K Subrahmanya Engineering Hydrology

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Engineering Hydrology THIRD EDITION c

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About the Author Dr K Subran1anya is a rclin:ar1n1e111 of Civil t:ngi11eeri11g, Z H College o/' £11xi11eeri11g "'"' Teclmology, Aligarh 1\.fusli111 Universit_y, Aligarh

Mol(r K111ty M V

Depurtnie.111 of (:ivil E11gi11eer;ng, Crescent E11gi11ccri11g l'o/lcge. Chc11nt1i

T/lir11venkatasan1}' K

Dept1r1n1e111 oj' Civil Englncering. Bhara1h University, Chennai

.lot/Ii Prakash V

Depar1111e111 oj' Civil Engineering . Indian /11s1itu1e of Technology, Mutnhai

M R Y Pully

Jtlatio11nl tnstitt11e of J;'ngineering, A·(vsore

I \vould also like to express n1y sincere thanks to all Lhose \Vito have dirc.clly or indirectly helped n1c in bring ing out Lh is revised edition. Con11nents and suggcs· tions for further in1provenlcnt oflhc book would be g reatly appreciated. I can be contacted al the follov,.ing c-n1ail address: .~uhra1na1n~akl®.gn1ai/.co1u . K SUBRA.\l&WA

April 2008

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Preface to the First Edition

Water is vital to life and development in all pan• of the world. In T hird World countries 'vhcrc the agricuhural sector plays a key role in l.hcir economic grO\\'th. the n1anagcn1cnt o f \Vatcr resources is an itcn1 of high pliority in their dc.vclop .. 1ncntal activities. The basic in put~ in the C\'aluation of \Vatcr resources arc fron1 hydrological pararnctc.rs a nd the subject of hydrology forn1s the core in the cvalu· a tion and dcvcloptncnt o f \Yater resources. In the civil engineering curriculutn, this subje.cL occupies an in1ponant position. During 1ny long teaching experience, I ha\le fe lt a s trong need for a textbook orienced to the Indian cnv ironn1enL and v,rritLen in a s in1ple and lucid s t) 1le. 1·11e present book is a response to the sat"ne. ·rhis book is intended LO serve as a text for a fi rs t course in engineering hydrology at lhe undergraduate- level in Lhe c ivil

cngiucerin,g discipline. Su1dco1s specializing io various aspccLs of\valer-resources cngiuceriog. sucb as '"aler-po,ver cogineeriug and ag_ricuhural engineering v.•ill fiud this book useful. This book a lso serve> as a source of useful inl0nna1ioo to professional engineers 'vorkiug in the area of v.•aler-resources evaluation and

develop1nent. Engineering hydrology cncon1passcs a wide spcctru1n of lopics and a book like Lhc present one 1ncanl for the fi rsl course 1nus l necessarily tnainlain a balance in the blend of topics. The subject n1attcr has been deve loped in a logical a nd coherent nlanncr and covers the prescribed syllabi of various Indian universities. The 1nathc 1natical part is kept to the mini1nu1n and cn1phasis is placed on the applicability lo fie ld situations rclc\•ant to Indian conditions. SI units arc used throughout the book. Designed essentially for a onewscn1es ter course, lhc n1alcrial in the book is presented in nine chapters. The hydro logic cycle and \vorJd ..\vater ba lance arc covered in Chap. I. Aspects of prccipilation, csscntiaJly rainfall, arc dealt in suf· ficicnt detail in Chap. 2. l~ydrologic abstractions including e\•a potranspiration a nd infiltration arc prcscntc.d in Chap. 3. Srrca1nflov.•· n1casurcn1cnt techniques a nd assess1ne.nt of surface-flo\v yield o f a eatcl11nenl fom1 rhe subject 111auer of C haps. 4 and 5 respectively. The characteristics of flood hydrographs and the unit hydrograph theory togethe r \Vith an introduction to instanta neous un it hydrograph a re covered in sufficienl delai l \Vith nu111e.rous v.•orked exan1ples in C hap. 6. Floods, a topic of cons iderable in1portance. c.o nstitute the subject 111aner of Chap. 7 a nd 8. \Vhile in Cha i>- 7 the flood-peak estitna tion a nd frequency s Ludies are described in detail. Chap. 8 deals \Vith che aspects of tlood routing, Oood control and forecasting. Basic information on tbe hydrological aspects of grouadwmer has been covered iu Chap. 9.

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xvi Pr.,face lo the First Editi0f1

Nu1ncrous v.·orked exan1ples. a set of proble1ns and a sci of objeclivc lype multiple-choice questions are provided at 1he end of each chapter to enable the s ludcnt to gain good con1prchcnsio11 o f the subject. Questions and problcn1s inc luded in the book arc largely original and arc designed to enhance the capabilities of co1nprchcns ion~ analysis and application of the s tudent.

I a1n gnllcfiil to: UNESCO for pcrn1ission to reproduce several figures from their publication, ,\'atural Resources q{H11111id Tropical Asio- f\'atural Resources Research XII. •• UN ESCO, 1974 ; the Director-General of Meteorology. India Meteorological Dcpart111cnt, Govcn1n1c111 of India for pcnnission to re.produce. several n1aps; .\ill s Leupo ld and Stevens, Inc., Bcaverlon. Oregon. U S1\ , for pho·

tographs of hydron1ctcorological instrun1c.nts; Mis Alsthon1·1\tlantiquc, Nc.yrtcc. Grenoble f rancc, for photographs o f sc.vcral Ncyrtec lnstrun1cnts; lv1/.s Lav.•rcncc. and Mayo. (India) PvL Led .• Ne\v l)elhi for lhe photograph o fa current 111cler. l 'hanks al'e due 10 Professor K VG K Gokhale for his valuable susgestions and to Sri Suresh Ku111ar for his help in cite production of che 111anuscripc. I \Vish to thank 111y scudenl friends \Vho helped in this endeavour in 1nany ways. 1'he financial support received under the Quality lniprovcment Programme (QJP), Govern1nerH of Ind ia, lhrough the Indian lnstilule o f Technology. Kanpur. for the preparation of the 11\anuscript is gratefully acknowledged.

