Unit-I-Introduction-to-Engineering-Hydrology.pdf

1.1 Introduction to Engineering Hydrology.

Hydrology is the science of water. Considering its etymology, the word hydrology is taken from
the Greek words, hydro and logo, which means water and study, respectively (Jain & Singh, 2019).
Subramanya (2008) stated that hydrology is the science that deals with the occurrence,
circulation, and distribution of water of the earth and earth’s atmosphere. He further emphasized
that, as a branch of earth science, it is concerned with the water in streams and lakes, rainfall and
snowfall, snow and ice on the land and water occurring below the earth’s surface in the pores of the
soil and rocks. Thus, according to him, it is a very broad subject of an inter-disciplinary nature
drawing support from allied sciences, such as meteorology, geology, statistics, chemistry, physics
and fluid mechanics.

1.2 BRIEF HISTORY OF HYDROLOGY

Ancient philosophers focused their attention on the nature of processes involved in the
production of surface water flows and other phenomena related to the origin and occurrence of
water in various stages of the perpetual cycle of water being conveyed from the sea to the
atmosphere to the land and back again to the sea. Unfortunately, early speculation was often faulty.
For example, Homer believed in the existence of a large subterranean reservoirs that supplied rivers,
seas, springs, and deep wells. It is interesting to note, however, that Homer understood the
dependence of flow in the Greek aqueducts on both conveyance cross section and velocity. This
knowledge was lost to the Romans, and the proper relation between area, velocity, and rate of flow 1

During the first century B.C., Marcus Vitruvius, in Volume 8 of his treatise De Architectura Libri
Decem (the engineer's chief handbook during the Middle Ages), set forth a theory generally
considered to be the predecessor of modern notions of the hydrologic cycle. He hypothesized that
rain and snow falling in mountainous areas infiltrated the earth's surface and later appeared in the
lowlands as streams and springs.
In spite of the inaccurate theories proposed in ancient times, it is only fair to state that practical
application of various hydrologic principles was often carried out with considerable success. For
example, about 4000 B.C., a dam was constructed across the Nile to permit reclamation of previously
barren lands for agricultural production. Several thousand years later a canal to convey fresh water
from Cairo to Suez was built. Mesopotamian towns were protected against floods by high earthen
walls. The Greek and Roman aqueducts and early Chinese irrigation and flood control works were
also significant projects.
Near the end of the fifteenth century, the trend toward a more scientific approach to hydrology
based on the observation of hydrologic phenomena became evident. Leonardo da Vinci and Bernard
Palissy independently reached an accurate understanding of the water

That is all of a short information

1. ENGR. EDGAR D. CELADA, JR.

2. Learning Outcomes:
•Distinguishtheprocessesinvolvedinthe
hydrologiccycleandtheapplicationsof
hydrologyinengineering
•Solveproblemsrelatedtowaterbudgetand
worldwaterbalance

3. HYDROLOGY
•Thescienceofwater.
•Itdealswiththeoccurrence,circulation,
anddistributionofwateroftheearthand
earth’satmosphere.
•Itisalsoconcernedwiththewaterin
streamsandlakes,rainfallandsnowfall,
snowandiceontheland,andwater
occurringbelowtheearth’ssurfaceinthe
poresofthesoilandrocks.
•Astoitsdegreeofapplicability,it’s
sometimesclassifiedasScientific
HydrologyandEngineeringorApplied
Hydrology.

4. ENGINEERING HYDROLOGY
•Itdealswith:
i.estimationofwaterresources;
ii.studyofprocessessuchas
precipitation, runoff,
evapotranspiration,and their
interaction;and
iii.thestudyofproblemssuchasfloods
anddroughts,andstrategiesto
combatthem.

