Disclosure to Promote the Right To Information

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.

इंटरनेट मानक

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“Invent a New India Using Knowledge”

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“Step Out From the Old to the New”

“जान1 का अ+धकार, जी1 का अ+धकार”Mazdoor Kisan Shakti Sangathan

“The Right to Information, The Right to Live”

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“Knowledge is such a treasure which cannot be stolen”

“Invent a New India Using Knowledge”

है”ह”ह

IS 11639-1 (1986): Criteria for structural design ofpenstocks, Part 1: Surface penstocks [WRD 14: WaterConductor Systems]

Gr4

18: 11639 ( Part 1 ) .. 1986(Reaffirmed 2001 )

flu/ian StandardCRITERIA FOR

STRUcrURt\L DESIGN OF PENSTOCKSPART 1 SURFACE PENSTOCKS

INDIAN STANDARDS INSTITUTIONM,~~.t\K £JIJ\V~". 9 1l,r\lI~\l)CK SJ1,\11 4.*\f.\R 1\L\1tO

NF.'V nm.m 1100(;2

AMENDMENT NO. 1 DECEMBER 2008

TO

IS 11639 (PART 1) : 1986 CRITERIA FOR

STRUCTURAL DESIGN OF PENSTOCKS

[Page 9, clause 6.1.5.1(b)] ― Substitute ‘A

PAf c1

3

µ= ’ for ‘ cPAf 13 µ= ’.

(Page 11, clause 7.1) ― Substitute ‘ 22

22,

yxyxyx q

ffffSS +

−±

+= ’ for ‘

( ) 22

22,

yxyxyx q

ffffSS +

−±

+= ’.

(WRD 14)

Reprography Unit, BIS, New Delhi, India

IS I 11639( Part 1) • 1916

Indian StandardCRITERIA FOR

STRUCTURAL DESIGN OF PENSTOCKS

PART 1 SURFACE PENSTOCKS

Water Conductor Systems Sectional Committee, BDC 58

Chairrrwl .

SlIal P. M. MAN.39 Sbivaji Co-operative Housing Society

Pune

M""b", R,prI"rding08181' ENODf&JIlR Bhakra Beal Management Board, Chandigarb

SKl\I SUDIlR8BAN KUMAR (AICIl'll4l, )C:smr ENOnnDn Mukerian Hydel Project Design, Chandigarh

DIBBCTOR (Alt"nal.)C B I 11., ENG I N 11 11 B (CIVIL Karnataka Power Corporation Limited, Bangalore

DJDSIGNS)SURI P. R. MALLmABJU:NA (Altlt1UJl,)

CalEr ENGINB.a ( GB1UmA.L ) Public Works Department, MadrasCRlllr EXGm_ ( IRRIGATION) ( .Alt"n." )

CHIB" ENGm.a (HP) Tamil Nadu Electricity Board, CoimbatoreSUPJIlRIN'1'1INDDfG ElfonfJum ( AIUr".t, )

CBIBI' ENGINBBB (IRBIOATIOK Public Works and Electricity Department, MysoreSOUTH)

SUPBRllftElmJXO EMGJ1C'DB. ( Alt",.at, )SIIBI C. ETTY DA.BWIN In personal capacity (Dunery Mutlada P.O.,

TrivtJntlrum)DIREOTOR Central Soils aDd Materials Research Station, New

DelhiD..UTY DIRIICTOB ( AlllrfUll, )

DIRZCTOR (HeD-I) Central Water Commission, New DelhiDEPUTY DIRECTOB ( HCD-I ) (Alt"".")

DB A. K. DUBS Central Minin, Research Station Unit, RoorkeeD1\J. L. jmTHwA (AlI",",t,)

Smu j. P. GUPTA Power House DesigDl, Irrigation Department,Roorkee

SR.l A. P. GtrPTA ( Alumau )SKBJ M. V. S. IYENOAR Hinduatan Construction Co Ltd, New Delhi

SHRI M. G. KHAN (AlterM")

( C",,';nUld 011/Jag' 2 )

IC>C~"'1986

INDIAN STANDARDS INSTITt1rIONThis publication is protected under tIM lrulia CoJ!1rilAt Ad (XIV of 1957) aDdreprodue:tloo la whol. or In part by aDy meaDi except with written penniulon or thepub"•• IhaII be deemed to be aD IDlrlapm_t of copyright under the laid Act.