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Abbreviations

AET A I Aridity Index AMC CBIP CGWB

CN

ewe DAil DRl l llVC ERll l'AO FEM l'RL GO! li'vlD IUH KWM MA I MCM MDDL MOC MSL MUSLE NBSS&LUP NCIWRD NRSA

PcT

Actual Evapolranspiration /\ntcccdcnt ?vtoisturc Condition Central Board of Irrigation and Power (India) Central Groundv.•alcr Board (India) Curve Nunlbcr Central \Valer Conlin ission ( India) Maxin1un1 l>eprh-/\ rc.a-l)uradon l)irect Runoff I lydrograph l)amodar Valley Corporation Effective Rainfall I lyetograph Food aud Agricu lture Organisa1ion Finite Elcnteot Method J;ull Reservoir Level Govcrmneot of India India Meleorological DeparL1nc11t lnstanlancous Unil J·lydrograph Kentucky Watershed Model Moisture Availability Index Million Cubic Meter Minhnu1n Drav.•down Level Method of Characteristics Mean Sea Level Modified lJni\•crsal Soil Loss Equation National Bureau of Soil Survey and land lJsc Planning National Con1n1ission fo r Integrated \Valer Resources Development ( 1999) National Rc111olc Sensing 1\gcncy Polential Evapou·anspiration

l•1 l'altner Index PMF

!'MP RHA RTW l l

scs SOR SPF

Probable f\rage co1npo11en1s ns belo\v:

Transportation components Pn;eipiUtlion

Evaporation Trnnspirnlion

Storage componcot.s $l(1ragc on 1hc hind surfitcc

(Depression Sh)mge. Ponds, Lnkes, ReserVl)irs, etc) Soil 1noistu.re storage Grounouttlo'v and storage \'Olun1cs arc the sa1nc +T - "1J = t:.S ( I.I ) ,vlJere +f = iuflO'A' vohnne of '"'ater into 1he problein area during the tirne period. +TI = ou1ao,v volun1c of '"'atc1· fronl 1he problen1 area during the tin1e period. and tl.S = cbau.gc iu lhe s1oragc of the \Vater volu1ue over and under the giveo area during the given period. In applying r 10 hours M>'ith 011 average

discharge of I .S nt.t/s. The streonr lras again di')' 0,{ier the runoff cve11t, (aJ JVhat is the flntt11111t nf 1v1uer 1rhich 1vas not a1·a ilohle ta riu1nffrluiY tn canthined l'.jfect nf i11Jiltration, ei·uporutiou and lran."plrution? ll'ltat is the ratio t?f'nutoff'to preclplt"tian?

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1'he \vater budget equation for the- catch1ne-nt in a U1ne tJ.t is

R=P - l

{l.2-b)

where: L = Looses= \\'alcr nol avaih)blc l\ elnp111ent, \fol. I, 1975, lnsl. l(>r Sci. Coop, Hunn(.1vc:r, \.rennuny, pp. 8-14. 3. UNESCO, "'\ \'cl. rld \Va1er Balance !ind \Vater Res(lun:~ or the Carth.., Sludie.s and Repons i11 Hydrology. 25. UNESCO, Paris. France. 1978.

2.

1

4.

\.~n

dcr Locdcn, rf~tcr Resources ofthe rJbrld, \Vatcr lnfom1ation Center, Pon \Vashuigton. N. Y.• USA. 1975. REVISION QUESTIONS

1.1 Describe the Hydrologic c:y-clc. Expktin bricOy 1bc man·s interference in various pans of this cycle. 1.2 Discuss the hydrologicaJ \Vater budget \Vith tJ1e aid or exan1ples. 1.3 What are the signilic.ant features of global \V3ter balance studies'! t .4 List the rnajor ncti\'ilies in which hydrological .'liudies are iinporta.nt I .S Desctibe btielly the sources of hydrological daut in India.

1-----------

PnoaLF.:MS 1.1 Ty.·oand half centimetres of ruin per day over an area 1n the reservoir v.·as 2.5 cnl, total precipilation on the reservoir \Vas 18.5 cn1 and the tofal evaporation y,·a.s 9.5 c.:m. 1.4 1\ river reach had a flood Y..ilve passing thrl)ug_h it A1 a given ins1an1tJ1e s1omge of \v:tter in the mich \\'aS cstim.;itcd as 15.5 ha.m. \\'Mt y.·ould be the storage in the reach aRcr an in1er...al or3 hour:; irthe average lnllO\\' and ou1floY• during the time peri(1d tu~ 14.2 nr'/ sand I0.6 n1'/s respec1ively'! 1.S J\ e~11 cl1111cnt has four sub-areas. The annunl pm:ipitttrion and cv:tporotion fro1n ~c b of the sub-areo..1:; are gi,,e n b.tlO\I/. Assu1nc that there is no change in 1hc ground,wtcr storage on ao annunJ basis and cnlcu· lu1e li.irlhe y,·h' (d) Australia li.1S the s1nalles1 value.or rl>' In 1he hydrological cycle the average l'esidence 1i1ne or\va1er in the global (a) a111l05pherie nWlisture is larger tllan thlll in t1le.global tivers (b) (ICcilns is s1naller than that of 1hc global grvun(hvalc:r (c) river.; is lurgc:r tha:n 1lut1 of lhi; : global grounc.hvnlc:r (d) occnns is larger than that of the global grouod\vntcr. 1\ \vatcrshod has an area of 300 ha. Due 10 u 10 cn1 rain.full event over the \Vatcrshod a s1rean1 flo''' is generated and at tJ1e outlet of tl1e.\\'atershed it lasts l'or 10 hours. 1\ssu1U· inga rw1otf/rainlb.l1 ratio of0.20 for lhis event, tJ1eaveragestreaLn flo,v rate at the oulJet in tl1is period of IOhours is (n) 1.33 1nl/s (h) 16.7 n~~is (c) JOO tn3/Jninute (d) 60.000 rrY/h Rainfilll of intensity of201nnvll f1ccurred ovel' a \\'ate-rshed l)f area 100 ha fOr a duration of 6 h. mc.a;Surtd direct runolf volume in the: SL~tn1 dn1ining lhe \\IUlershtd \WS fou nd 10 be 30,000 ml. TI1e pm:ipi1a1ion nol available ltl runoff in Lhis case is (:il 9 cm (b) 3 cm (c) 17.5 mm (d) 5 mm t\ ca1ch1nen1of ~1~1 120 kn11 has llll\X djstJnct zones as bck1\v:

Zone

Arcu (km')

Annuol runol'I' (c.m)

A

61 39

52 42

20

32

n c

111e annual runoff fro1n the catchn1ent. is (•) 126.0cm

(b) 42.0 cm

(c) 45.4 cm

(d) 47.3 CHI

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I Chapter

2 PRECIPITATION

2.1 INTRODUCTION The tcnn precipi1ario11 dcnotl'S all forms of water Lhat reach lhc earth from the atmosphere. ·111e usual forms are rainfall, snowfall, hail, frosl and dew. Of all rhese, only the first 1wo contribute signilican1 anloun1s of"•a1c.r. Rainfall being. the predoroinanl forn1 of precipitation c.ausing stream flo\v, especially I.he flood flo\\' in a n1ajority of rivers in lndia, unless other,vise stated the term rai11Jilll is used in this book syuony1nously '"ith prccipihHion. The n1agniludc of precipitation varies with time and space. Differences in die. 1nag.nitudc of rainfall in various pans of a country ar a given tin1e and varialions of rainfall at a place in various seasons of the year arc ob,1ous and need no claborarion. It is this variation that is rcsp:>nsiblc fi1r many hydrologic-.aJ problems, such as floods and droug)us. The s1udy of precipi1alion lbnns a major ponion of the subject ofhydromctoorology. la this chapter>a brief introduction is given to fun1iliarize Lhe engineer \Vith imporLanL aspects of rninfal I. and., in panicular, \Vith the collection and analysis o f rainfall data. For prcripitation to fonn: (i) the atn1osphcrc: niust have n1oisturc, (ii) there niust be sullicic.nl nuclei present to aid condensation. (iii) \Veather conditions must be good IOr condcnSaliOn of \Valer vapour to take place, and (iv) Lhc products of condeasation niusLreach the earth. Under proper 'veather conditions. Lhe V.'aler vapour condenses over nuclei to fonn tiny v.•atcr droplets of sizes less than O. l mm in diameter. The nuclei arc usually sail particles or producL 7.5 n1m/h

3. Heavy rain SNOW

.)noh' is another important forn1 of precipitation. Sno\V consists of ice crystals which usually co1nbine to forn1 flakes. \\/hen fTesh, snO\\' has an inicial density varying from 0.06 to 0. I 5 g/cm3 and it is usual to assume an aver.tgc dcnsily of 0. I g/ cn13. In India, sno\V occurs only in the l·lin1alayan regions. DRIZZLE A fine sprinkle of nun1erous \Vater d.ropleLS of siz.e less Lha.n 0.5 1nn1 and intensity ll-ss than Lrnm/h is known as drizzle. La tbis the drops arc so sn1all Lb.at Lhcy appc.ar to float in the air. GLAZE \Vhcn rain or drizzle conics in contacl \Vith cold ground at around er C, the 'vater drops freeze to fonn an ice coating called .~laze orfi·ef!Zit1g rt1i11.

SLEET II is frozen raindrops of1ransparen1 gi;iins which fonn when rain falls through

air at subfreezing tcnlpcraturc. Jn Britain, sleet denotes precipitation of sno'v and rain sin1uhaneously. HAIL

h is a showery precipiUltioo in the fonn of irregular pellets or lumps of ice of

s ize n1orc than 8 n1n1. 1-lails occur in violent thundcrstonns in \vhich vertical currents arc very scrong.

2.3 WEATHER SYSTEMS FOR PRECIPITATION

or

For 1he IOnnation C·IOuds and subsequent precipitalion. ii is IlOC¢SSflry 1ha1 •he tnoisl air 1nasscs cool to lOnn condensation. This is normally accomplished by adiabatic cooling of111oist air through a process of being lifted co higher akin1des. So111e of the terms and proc¢sses connected " 'ith the 'vea1hersys1ems associated 'A'ith precipitation are given bclO\V. FRONT Afro1u is Lhe interf.1ce betv.•een L\VO distincl air 1nasses. Under certain favourable condi1ions y,•hen a 'varm air mass and cold air mass rneet. 1hc "'finner air 1nass is lifted ove.r the colder one v.•ith lhc fom1ation of a fronl. The ascending \Vamx:r air cools adiabalically \Vilh Lhe consequent fonnat.ion of clouds and precipitation. CYCLONE A c)·c/011e is a large low pressure region 'vilh circular 'viud n101ion. T'vo typ...-s of cyclones arc recognised: lropical cyclonl-s and cxtnuropical cyclones. 1i'O/Jical cyclone: A tropical cyclone-. also called cyclone in India, hurricane in USA and syphoon in South-East 1\sia is a \Vind syslcn1 \Vilb an intensely strong depression \Vith ?vtSL pressures sonlctimcs below 915 n1bars The norn12J areal extent of & cyclone is about 100- 200 km in diameter. The isobars arc closely spaced and the \vinds arc anticlocki.visc in the northern hc1nisphcrc. The centre of the stonn, called the e)'i!, v.•hich n1ay extend to about 10 50 kn1 in diameter, v.•ill be rclative-ly quiet. Hov.•cvcr. rigln outside the eye. very strong \Vinds/rcaching lo as n1uch as 200 kmph 1

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Prccipita1ion

cxisc. The \vind speed gradually decreases to\\1ards the outer edge. The pressure also increases outwards (Fig. 2.1). The rainfall will normally be heavy in tbe entire area occupied by Lite cyclone.