5. •Fromabout1930to
1950, rational
analysisbeganto
replaceempiricism.
Sherman's unit
hydrograph,
Horton'sinfiltration
theory,undTheis's
nonequilibrium
approachtowell
hydraulics are
outstanding
examplesofthe
great progress
made.
•Since1950,a
theoreticalapproach
to hydrologic
problems has
largelyreplaced
lesssophisticated
methodsofthepast.
•Neartheendofthefifteenthcentury,thetrendtowarda
morescientificapproachtohydrologybasedonthe
observationofhydrologicphenomenabecameevident.
•Leonardo daVinciandBernardPalissy
independentlyreachedanaccurateunderstandingof
thewatercycle.
•Theadventofwhatmightbecalledthe"modern"
scienceofhydrologyisusuallyconsideredtobeginwith
thestudiesofsuchpioneersasPerrault,Mariotte,and
Halleyintheseventeenthcentury.
•Theeighteenthcenturybroughtforthnumerous
advancesinhydraulictheoryandinstrumentation.The
Bernoullipiezometer,thePitottube,Bernoulli’s
theorem,andtheChézyformulaaresomeexamples.
•Duringthenineteenthcentury,experimentalhydrology
flourished.Significantadvancesweremadein
groundwaterhydrologyandinthemeasurementof
surfacewater.SuchsignificantcontributionsasHagen-
Poiseuille’scapillaryflowequation,Darcy’slawofflow
inporousmedia,andtheDupuit-Thiemwellformula
wereevolved.Thebeginningofsystematicstream
gaugingcanalsobetracedtothisperiod.
•A dam was
constructed
acrosstheNileto
permitreclamation
of previously
barrenlandsfor
agricultural
production.
•Severalthousand
yearslateracanal
toconveyfresh
waterfromCairo
toSuezwasbuilt.
•Mesopotamian
towns were
protectedagainst
floodsbyhigh
earthenwalls.
•TheGreekand
Romanaqueducts
andearlyChinese
irrigationandflood
control works
were also
significant
projects.
History of Hydrology
4000 B.C. 100 B.C. 15
th
to 19
th
Century 1930-1950
•Duringthefirst
century B.C.,
MarcusVitruvius
Polliosetfortha
theorygenerally
consideredtobe
thepredecessorof
modernnotionsof
the hydrologic
cycleinVolume8
ofhistreatiseDe
Architectura
LibriDecem.

6. Hydrologic Cycle
•Thehydrologiccycle,orthewatercycle,isthecycle
ofcirculationofwater,involvingchangesinthe
physicalstateofwaterbetweentheliquid,solid,and
gasphases.
•Thiscycleisthecontinuousexchangeofwater
amongatmosphere,land(involvingsurfaceand
subsurfacewaters),oceansandseas,and
organisms.

7. Hydrologic Cycle
•Threemajorsystems:
i.theoceansandseas,constitutingthe
hydrosphere,majorreservoirandsourceof
water;
ii.theatmosphere,carrieranddelivererofwater;
and
iii.theland,constitutingthepedosphereand
lithosphere.

8. Hydrologic Cycle

9. Hydrologic Cycle
•Eachprocessinthehydrologiccycleinvolvesoneor
moreofthefollowingaspects:
i.transportationofwater;
ii.temporarystorageofwater;and
iii.changeofstate.

10. The Water Budget Equation
•Thequantitiesofwatergoingthroughvarious
individualpathsofthehydrologicalcycleinagiven
systemcanbedescribedbythecontinuityprinciple
knownaswaterbudgetequationorhydrologic
equation.

11. Catchment Area
•Thelanddrainingintoastreamorawatercourseat
agivenlocation.
•Itisalsocalledasdrainageareaordrainagebasin.
InUSA,itisknownaswatershed.
•Acatchmentareaisseparatedfromitsneighboring
areasbyaridgecalleddivideinUSAandwatershed
inUK.
•Thearealextentofthecatchmentisobtainedby
tracingtheridgeonatopographicmaptodelineate
thecatchmentandmeasuringtheareabya
planimeter.

12. Planimeter

13. Catchment Area

14. The Water Budget Equation

15. The Water Budget Equation

16. The Water Budget Equation

17. The Water Budget Equation
ProblemNo.1:Twoandahalfcentimetersofrainperdayoveranareaof200km
2
is
equivalenttoaverageofinputofhowmanycubicmeterspersecondofwatertothat
area?
Given: ����??????�??????�??????�??????���??????��, �=2.5��/�????????????
??????��??????,??????=200��
2
Required: ??????���??????��??????����,�,??????��
3
/�
Solution:
1. Convert �from��/�????????????to�/susing dimensional analysis.
�=2.5
��
�????????????
×
1�
100��
×
1�????????????
24ℎ����
×
1ℎ���
60�??????��
×
1�??????�
60����
=2.8935…×10
−7
�/�
2. Convert??????from��
2
to�
2
using dimensional analysis.
??????=200��
2
×
1000�
1??????�
2
=200×10
6
�
2
Note:Do not round
off if it’s not yet the
final answer. Use the
complete value in the
calculator, as much
as possible.