II • 11631 ( ....t 1 ) .. 1..

( Con'inuld .from /HII' 1 )

Mmajn.l

JOJN'1' D'.BlIlOTOB, RUB"RCU(GE·I1 )

SURt P. N. KIIAB

SHRt A. K. M:&STA

R''''''IfI'in,Reaearch Desi._ and Standard. OrranizatioD,

LucknowNational Hydroelectric Power Corporation Ltd,

New DelhiNadonal Projects Construction Corporation Limited,

New Delbi

Board,Central Electricity Authority, New DelhiHimachal Prad.b State Electricity

SundemaprSHaI RutJODH SINGH (AlI"na")

SURI G. RAMAN, Director General, lSI (&-of/ido Mllllh,,)Director ( Civ En" )

S",,'arySHar HBKANT KtrKAR

Deputy Director ( Civ Enn ). lSI

SUI S. C. BALI ( AI,,,,",,,)MBKBER ( CIVIL) Kerala State Electricity Board, TrivaadrumDR B. PAn Water Resources Development Trainiq Centre,

Roork..SIlBI G. P AKT Geololical Survey of Iadia, New D.lhi

SHRI N. K. MANDWAL ( AllmuJl,)SHIU A. R. RAIOHU. In personal capacity ( 147, Gartd;',..,ar, BomN.1 )SUllI Y. RAilA KRISHNA RAO Andbra Pradesh State Electricity Board, Hyd4Prabad

S'O!'llBl1ftmfDINO EIfGDfJDlt( DUIOK AND PLAN1(ING ) ( Altma4U)

REFR.SUTATIVJD .. Central Water and Power Research Station, PuneSHBI A. V. GOPALAJcBJ8BNA (AII6f'1UJu)

SURI G. V. SATHAY1II General De.ilftS Or,uization, N..ik88RI S. C. SilK Allam State Electricity Board, Guwahati

SBBIN.K.DA8(~hnuu)

DB H. R. SUARMA*SSRI A. K. SaIXANTIAB

Panel for Penstocks and Anchor Blocks, BDC 58: P6

C"IIHn',.KUKAJU E. D1VATIA National Hydroelectric Power CorporatioD Limited,

New Delhi

( CMlillIIId", /141' IS)

Mnnhn,SURI M. L. AQ()AawAL Bhakra Deal MaD.gement Board. Chandigarb

SSKI Y. P. NAYAR (All,mat,)DIRECTOR (T & P) Irrisation Work&, GovemmeDt of PuDjab. Chandigarh

SmnoR Da10N EWOINlIlER ( Altmlat. )DtRlIlCTOB (HOD·} ) Central Water Commission, New Delhi

DEPUTY DIRECTOR ( HOn.! ) ( AltmalJ")SJl1\l N. C. J,UN Irrigation Department, Government of Uttar Pradesh

LucknowDR ZAWAR MaBDI Bharat Heavy Electric." Ltd, Bhopal

SSRI j. L. KBoal: ( Altmaat, )

.Chairman for the meetins.

2

II, 11631 ( ••"t 1 ) • 1986

Indian StandardCRITERIA FOR

STRUCTURAL DESIGN OF PENSTOCKSPART 1 SURFACE PENSTOCKS

o. FOR EWOR D

0.1 This Indian Standard (Part 1) was adopted by the IndianStandards Institution on 31 January 1986, after the draft finalized bythe Water Conductor Systems Sectional Committee had been approvedby the Civil Engineering Division Council.

0.2 Conduits carrying water from surge tanks or directly from areservoir, forebay , to the power house are known as penstocks. Penstocksare generally of concrete or steel or a combination of both. The pres­sure varies from minimum at the upstream end to the maximum at thejunction with the scroll case.

1. SCOPE

1.1 This standard ( Part 1 ) lays down the various forces acting on surfacepenstocks and structural design of penstocks conveying water underpressure flow cpnditions. However, this does not cover specials of pen..stocks like penstock supports, manifolds, bends, expansion joints,manholes, branch outlets, etc.