,,...

1000

"E !, e ~

Q

..

Q.

980

40

-

Pressure

960 /

---

I I I I I \ I \I;

/

""f. Rainfall

Intensity ~

a.

Wind speegy

condcnsac-ion and precipitation. Such a prccipiralion is kno\vn as Orog1'011ltic 11rocipi-

u11io11. Thus in moun1ain ranges. the v"ind\vfH'd slopes have heavy precipi1a1ion and

the leeward slopes light rainfall.

2.4

CHARACTERISTICS OF PRECIPITATION IN INDIA

f ron1 the poinl of vie\\• ofc li1natc the Indian subcontinent can be considered to have l\li.'O rnajor seasons and l\VO lransilional periods as: • South-v.•cst monsoon (Junc..- sc...,,1cmbcr) • ·rransition-1, post-nlonsoon (OcLober Noven1ber) • Winier season (December- February) • Transition·ll, Summer, (March May) The chief precipitation characteris1ics of these seasons are given belo\v, SOUT H-WEST M ONSOON (JUNE-SEPT EMBER)

'Ille SOUlh-\\·esc 1no11soon (popularly kno,vn as monsoon) is the principal rainy season or lndia 'vbeo over 7511/o of lhe annual rainfall is received O\'er a 1najor poriion of the country. Excepting I.he sout.h--caslcm parl of t..hc peninsula and Jan1mu and Kashmir, for the rest of the country tile south-,vcs• rnoasoon is the principal source of niin \vilh July as lhe n1onlh v.:hich has maximum rain. The monsoon originates in lhe lndian ocean and heralds its appearance in the southent part of Kera la by the end of May. 1'he onset of monsoon is accompanied by high sou1b-westerly wiuds al speeds or 30- 70 kn1ph and lo\v prcssure regions at the advancing edge. The monsoon \vind.s advance across 1he country in two branches: (i) the Arabian sea branch, and (ii) the Bay of Bengal branch. The fonner sets in al lhc cxtrcn1e southen1 part o f Kcrala and lhe laucr at 1\ssan1. aln1oscsi111ultaneously in 1..he firsr v.•eek of.lune. ·rhe Hay branch first covers the north-eastern regions of the up o.f teu 11eir.!11bourin~ stations locate(/ in a meteorological/1: llomogc11eous region are given be/0111, ,\ _nnual Rain fall of

\ 'car

Station l\'1 (mm)

1950 1951 1952 1953 1954 1955 1956 1957

1958 1959 1960 1%1 1962 1%3 1964

AY\'rage An nual Rainfall or the group (mm)

780

676 578

66-0

95

110

462 4 72 699 479

520 54-0 800 540

4 31 493 503

56()

415 53 1 504 ~28

679

490 575 480 600 580 950 770

Year

1\nnual

1\ vcragc

Rainrau or

..\nnual Rainfall of

Station l\'I (mm)

the J!roup (mm)

1965 1966 1967 1968 1969 1970 197 1 1972 1973 1974

1244 999 573 596 375 635 497 386 438 568

1400 1140 650 646 350 590 490 400 390 570

1975

J56

377

1976 1977 1978 1979

685 825 426 612

653 787 4 10 588

1t:>st the co11sis1e11c1: of the t11111ual rainfall data o.fstarion !\ti and corrFCI the 1v.>cord ifthert~ is

8.

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1nultiplied by the COJ'tt(;lion ratio or 1.1 73 h) get tlle adjusted \•alue-. The adjusted \•alues at s1ation i\f arc sbo,vu in Col. S of Table, Tbc finalized values of Pm (rounded off to ocarcst

1n1n) fOr all the 30 years of record are shown in Col. 7. The 1nean annual precipitation at station J\rf (based on the corrected ti1ne series) ( 19004;30) = 633.5 mm

Table 2.1 Calculation of Double Mass Curve of Example 2.3

Year

4

s

6

7

P.

3 '£.Pm

P,.

P.,

1\djusted

(mm)

( mm)

( mm)

(mm)

\'alucs or

Finalised \'alues or p,,,

2

P,,, (n1n1) 1979 19n 1977 1976 1975 1974 1973 1972 197 1 1970 1969 1968 1967 1966 1%5 1964 1963 1962 1961 1960

1959 1958 1957 1956

1955 1954 1953 1952 1951 1950

6 12 4 26 825 685 356 568 438 386 497 635 375 596 5 73 999 1244 679 828 504 53 1 4 15 503 493 43 1

479 699 472 462

95 5 78 676

612 1038 1863

2548 2904 3472 3910 4296 4793 5428 5803 6399 6972 797 1 9215 9894 10722 11226 11757 12 172 12675 131 68 13599 14078 14777 15249 15711 15806 16384 17060

588 410 787 653 377 570 390 400 490 590 350 646 650 1140 1400 770 950 5801 600 480 575 560 490 540 800 540 520 110 660 780

588 998 1785 2438 2815 3385 3775 4 175 4665 5255

5605 625 1 690 1 804 1 944 1 10211 11161 11741 1234 1 1282 1 13396 13956 14446 14986 15 786 16326 16846 16956 17616 18396

698.92 67 1.95 117U l 1458.82 7 96.25 970.98 591.03 622. 70 486.66 589.86 578.1 3 505.43 561. 72 819.7 1 553.5 1 541.78 111.4 1 677.8 1 792.73

(mm)

6 12 426 825 685 356 568 438 386 497 635 375 699 6 72 1172 1459 796 97 1 591 623 487

