFig. 7 gives rhe approximate relation between age and percentage reduction in dischargefor various degrees of corrosive attack and diameters.

4. FRICTION CHARTS AND TABLES

4.1 Whilst the frictional resistance offered during the flow of any liquid inany pipe under any given circumstances can be calculated on the basis ofthe recommendations in 3, it is often found more convenient to prepare and

II

.,2951 (Put 1)-1965

20 40 60 80 100

AGE OF PIPE IN YEARS

- ~.,...

_1.-- _ •• i-ol

-----_.-..·r ... -- -'"......-4 i'"..-.-. )0'"".....-- ~ ...

.....,.,.)"""_............ .-

0 o SEVERE -~ 0------0 APPRECIABLE

0----0 MODERATE 'f-

0- - - -0 SLIGHT

..

usc pipe friction charts and tables using the recommendations in 3 as tpebasis. An example of the typical pipe friction chart and the method ofconstruction and use of chart is given in Appendix A and another eXaJJ1pleof a typical table is given in Appendix B.

e...~

i wo

~ 80

~ 60

Ncn. - a) For' slight' trend-s-rate of-growth of roughness is 0·002 5 em per annum,for' moderate' 0·007 5, for' appreciable' 0·025 and for 'severe' therate of growth g 0·075 em per annum.

b) The values of 'b' for difl'erent trends are given below:

T,mtl Yalwoj'b'

Slight 0·17

Moderate 0·15

Appreciable 0·12

Severe 0·12

FIG. 7 RBL~TION BBTWBBN AGB ~ND RBDUCTION IN DI8CBUGIl~a CUT I.ON PIl'ES

12

IS I 2951 (Pan I} -INS

APPENDIX A(Clause 4.1)

CONSTRUCTION AND USE OF PIPE FIUCTlON CHARTS

A-I. CONSTRUCTION OF THE PIPE FRICTION CIIA1l1'

A-I.I For the construction of the pipe friction cnart the following proceduremay be followed:

a) The kind and size of pipe, its actual internal diameter and thevalue of absolute roughness are either determined or the relevantdata is used.

b) For any particular liquid, for a given temperature the kinematicviscosity \) in centis tokes is obtained from .Fig. 2 or assessedreasonably.

c) The diameter and the kinematic viscosity hein' known, theReynolds numbers for various -velocities are computed.

d) The friction factors f for various Reynolds numbers of the given~pe are taken from Fig. 3, 4, 5 or 6.

e) The loss of head (h,) (in metres) for ten metres length, iscalculated from the equation:

10 OSh,=f-D -2,

wheref = friction factor,

v= average velocity in mIs,D = average internal diameter in m, andg = acceleration due to gravity m/s·.

f) Discharge (Q) is computed from the equation:Q = 2501tD!ii l/sec

whereD = average internal diameter in m, and

ii = average velocity in m/s.With discharge Q as abscissa and loss of head ", as ordinate, ~

graph is plotted, for laminar flows on the left hand side and forturbulent flows on the right hand side, on log-log graph paper. Twostraight lines, differing in slopes, are obtained on the chart. Valuesof hf fur Reynolds numbers between 2 000 and 3 000 are indeter­minate and this region ~s marked off as the critical zone.

13

IS: 2951 (Part I) - 1965

g) Similar computations are made for varying values of kinetnat,icviscosity, that is, for different liquids, or the same liqui(f atdifferent temperatures. Several lines are obtained on the chart,on each ofwhich the value of the kinematic viscosity is marked•

.\-2. USE OF THE CllA.B.TS

.\-2.1 Frictional Jossof head for laminar flow are shown by the 45° linesin the upper left hand portion of the chart ( Fig. 8 )" Loss of head forturbulent flow are shown by the steeper curves in the lower right. handside. Both these regions represent stable states of flow. The space libelledas critical zone between two broken lines represents the zone where theflow characteristics vary from laminar to turbulent and is, therefore.,unstable. Therefore, it is difficult to predict the state of flow and hencethe frictional Ioss.of head in the critical zone•

.A-2.2 To use the chart, the following procedure shall be adopted:a) Follow the vertical line representing the flow in .l/s to Its inter-

section with the desired viscosity curve. 'b) If the intersection is above the critical zone, follow horizontally

to the left vertical scale to obtain the frictional loss of headfor 10 m,

c) If the intersection is below the critical zone, follow horizontallyto the right vertical. scale to obtain the frictional loss Qf heaifor 10 m.

A-3. EXAMPLE

A-3.1 The typical pipe friction chart ( Fig. 8 ) shows the frictional loss ofhead for the flow of viscous liquids, including water, for a new clean steelor wrought iron pipe of 3 em nominal diameter. The chart covers thelosses for the given size of pipe based on the kinematic viscosity in centi­stokes at 27°C. Similar charts may be constructedfor other sizes of pipes.No allowance has been made for abnormal conditions of interior surfaceor )JIStanation or for deterioration with age.

APPENDIX B( Clause 4.1 )

CONSTRUCTION OF PIPE FRICTION TABLES

8-1. CONSTRUCTION OF TIlE TABLES

8-1.1 For the construction of the pipe frictIon tables, the followingprocedures may be followed:

a) The internal diameter and absolute roughness values K. of thepipe are either determined or the relevant data is used. .

14

-1-5

IS: 2951 (Part I) .1965

LlTII£S/S

FIG. 8 PIPE FRICTION CHAR'r

15

IS : 2951 (Part I ) .1965

b) The relative roughness ~ of pipe is calculated.

c) A discharge rate in the: pipe is assumed.

d) For this rate of discharge, the velocity of flow in the pipe iscalculated by dividing the rate of flow by the cross-sectional area.

of the pipe (~f2).

e) The Reynolds number of the flow R. is calculated from theequation:

vDR. =

uwhere

v= average velocity in mfs,D = average internal diameter in m, andu = kinematic viscosity in m2/s.

f) Knowing the relative roughness and the Reynolds number of theflow, the friction factor f is obtained either from relevant equationsor from relevant figures.

g) The friction factor having been found out, the loss of head h, .for '.ten metres length of the pipe due to friction is obtained by using"the formula:

10h,=f D

-2fI--2 metres

II .

wheref = friction factor,D = average internal diameter in m,

ii = average velocity in mIs, andK = acceleration due to gravity in m/s".

h) The values of the discharge rate, velocity ii, and loss of head h,are tabulated.

j) The same procedure is repeated for other assumed dischargerates, and tabulation of the values obtained for these assumeddischarge ra tes is done as before.

B-2. EXAMPLE

B-2..! A typical table showing the loss of head due to friction for tenmetres ofleJ!gth-of the pipe for various rates of flow is given in Tabll 2.

16

IS I 2951 ( Part I) • 1965

For any required discharge rate, the fiictionalloss of head at27°C forapipe of one centimetre diameter and having an absolute roughness valueof 0-046 .millimetres, can be obtained from this table. Similar tables maybe collStruCted for other pipes of different diameters, absolute roughnessand for variOUs ra~of&w. .

TAIILB 2 nuanONAL HEAD LOSS IN A sn:EL PIPE FOR TENMETRES LENGTH OF PIPES

(~B-;I)

I)wlpA.a VIILOOlTY o~ FLOW Loss o. HEA.D

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17

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