2. NOTATIONS

2.1 For the purpose of this standard, the following notations shall havethe meaning indicated against each:

A = cross-sectional area of pipe shell material, mm!Ar = cross sectional area of stiffener ring, mms

b =- width of ring girder or stiffener ring, mmC == moment coefficientE - modulus of elasticity

fl, fl, fa == longitudinal strelsel, N/mml

If, = secondary bending Itress, N/mm l

IS I 11&31 ( Part 1 ) • 19.

fa - total circumferential Itres., N/mml

f, - total longitudinal stresl, N/mml

I = height of .tilFener ring or riDg girder, mmL = span length of pipe, mm

M, Ml = momentsP - internal pressure including water hammer, N/mml

PI = total reaction at support, Nql =- shear stress, N/mm2

, == radius of pipe shell, mm

'1 - mean radius of shell, mmS =a hoop stress in pipe, N/mml

S, .. equivalent stres., N/mml

S., S. = principal stresses, N/mml

T = temperature rise or drop, 00I = thickness of pipe shell, mm

'1 == thickness of stiffener ring or ring girder, romW =- total distributed weight, that i., lelr-weight of shell +

weight of water, N/rn l .

WI = total weight, that is, weight of shell + weight of water,N

Z os section modulus of pipe shell, rna~ =s coefficient of linear expansion or contraction of pipe shell

material, per 00.",. =a coefficient of friction.

3. DATA REQ,VIRED

3.1 The following data is required for the structural design ofpenstocks:

a) General drawing of installation;b) Complete longitudinal profile;c) Type of penstock;

i) Free penstock pipe laid in a tunnel, andii) Steel lined pressure shaft.

d) Geological data;i) Geology of area.

ii) Type of ground/rock,iii) Bearing capacity of ground,

4

• a 11&39 ( Part I ) • 19.

iv) Shear properties of soil,v) Modulul of deformation, and

vi) Seismic coefficient.e) Climatic conditions;

i) Temperature ( maximum, mean, minimum, by day andnight and in summer and winter ),

ii) Wind conditions ( direction and maximum speed ), andiii) Snow conditions ( period and average depth of snow).

f ) Hydraulic data;i) Diameter of penstock, and

ii) Discharge through penstock.

4. LOADS ON PBNSTOCK

4.1 The following are the main loads considered for the design ofpenstocks:

a) Internal water pressure,b) Weight of penstock and water, andc) Temperature.

In addition, the other loads considered depend ing on locationare:

a) wind load,b) snow load, andc) seismic forces.

4.2 The loads given in 4.1 are of the following nature:

a) Permanent loads,b) Intermittent loads, andc) Exceptional load •.

f.2.1 The loads of permanent nature are the forces which act uponthe penstock in normal operation. They correspond to:

a) The maximum operating pressure which is the sum of maximumItatic pressure and over pressure due to water hammer undernormal operating conditions, taking into account the oscillationsin surge tank;

b) The weight of penstock and water between the supports;c) Spacing and type of supports;

5

IS a 11639 ( ....t 1 ) • 1911

d) The difference between the temperature which may exist in thepenstock in normal operation and the temperature exi.ting whencoupling up the sections during erection;

e) Friction at suppon,; andf) Temperature variation.

4.2.2 The loads of intermittent nature are the forces which though notexcep tional, do not arise often.

The two main cases are:

a) Penstock during filling, andb) Empty penstock under partial vacuum.The forces to be taken into account in each case correspond to:a) The weight of penstock and water between the supports,b) The type and spacing between supports,c) The temperature effect, andd) Friction at supports.

In addition to the forces enumerated in <a> to (d), intermittent loadsmay also occur due to wind or snow load and earthquakes.

4.2.3 The loads of exceptional nature that may act upon the penstocksare:

a) Shop or site test;b) Erection stresset;c) Bad operation of safety devices during filling such al non-opera­

tion of air valves which would create vacuum inside duringempting operation of penstocks;

d) Pressure rise caused due to unforeseen operation of regulatingequipment of turbine/pump distribution:

i) In case of impulse turbine. pressure rise due to needle slamon JOSI of oil pressure or mechanical failure; and

ii) In case of reaction turbine, turbine gates may be closedinstantaneously at any time by action of governor manualcontrol of main relay valve or by the emergency solenoiddevice.

e) Stresses developed due to resonance in penstock (A. rar aspossible, the frequency of penstock pipe in any reach shall notmatch with the frequency of machine, frequency of vortex shed­ding in the draft tube, frequency of the system, etc, and resonanceshall be avoided )j and

f) Seismic forces.