590 578 505 562 820 554 542 111 678 193

Total of P'" = 19004 mn1 Mean of PM= 633.5 mm

2. 8 PRESENTATION OF RAINFALL DATA A few commonly used mechods ofpresencation of rainfall da1a which have been found to be uscfi.LI in interpretation and analysis of such data arc given as tOllov.•s:

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rrcc:ipitJtion

MASS CURVE OF RAINFALL

T'hc n1ass cun•c of rainfull is a plot of the accumulated precipitation against tin1c,

ploued in c.hronological order. Records of float type and v.·eighing buc.ket type gauges arc of this tOnn. A typical mass curve of rainfall at a station during a stonn is sho,vn in Fig. 2.9. 1\otass curves of rainfall are veC)' useful in extracLing d1e information on the duration and rnagniu.1de of a storm. Also. intensities at various tirne intervals in a storm c.an be obtained by the slope of the curve. for nonrccording raingaugcs, nlass curves are prepared from a kno,vledge of the approxin1ate beginning and end of a storm and by using the mass c urves of adjacent recording gauge stations as a guide. 1st storm

(10 cm)

\_2nd storm (4 cm)

2

Time (days)

Fig. 2.9 HYETOGRAPH

A hyctogrnph is a plot of the

imensity of l'ainfall against

Mass Curve of t{ainfall

~u 0.3

Hye109raph of 1he

first storm in Fig. 2.9

;:.

·~

hyctograph is derived 1Ton1 the rnasscurveand is usually

c

Vt.'llicnt \vay of rcprc.•--scnting the characteristics of a stom1 and is particularly inlponant

4

0.4

the l ime inte rval. The

rcprc-s cntcd as a bar chart (fig. 2.10). le is a very con-

3

Total depth= 10 cm Duralion = 56 h

; 0.2

]! c ·;;

cc

o. 1 QLLI'-'-"'--'--'--'--'--'---'--'--'--'--'-_.__, 0

8

16 24 32 Time( hours) ~

40

48

56

Fig. 2.10 Hyetograph of a Storm

in the dcvclopn1cnt of design storn1s co predict extre1ne floods. 1'he area under a hyerograph represents the total

pn."Cipitation rc..-ccivc..-d in the period. The time interval used depends on the purpose, in urban-drainage problcn1s sn1all durations arc used while in flood·tlo\v con1putations in larger catchnlenlS the intervals are of aboul 6 h. P OIN"I' R AINFALL

Poinc rai nfall, also kno,vn as Sh}tion rainfall refers to the rainfall data of a staLion. Depending upon the need>data can be listed as daily> v.'c..."Ckly, n1onthly, seasonal or annual values for various periods. G raphically these data arc represented as plots of

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n1agnitudc vs c-.hronologic-al tin1c in the form ofa bar diagran1. Such a plot, however, is not convenient for discerning a trend in the rainfall as there 'viii be considerable variations in the rainfal1 values leading to rapid changes in tJtc plot. The trend is often discerned by lhe n1ethod of 11Joving averages, also kno,vn as moving 1neans. Moving average Moving average is a technique for s1noorhening out the hig.h frequenc.y fl uctuacions of a ti1ne series and LO enable che crend, i f any. LO be

noticed. The basic principle is 1hal a '-'' indO'A' of1inle range 111 years is selected. Starting fron1 the first set of 1n years of data, the average of the data for 1n years is calcu· laced and placed in che 111iddle year of the range '"· ·n1e \Vindo'v is next n1oved sequenlially one time unit (year) al a time and the mt.'Bn o f the 11J terms in the 'vindo'v is dctcrn1incd at each \Vindo'v location. The value o f 1n can be 3 or n1orc years; usually an odd value. Generally, the largcrthe siie ofibe range 111, the grea1cr is 1he smoothening. There arc many \vays of averaging (and consequently the plotting position of the n1can) and the meihod described above is called Cenlral Simple Moving Average. txample 2.4 describes the applicalion of the method o f moving avcragc..--s. Annual ,.aiu/all values recorded at su1tion ll1 jnr tire period 1950 to

EXAMPLE 2.4

1979 is g1\ en iu Exa111plc 2.3. ReprcsCJ11 this data cific duration tOr any n."Currcncc interval can be estimated. ~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~

0

190 .0

/

tSO.O 170 .0

~

160.0 ~

E

~

~

·~

;;; ~

c c

and che iso-1.>luvial (lines connecting equal depchs of rainfa ll) n1aps covering the entire cotmlry have bcx.'O prepared. These arc available tOr rainfall dur:itions of 15 nlin, 30 n1in, 45 min, I h, 3 h, 6 h, 9 h, 15 hand 24 h for rctunt periods of2. 5. LO. 25. 50 and LOO years. A typical 50 ycar- 24 h maximum rainfall map of the southern peninsula is given in Fig. 2.21. The 50 year-I h maximum rainfall

•••

..

..

,

, 280

MOS

12"

'2'

•••

•••

••

~~~~~~~~~~~~~~~~~~~~~~~~-

..

ao• a2• s4• Fig. 2.21 lsoplu vial Map of 50 yr·24 h Maximum Rainfall (mm) (Reproduced with permission from India f\·feteomlogical Department) 14 ~

Based upon Sut\'f)' of lndi.l

1a ~

n~p

1e·

\\•ilh llw perm.is.. intertl.'I det.iils on the n\i'lp resl.S with the publ.ishn.

EXAMPLE 2.9 The n1ass 47 cm (c) = 47 cm (d) inadequate infor1natio1110 oonclude. Depth-Area-Duration curves of precipitation are dra,vn as (a) 1nini1n.i:.dng envelopes Lhrough Lhe appropriaLe data point~ (b) 1naxi1n.ising en,·elopes Lhrough Lhe appropriaLe data point (c) bes1 lit n1ean cuives 1hrough lhe appn:>priale da1a poinLS (d) bes1 lit stmigh1 lines thro11gh lhe appropri ~1le data points Dcptb-Area-Ouration curves of precipitation al a station would nom:mUy be (a) curves. concave UP'''ards. wiLb dura•ion incrcasiog out"'1lfd (b) curves... ooncave do,vn,vards. with duration increasing outward (c) curves. ooncave up,vards, with duration decreasing outward (d) curve~ ooocave dl)"'n"·ards, \ViLh duration decreasingout,vard 1\ study oftlle Li;oplu,·ial 1naps re,·eaJed Lhat at Calcutt.a a nlil.xi1nwn rain fill I depth of200 n1m in 12 h has a return period or 50 ye~1rs. The pn.:>~bi li1y of a 12 h roinf;ill equal 10 or gn:~1ter th~1n 200 mm occurring at Calcuua al IC" l!'ITit(lrfal w.iw~ (lf Ind ia e>Xlt"nii into 11'11' i;.' a dry soil Time from start o f infiltration {h) can absorb n1ore \Valer than Fig. 3.11 Variation of Infil tration Capacity one 'vhose pores arc already full (Fig. 3.11). The land use has a sig:nitic-ant influence on/,,. For cxan1ple, a forest soil rich in organic mauer will have a rnuch big.her value o(f,, under idenlical conditions than the san1c soil in an urban area 'vhcre it is subjected to compaction. S URFACE OF E NTR Y

At the soil surface~ the impact of raindrops causes the fines in 1he soil to be displaced and 1hese in tum can clog 1he pore spaces in lhe upper layers o f the soil. This is an in1portant factor aftt..-cling the infiltration capacity. Thus a surface covered \Vich grass and other vegeracion \vhich can reduce this process has a pronounced influence on the value of}~ F LUtO CHARAC'f'/:;"'RtST'ICS \Vatcr infihrating into the soil will have mm y impurities, boch in solution and in suspension. ·n1e turbidity of the v.cater. especially the clay and colloid content is an impo11an1 factor and such suspended particles block the tine pores in the soil and reduce its intihration c-apacity. The temperature of the v.•atcr is a factor in the sense thac icaffects the viscosity of the v.•acer by whic.h in turn affects lhc infiltration rate. Contruninalion of lhe \vater by dissolved salts can aftt.-ct lhc soil structure and in cum affect the infiltration rate-.

3 . 17

M E ASUREMEN T OF INFILTRA TION

Infi ltration c.haracteriscics ofa soil at a given locaLion can be esLin1ated by • Using ilooding type iniillrornecers • Mcasurcn1ent of subsidence of ITce water in a large basin or pond • Rainfall simulator • Hydrog.raph analysis

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Abslrad ions from Precipitation

F LO ODING-1YP E IN FILT ROM ETE R

flooding-type infiltron1ctcrs arc experimental devices used to obtain data relating to variacion ofi nfilcration capac.ity v.t id1 ci1ne. 1V.·o cypes of flooding type infiltron1eters arc in wmmon use. They arc (a) Tube-type (or Simple) intihromctcr and (b) Doublcring infihro1neter. SIMPLE m.JBE TYPE) INFIL TROMETER 'J11is is a si1nple instrun1enl consiscing essentially of a metal cylinder, 30 cm diameter and 60 cm long, opc'tl at both ends. The cylinder is driven into the ground to a depth of 50 cm (Fig. 3. 12(a)). Water is poured into che top pat1 to a depth of 5 crn and a poin1e.r is set 10 mark the \VfHer level. As intihration procc.'t. . 'Cls) the volun1c is made up by adding \Valer from a burcltc to kc..-cp the \Valer level ac the tip of che pointer. Kno,ving the volun1e of,vater added during diffcn.-nt tin1c intervals, the plot of the infi hration capaeily vs lin1e is oblaincd. The experi111ents arc continued till a uniform rate of infiltration is obtained and lhis may take 2- 3 hours. The surface o f the soil is usually protected by a perforalcd disc to prevent forn1ation o f turbidity and its settling on cite soil surf.tee.

~ 30cm dla. ~

_j

S . o.9713 the plotted points is obtained 2.00 as 0 .00 J~ = 3.2287 r"' + 1.23 o.oo 1.00 2.00 3.00 4.00 The coefficients of Philip's t-0.6 equation ares 2 x 3.2287 Fig. 3.15 (b) Fitting of Philip's Equation 6.4574 and K = 1.23 Kostiakov equation KostiakQv's Equufi(J11: 3.00 Fp (1). =al' y = 0.6966x+ 1.8346 2.50 li.q. (3.25) R2c 0 .9957 / 2.00 Taking logarithms of

"'

both sides of the equation (3.25) ln(F,) = In a + b ln(1). The data set is plotted as graph

/

.

.......

5

Ln(/·~) "' ln(1)on anarith-

n1ctic

/ ·

paper

1.50

..Y

t .OO

0.50 o.oo -3.00

./

.

.

/

/

/

-2.00

(Fig. 3.15-c) and the best fig. 3.15 (c) Iii straight line through the ploltcd points is obtained as

- 1.00 o.oo Ln l(h)

1.00

2.00

Fitting of Kostiakov Equation