6

IS I 1163. ( Part I ) • 1••

5. STRESSES IN PENSTOCK SHELL

5.1 The streases in the penstock shell of surface penstocks are subjected tocircumferential and longitudinal Itrelsel. The Itreuel in pipe at themid-span and at the lupports are as below:

a) AI mid-J/Jdn:

i) Hoop strelses developed due to internal pressure equal tosum of static pressure due to maximum water level in reser­voir or surge tank plus the dynamic pressure due to waterhammer al calculated for operating conditions,

ii) Longitudinal stressel developed due to its own weight aDdweight of water by beam action,

iii) Longitudinal streue. developed due to sliding friction overthe supports, and

iv) Longitudinal stresses developed due to expanaion or contrac­tion of penltock shell due to variation of temperature.

b) AI supports:

i) Circumferential Itresses developed at the supports due tobending caused by internal pressure,

ii) Longitudinal Itresses due to secondary bending momentscaused by the restraintl imposed by ring girder or stiffenerrings,

iii) Longitudinal stresses developed at the supports due to beamaction, and

iv) Longitudinal stresses developed by forces enumerated in 4.1.

5.2 The stresses in penstock shell shall also be checked to withstand thestresses developed due to intermittent and exceptional loading and forthe following forces:

a) Longitudinal stresses developed due to earthquake and wind,b) Circumferential stresses developed due to pressure rise called by

non-operation a8 specified in 4.2.3 (d),c) Longitudinal stresses developed due to wind, andd) Stressel developed due to filling and draining of penstocks.

6. METHOD 01' CALCULA.TlON or STRESSES IN PIPE SHELL

6.1 The streues for different force. shall be calculated .. given in 6.1.1to 6.1.7.

7

.. r 11639 ( Part 1 ) .1986

6.1.1 Hoop Stress Du« to Int"."al p"uu"'.1.1.1 The hoop stress developed due to internal pressure i. given

by:

S =- .!!-t

NOTB - The internal pressure P is due to stacic head + dynamic head.1.1.2 Longiludinal Joint Effiei,,,e} ( , )

6.1.2.1 It Shall be taken as 1-0 for fully radiographed joint.6.1.3 LOfI,;tudinal StrtSJtJ DUI to B,arn Action

6.1.3.1 The stress developed due to self-weight and weight of waterpipe Ipanning over supports due to beam action .hall be calculated bythe following formula:

Mf-T N/m l

whereAI - bending moment caused due to self-weight and weight

of water.NO'1'JI - BeDdiq moment, M. at mid-span and at support shall be calculated for

each ca.. eoDiideriDi the pipe a. a beam Ipaoninl continuoUily over intermediatesupporta

6.1.3.2 The longitudinal stre,sea developed due to radial straineaused by internal pressure may be taken equal to 0'303 times the hoopten'ion.

1.1.3.1 The longitudinal atressel developed due to seismic forces inthe pipe spanning over the support due to beam action is equivalent toseismic coefficient times stresses calculated in 6.1.3.1. These stressesshould be added to stresses calculated in 6.1.3.1.

6.1.3.4 The longitudinal stresses developed due to wind or snowload acting on the pipe spanning over the support are calculated as givenin 6.1.3.1, where bending moment, M, is caused due to wind load or snowload.

6.1.t Longi'~tlinalS"'SJ DIAl to Sliding Fritl;t)n

6.1.t.l The maximum longitudinal stress developing over allsupports within a section between an expansion joint and the subsequentsupport .haJl be calculated by the formula:

I'. IPf + aEP/J2 = -A- ---r-'

wherePf =- total sliding friction in section between an expansion

joint and subsequent support = ,..W, Cos ~,

8

IS I 11639 ( Part 1 ) • III'

a = eccentricity of frictional force relative to centre line ofpenstock,

Z = section modulus of pipe shen, and~ = angle of section under consideration with the horizontal.

The coefficient of friction, "" between shell and support shaU betaken from Table 1.