ln(Fp) = 1.8346 + 0.6%6 in(t). T he coefficients of Kostiakov equation arc b = 0.6966 and In a = 1.8346

and hence"= 6.2626. Best liuing Kostiakov equation for the data is F, = 6.26261'"'66 EXAMPLE 3.8

111e ilrfillratio11 capacily in a basin is represe111ed bJ' Horton S equation as 3.0 I e .'1

j~

'

11•he.1v:}~ is in ('/11111 a11d t is in hours. Assu111ing rllc i1tji/11y11io1t to take place at capociry rrue:i: i11 a .~torn1 of60 '11i1111tes d11rr11ion. estinuue the dtquh ofi11jil1r111io11 in {I) tire first 30 111inutc>.\' and (il) the .w:c:ond 30 n1b1utes qj.1/u: stornt.

SOLUTION.'

F,?

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'

J~. d1 "

and

j~

3.0 + e

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Abslradions from Precipitation

(i) In the first 0.5 hour

f

o .~

FP' =

'

(3.0 + e- •) dt = [ 3.01 - ~e-2 ' 2

= 1(3.0 x 0.5) = 1.8 16 cm (ii) In 1he second 0.5 hour

l ( 112)1= ( 1.5 0.1 84) + 0.5

(1:'2)(e-thal satisfies the relation .II

RJ

'L,(I; - rp)t.J I

3. Using the value of tpofStcp 2, find the nun1bcr of pulses (A1r) \Vhic.h give rain· fall excess. f l"hus Arie nun1ber of pulses v.·iLh rainfall inlensity 11 ~ ¢). 4. lf Mr. = M, then 9' of Step 2 is the correct value of 9'-indcx. lf not, repeat the procedure Step I on\vards \Vith nev.• value of !W. Result of Step 3 can be used as guidance to the nexl trial.

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Abslradions from Precipitation

Exan1plc 3. 10 illuslratcs lhis procedure in detail. EXAMPL E 3 . 1 O

A stt)1-,,1 u1itlt /() c1n oj/11u:ipitution 111lx11u.:ed a diret:t 1;111tif/·a j·5.8 cn1.

T!te durario11 oj' the rainfall i,•as J6 flours and i1s tin1e dis1rib11tio11 is 1-:iven belou~ Esti111atc r/Jc tp-i11dex oj·r/Jc stor111, Ti1ne ti·oo\ start (h)

0

2

4

6

Cu1nulative rainfall (cn1)

(>

0.4

1.3

2.8

10 6.9

8 5.1

12 8.5

14 9.5

16 10.0

Pu l se~'i of unifOnn tirne duratil)O 13.t 2 It are considered. 111e pulses are nu111bered sequentially and intensity of rainfall in each pulse is calculated as sJ10,vn belo''"

SOLUTION:

Table3.12 Calculations for Example 3.10 l.,ulse nuntber

2

J

4

s

6

7

8

Ti1ne fro1n start of rain (h) 2 Cu1nulative rainfall (cn1) 0.4 lncrc1ncutal rnio (cnt) 0.40

4 1.3

0.90

6 2.8 1.50

8 5.1 2.30

10 6.9 1.80

12 8.5 1.60

14 9.5 1.00

16 10.0 0.50

0.45

0. 75

1.15

0.90

0.80

0.50

0.25

rn1 ensityo fr~1 in

(11) in

c1nlh.

0.20

Mere duration ofroinfall D

Trial I:

.

16 h, ill

2 hand ,v

Assuntc .W = 8. 61 = 2 h and hcu-+--+--1--~f-_,f-~-0.275 0 .275 0.275 0.275 0 .275 0 .2 75 0 .250 \P= 0 .2 7S cmfh • 0 200

5

7

._'71'"~.-'-._..__...___..__._.___..__ •_,

T

Pulse number (pul se of 2 -hour duration)

Fig. 3.17 Hyctograph and Rainfall Excess of the Storm - Example 3.lO

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Engineering Hydrology By inspection o f rov.· 5 of Table 3.1 2, iWr = number of pulses having 11 ~ (/J. lhat is 11 ~ 0 .263 cm/b is 6. Thus ,w= 9.1 - 12 I" index the initial losses are separated fro1n the total abstracLions and an average value of infiltration rate, called H1-i1xlex. is defined as W=

P-R-1

"

(3.29)

l,1

\\/here

P = total storm precipitation (c.n1) R = total stonn runo lf(cm) / = Initial losses (cm) 0 tit= duration of the rainfa ll excess) i.e . the total tin1c in \vhich the rainfall intensity is greater than W(in hours) and W =defined average rate ofinfiltration (cm).

Since /11 rates are dil1lcul1 to obtain, the accura1e es1ima1ion of f·V-index is rather

difficulL 1·11e n1i11in1um value o f the IF-index obtained under ve1y 'vet soil eondicio1is. representing the constant n1inin1um rate o f infi ltration of thceatchn1cnt, is kn0\\111 as JJ"min· It is to be noted dtal both the IJ>index and JV-index vary front stom1 to storm. COMPUTATION OF W.!N0£X To compute W-indcx from a given stoml hyetograph \\lilh knO\\lll values or 'l,J and n1noff R. lbe follo,ving procedure is Collo1A·ed:

(i) Deduct the initial loss 10 fro m the swm hyetograph pulses starting from the fi rst pulse

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Abslradions from Precipitation

(ii) Use the resulting hyctogrnph pulse diagram and follow the procedure indicate'-indcx except for

the face that che sLorn1 hye.tograph is appropriately 1nodified by deducting /0 • tp-IND£X FOR PRACnCAL US£ The 9'-index for a catchment. during a storm. depends in general upon lhc soil type, vcgctal cover, initial n1oisturc condition, storm duration and intensity. 1°0 obtain con1plete inforn1ation on the interrelationship between these factors. a de1ailed expensive study of the catchment is necessary. As such. for practical use in the estimation of flood magnitudes due to critical stom1s a sin1pli· foed relationship for 9'-index is adopced. As the maximum flood peaks are invariably produced due to long stonus and usually in the \VCt Sthe initial losses arc assumed to be neglig ibly small. ~·urther, only the soil cype and rainfall are found co be crilical in theestima1e of the g>-index for maximum Oood producing s1onns.

On tJte basis of rainfall and n utoff correlations, C\\'C 1 has found the fol lov.ring