TABS 1 DICTION COEFFICIENTS FOR DIPnRENT MATERIALS( Claus, 6.1.4.1 )

SL TVI'E OJ' SOI'I'ORTNo.i) Steel OD concreteii) Steel on concrete with asphalt rootiDI paper in

hetwe~n

iii) Steel on steel ( rusty )iv) Steel OD ItMI ( Irea~ed )v) Steel on steel with two layers of graphite

service .heets in betweenvi) Rocker support

vii) Roller supportYiii) Concrete on concrete

0"600'50

0'150'100'75

6.1.5 T emplraturl StrlSS

6.1.5.1 Longitudinal stresses caused due to expansion or contractionof pipe shell shall be calculated by the following formulae:

a) Pipe shell without expansion jointfa = EccT

b) Pipe shell with expansion jointfa = 1-'1, PAc,

where1-'1 = coefficient of friction between packing material and pipe

shell. andAc -=- contact area between penstock shell and packing material

in rnrn'[,

6.1.6 Circumfirent;al BendingStress,s at SupjJorts

6.1.6.1 Circumferential stresses at supports due to bending causedby internal pressure shall be calculated by the following formula:

M - C PI r

9

II • 1113. (Part 1 ) • 1986

The value of C for different angles of support is given in Fig. 1. Theeffective length or shell resisting the bending moment is equal to 4 timesthe radiu. of the shell.

0·10

0-08

0-08

u.....~ 0-0'u\:\£.

~ 0·02u

0'02

I I I I I II I I I " , I '"

,~, I~I.' . '.

j

, IJ 1

Pw.~~Tt~o=fACT~N OF I'I ~

,. RADIUS OF SHELL j J-1"'l'iI~ MOMENT M.CX~' J J 'I

""'lli Ir-_ ......

"'" I I I I ~ J,.. ... "- "" IV IJ I J--- ~ ......~j- .....~~ "- • ~ ~:,,- v J

....~ '~~:'V ~ I~~~"""" ~,....~~ j

~ ,~,_,: If~"'"

~ ~~J--....~ ,f/

l/...... V- .....

12020 40 60 80 100

~AlU£S Of 8 IN OEGREES

Fro. 1 VARIATION OP CIRCUMPBRBNTlAL MOMENT AROUNDSHELL RBSTINO ON SADDLB SUPPORT

6.1.7 Longiludin41 B",ding StrlSI DUIto &sl,a;,. by Rin, Girders or Sti/fi"".Rill,s (JI IhI Supports

6.1.7.1 The secondary bending strea due to restrain shall becalculated by the formula:

It == 1°82 ( A'-~ x.!!-A, + 1-561 ttl " t

NOTa - Thil stre.. is local and tbe efFect shall b. talkeDfor a distance of Slf wheref - 1°285 on either side of tb. supportiq riaa and pipe thickness shall be increased.

tIrtif required, in this zoneo

10

IS I 11639 ( Part 1 ) • 1118

7. EQ,UIV ALENT STRESSES

7.1 The circumferential and longitudinal stresses obtained as lpecified in6.1.1 to 6.1.7, shall be combined to obtain equivalent strellel in accord­ance with Hencky Mises Theory, given by the formula:

s, = ttl Szl + 811 ± SX S"5

z, S., = f z ; f., :l: 4~(~/s~--2-Ji~.,~)ir--+-r

whereIz - longitudinal stress,!., c= hoop stress, and

q = shear strel.

The equivalent stresses may be readily obtained from Fig. 2.

8. LINER THICKNESS

8.1 The liner thickness of an exposed penstock shall withstand theequivalent stress as specified in 7_

8.2 Notwithstanding the thickness obtained as specified in 8.1 andregardless of pressure, a minimum thickness of liner shan be provided toresist the distortjon during fabrication and erection. A minimum thick-

ness of D ~o50 em is recommended where D i. the diameter of shell

in em.

8.3 No corrosion allowance i. recommended. Instead, it is suggested topaint the inside and the outside surface of pipe with a paint conformingto the relevant Indian Standard.

9. WORKING STRESSES AND FA.CTOR OF SAPETY

9.1 Normal Operatbal CODdidoa9.1.1 It is recommended that under normal operating condition AI

specified in 4.2.1, the working stresses with a factor of safety of 3 basedon the minimum ultimate tensile strength shall be adopted for designbut in no case the maximum stress.s obtained in 7.1 shall exceed 0'5times the specified minimum yield strength of material.

9.2 latermltteat LoacU•• CODdltlo.9.2.1 I t is recommended that under intermittent loading condition as

specified in 4.2.2, the working stre••es with a factor of safety of 2-5 basedon minimum ultimate tensile strength shall be adopted for designs but inno case the maximum lueues obtained in 7.1 shan exceed 2/3 thespecified minimum yield strength of material.

11

18 • 11639( Part 1 ) • 1986

20

,"""~ ~~~I"""'" "'"- ~V I'

"""~

~~--..

"- -, 1/ , \.....~ ~

~ """"'" r--- -, r'\ /' r'\ ~ \,L ---l/~ ~~~ r"""-- r-, ,V '\ ~

,~-

2 ..........~ .....~ ~ r""'- "- '""./ '\ ~ \~ -- ""'- / '\ \~ ~ --- -~ \ ,

O~~ ,-.. '-- "V '\ r\ \ I'

"""'"~~ -_..... - ~V " ~

, ,8~

I.-"'""'"-- "-V " ~ \

~~ ~ / '- \ \ l

6~~ "..

~V '\ l , , :J J

~~--<,/ \ .l , I J ' ,

4./~~~ / l\ l I I J I I J J J J

.J!I'".....~ / \ \ ,' J J J 1/ Il I I I I

2~, V \ 1 J ~ 1/ if r II I I{ II If

- /' ~, I J J J J J I I I J I I I J I I

oV ~ ~ if I 1/ 1/ 1// 1/1/ 1/ II II 1/ V 1/ II. I

l>< ) 2/ J rt.j J ltij I a, j to) / ~21 J tV / ~/ / rJj J2[/~ / ( I If If f v , f V I I I v if I I

l/ ~~~ / / If V V !/ / / 1/ / / / / / /,V ~V ~V / V1/ J I ~ J ) J j I j J

i> ~v / x:/~ ) ~~lf~:, ~~v / / , VJ

6[/ ~V / [/ I)( v / V V V / V / 1/ /./

,~ / ~V / / / / / / ) )

8/~ , V /~ ~ P' / / / / ~

,~

1/ "l/ ~';'~V V )< / ~,.~v V /

1/~ ~l/ ./'" v:l/ /').~ V V V~

/ill""" ,/V ~'" ~l/ ~' r\V /

1/ill""" ,/' l/ V / ~

V V ~l/ """'" ~ ./

~ V 1/ /" V V ~

..1../.,..~ /" V V I'V

L/ if""'" ,;' ~"V .-/" V6/

,.,..V ~V Y ~~

l/~ V .,V t>

TENSION. THOUSANDS

Flo. 2 EQ.UIVALENT STRESS DIAGRAM

9.3 Exceptio. COllciltloD9.3.1 Under exceptional loading condition as specified in 4.2.3, it is

recommended that the working stresses with a factor of safety 2'0 basedon minimum ultimate strength shall be adopted for design but in nocase the maximum stresses obtained in 7.1 shan exceed 0'8 times thespecified minimum yield strength of material.

12

IS a 1163' ( Part I ) · 1986

( Conl;nu,dfrom pag. 2 )

Mmabers R,prls,nt;",SlUU c. GENlt8A PILLAl Kerala State Electricity Board, TrivandrumSHRI A. R. RAGHAVAN Tamil Nadu Electricity Board, MadrasSnn r T. RAMASWAMY Indian Hume Pipe Co Ltd, Bombay

81)1\1 B. RAMA8WAMY (AII,rnat,)DR H. R. SUAHMA Central Electricity Authority, New DelhiSlUU B. TnoMA8 Central Water & Power Research Station, PuneSHRI R. VIJAYAN' In personal capacity ( ECONS-Engi",,,s & Corantltllllts,

35/136 KamalhHath LAn" eIKh", )SURl N. G. KURUP ( Altlf"a/, )

13

INTERNATIONAL SYSTEM 0. UNITS ( 81 UNITS)•••• VDlt.

Q;UAlftl'l'Y UNIT SYIIBOL

LenKth metre mMau kllopam klTime secondElectric current ampere A

Thermodynamic llelvin Ktemperature

LuminoUi intenalty candela cdAmount of substance mole mol

...........tarJ Valt.

Q.uAlCTnr Ul'II'r SYMBOL

Plane augle radiaD radSolid IUIIle Iteradian It

Derlyed Ualta

Q,U.&.NTITY UlfIT 8'1'1180£ n.rmJTIOK

Porce newton N N =- 1 kl.m/sl

EnefIY joule J J-1N.mPower watt W I w- t J/sFlus weber Wb 1 Wb - 1 v.,Flus deDiity t.la- T 1 T .. 1 Wb/ml

Prequency buts H. I Hz - I cIs (a-I)Electric conductance ,iemea S I S-IA/VElectromotive forc. volt V I V-IW/APr-.ur., Itrea palCal P. I P. - I N/m l