relationships for che cscimacion of 9'-index for Oood producing storms and soil conditions prevalent in India

R = a/ 12

(3.30)

1-R

rp= - -

(3.3 1)

24 \vherc R = runoff in cm from a 24-h rainfall o f intt.'llsity I cnvh and a= a coefficient \\lhich depends upon the soil type as indicated in Table 3.13. Jn cstintating the ma.xi·

mum iloods for design purposes. in the absence of any other data. a 9'-index value of 0. 10 cmlh can be assun1cd.

Table 3.13 Variation of Coefficient ain Eq. 3.30 SI. l"o. I.

2. 3.

4. 5.

Type or Soll Sandy soils and sandy loam Coastal alluvhun and silty lo.a1n Red soils. clayey loan1. grey and brown alluviu1n Black-r /111egrr11ed H~1ter Resources /)ei"Plt>Jnrient, Vol.-1, Nev.· Delhi, Scpl 199!>.

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Engineering Hydrology REVISION QUESTIONS

3.1 3.2 3.3 3.4 3.5

3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.1 5

Discuss brielly the various abstractions l'ron1 precipitation. Exph1in brielly the evaporation process. Discuss the l'ilctors tltat atlfcl the evaporation tro1n a 'vater body. Describe a oommouly usod cvaporimctcr. Explain the energy budget n-.e1hocJ of es1in-m1ing evapora1ion from a lal:e-.

Discuss the intportaooe of evaporation control of reservoirs and possible n1ethods of achieving the ti3nle. Describe tlte fhCU)fS allE:cting evapotranspiration pnx:ess. List the various data needed to use Penman's equation for cstin1ating the potential evapo1ranspira1ion from a given area Describe brielly(a) Jteferenoecrop evapotranspiration and (b) ActuaJ evapotrans-piration. Explain briefly the infiltration process and the resulting soil n1ois:turo zones in the soil. Discuss the l'ilctors anecting lhe inlihnuion capacity or an area. Describe the commonly used procedures for dctenniniog tbc infi.ltratioo cbaracteristics of a plot of land. f;xpl.ain clearly the rela1ive i:1cJw ntagcs and disadvan1.ages of the enu1nerated 1nethods. ();:scribe various mcxlcls adq;,tOO to rcprcscnl tl~ variatioo of infiltration capacity \Vitb tin1c. Explain a pn)Cedure IOr lilting I h)11on•s infiltration equatil)1\ li.)r experi1nental data fi'l)ll\ a given plot Distinguish beh,·een (a) Infiltration capacity aod infiltration rate (b) 1\ctual and potentiaJ evapotrnnspiration (c) Field capacity and pcnnancnt wilting point (d) Depression storage and interception PROBLE.MS

3.1

3.2

3.3

3.4

1------------

Calculate the

Ott

>-lov

Dec

52

78

8.0 5.5

For tbc lake in Prob. 3.4. csti1natc the evaporation iu the 1nouth or June by (a) Penman fonnula and (b) Tbon1tbwaitc equation by assuming that lbc lake evaporation is the sanie as PJ:."J'. given latitude =28° N and elevation = 230 0 1 above f\•ISL. f\•lean observed sw1shine = 9 h/dav. 3.6 1\ reservoir had ~ average surfhoe area of20 krn2 during Jw1e 1982. In lhal 1nonth the 1nean rate l)f in Ill)"' 10 1nl/s, l)utOO\I/ 15 1nl/s, 1nonthly ro.inlilll 10 c1n and change in $l()rage = 16 million n1 3. As.suming 1he seepage losses to be 1.8 cm, csLimate the e\'aporation in that n1onth. 3. 7 For an area i.u South India (latitude= 12° N). the ntcan mouthly temperatures arc given. 3.5

Month

J une

July

Aug

Sep

Ocl

Temp ('C)

3 1.5

31.0

JO.Cl

29.0

28.0

Calculate tbe seasonal con.sumptive use of '''atcr for the rice crop in the season June 16 to October 15, by using the Blaney Criddle forn1ula. 3.8 1\ catclunent area near .:vlysore is at latitude 124 18' >-i and at an elevation of770 n1. 1·he 1nean rnonthly te1nperatures are gh·en belon>.

Montl1

Jan t'tb Mar Apr May Jun Jul

Au~

Sf.p Oc.t :-lo" Der

Mean 1noutbly ten1p. ("g log paper and l)btain the equation o r the best lit line, and (ii) Cu1n ula tive inliltn1Lion (nln1) FP \W 1in1e (h) on a serni-log p~1per and obtain the equation of 1he b~1

fi t line. (b) Establish Horton's inlilLrnlion capaci1yeq11ation for this soil.

TinlC since stan in minutes Cuntt1la1ive Infiltration in cn1

2 7.0

10

30

60

20.0 33.S 37.8

90

120

240

360

39.5 41.0 43.0 45.0

3.16 The inJiltnuion capacity or a catchnlCut is represented by Horton·s equation as

fp 0.5 + l.2e-05' where/pis in cn\lh and tis in hours. Assun1ing the infiltration to take place at capacity

rates in a stonn of 4 hours d uration, estirnate the average rate of infiltration Ji.)r the dura til)n of the stottn.

3.17 The infihra1ion proc™ al c.."ttpac.;-ity rates in a soil is described by Kostiakov's equation as F" = 3.0 />·1 where F" is cun111lative infiltration in cm and tis time in hours. Es1im~1te the inlillm1ion capacity al (i) 2.0 h ancJ (ii) 3.0 h from the s1.ar1 of infihration.

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Abslradions from Precipitation

3.1 8 The mass curve oran isola1ed storm in a 500 ha v.·a1ershed is a.5 follo"·s:

TinlC from start (h) Cunu1huivc rainfall (cm)

0

2

4

6

8

0

0.8

2.6

2.8

4. 1

10

12

14

16

18

7.3 10.8 11.8 12.4 12.6

If the direct n1ooffproduccd by tbc stonn is measured at the outlet of tbc \\'atcrshcd as

0.340 Mm~. estimate tbc an1 ga11gi11g sire in a }'e.a1: Upstrea111 o.fthe gauging sire a " 'eir builr a