18. The Water Budget Equation
Given: ����??????�??????�??????�??????���??????��, �=2.5��/�????????????
??????��??????,??????=200��
2
Required: ??????���??????��??????����,�,??????��
3
/�
Solution:
3. Compute the �by multiplying �and??????to obtain the required unit.
�= �??????
�=2.8935…×10
−7
�
�
200×10
6
�
2
�=��.���??????
�
/??????
ProblemNo.1:Twoandahalfcentimetersofrainperdayoveranareaof200km
2
is
equivalenttoaverageofinputofhowmanycubicmeterspersecondofwatertothat
area?

19. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Given: ??????�??????�????????????��??????�������??????��??????���??????�??????��,ℎ
??????=103.200�
����??????��??????��??????���ℎ��??????��, ??????=5,000ℎ??????�.
??????���??????��??????������??????��, �
??????=6.0m
3
/s
??????���??????����������??????��, �
�=6.0m
3
/s
����??????�??????�??????�??????��, �=145mm
??????�??????���??????�??????��, ??????=6.10��
�??????��, ∆�=1����ℎ
Required: a.) Water Budget Equation
b.) Water surface elevation of the lake at the end of the month, h
f, in meters.

20. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for writing the water budget equation:
1.Identifythecomponentsforthemassinflowwhichistheamountofwaterthatenteredthelakeat
specifiedperiodandthemassoutflowwhichistheamountofwaterthatwentoutfromthelakeat
specifiedperiod.Inthisproblem,theaverageinflowratefromsurfacerunoffsurfacesandamountof
rainfallthatwasreceivedbythelakeconstitutethemassinflow.Ontheotherhand,forthemass
outflow,itincludestheaverageoutflowrateandquantityofevaporationfromthelake.
2.Theamountsforthemassinflowandmassoutflowcanbequantifiedasvolumes.Withthis,the
changeinstorageshouldbealsomeasuredasanamountofvolumebygettingthedifferenceofthe
formerandthelatter.However,takenotethattheaverageinflowandoutflowratesarebothmeasured
asvolumesperunittimewhichisin�
3
/�.Hence,tocalculateforthetotalvolumethatenteredand
leftthelakeconsideringthesaidflowrates,theinflowandoutflowratesshouldbemultipliedwitha
unitoftimewhichistheperiodbeingemphasizedintheproblem.

21. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for writing the water budget equation:
3.Thegivenquantitiesforprecipitationandevaporationareexpressedasdepthsovertheareaofthe
lake.Thus,thegivenamountsofprecipitationandevaporationmustbemultipliedwiththeareaofthe
lakeforthemtobeexpressedasunitsofvolume.
4.Thus,thewaterbudgetequationforthelakecanbeexpressedas:
�??????��??????�����−�??????���������=�ℎ??????���������??????��
�
??????∆�+�??????−�
�∆�+????????????=∆�

22. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for calculating the water surface elevation of the lake at the end of the month:
1.Calculateforthechangeinstorage.
a.Calculatefortheinflowvolumeattributabletoaverageinflowrate,�
??????,incubicmeters,�
3
.
�
??????=�
??????∆�=6.0m
3
/s1month×
30�????????????�
1����ℎ
×
86,400�
1�????????????
=15,552,000m
3
b.Calculatefortheinflowvolumeduetoprecipitation,�
??????,incubicmeters,�
3
.
�
??????=�??????=145��×
1�
1000��
5,000ha�.×
10,000�
2
1ℎ??????.
=7,250,000m
3
c.Calculatefortheoutflowvolumeattributabletoaverageoutflowrate,�
�,incubicmeters,�
3
.
�
�=�
�∆�=6.5m
3
/s1month×
30�????????????�
1����ℎ
×
86,400�
1�????????????
=16,848,000m
3
d.Calculatefortheoutflowvolumeduetoevaporation,??????
�,incubicmeters,�
3
.
??????
�=????????????=6.10��×
1�
100��
5,000ha�.×
10,000�
2
1ℎ??????.
=3,050,000m
3
Note: These volumes can be expressed as M-m
3
. By using the conversion factor that for every 1 M-m
3
there are
1,000,000m
3
or 1x10
6
m
3
.

23. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for calculating the water surface elevation of the lake at the end of the month:
1.Calculateforthechangeinstorage.
e.Calculatethechangeinstorage,∆�.
∆�=������??????�����−�������������
∆�=�
??????+�
??????−(�
�+??????
�)
∆�=15,552,000m
3
+7,250,000m
3
−(16,848,000m
3
+3,050,000m
3
)
∆�=22,802,000�
3
−(19,898,000�
3
)
∆�=2,904,000�
3
The total inflow volume is greaterthan
the total outflow volume. Hence, the
change in storage means additional
volume for the lake and the water
surface level will rise at the end of the
month.

24. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for calculating the water surface elevation of the lake at the end of the month:
2.Calculateforthechangeinelevation.
Takenotethatthegeneralformulaofdeterminingthevolumeofaprismismultiplyingtheareaof
itsbaseanditsheight.Thus,whenthechangeinstoragewhichismeasuredincubicmetersisdivided
bytheaveragesurfaceareaofthelakeinsquaremeters,itresultstofindingthechangeofelevation,
∆ℎ,inmeters.
∆ℎ=
∆�
??????
∆ℎ=
2,904,000�
3
5,000ha�.×
10,000�
2
1ℎ??????.
∆ℎ=0.058�

25. The Water Budget Equation
ProblemNo.2:Alakehadawatersurfaceelevationof103.200mabovethedatumatthebeginningofa
certainmonth.Inthatmonth,thelakereceivedanaverageinflowof6.0m
3
/sfromsurfacerunoffsources.In
thesameperiod,theoutflowfromthelakehadanaveragevalueof6.5m
3
/s.Further,inthatmonth,thelake
receivedarainfallof145mmandtheevaporationfromthelakesurfacewasestimatedas6.10cm.The
averagesurfaceareaofthelakecanbetakenas5,000hectares.Assumethatthereisnocontributiontoor
fromthegroundwaterstorage.
a.Writethewaterbudgetequationforthelake.
b.Calculatethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
Solution for calculating the water surface elevation of the lake at the end of the month:
3.Determinethewatersurfaceelevationofthelakeabovethedatumattheendofthemonth.
ℎ
�=ℎ
??????+∆ℎ
ℎ
�=103.200�+0.058�
??????
??????=���.���??????

26. The Water Budget Equation
ProblemNo.3:Asmallcatchmentareaof150hectaresreceivedarainfallof10.5cmin90minutesduetoa
storm.Attheoutletofthecatchment,thestreamdrainingthecatchmentwasdrybeforethestormand
experiencedarunofflastingfor10hourswithanaveragedischargeof1.5m
3
/s.Thestreamwasagaindry
aftertherunoffevent.
a.Whatistheamountofwaterincubicmeterswhichwasnotavailabletorunoffduetocombined
effectofinfiltration,evaporation,andtranspiration?
b.Whatistherunoffcoefficientortheratioofrunofftoprecipitation?
Given: ??????��??????���ℎ��??????��ℎ����, ??????=150ℎ??????�.
??????��������????????????��??????��, �
??????=10.5��
??????���??????���??????��ℎ??????���, �
??????=1.5m
3
/s���∆�=10ℎ����
Required: a.) Losses, L, in cubic meters.
b.) Runoff coefficient, �
�.

27. The Water Budget Equation
ProblemNo.3:Asmallcatchmentareaof150hectaresreceivedarainfallof10.5cmin90minutesduetoa
storm.Attheoutletofthecatchment,thestreamdrainingthecatchmentwasdrybeforethestormand
experiencedarunofflastingfor10hourswithanaveragedischargeof1.5m
3
/s.Thestreamwasagaindry
aftertherunoffevent.
a.Whatistheamountofwaterincubicmeterswhichwasnotavailabletorunoffduetocombined
effectofinfiltration,evaporation,andtranspiration?
b.Whatistherunoffcoefficientortheratioofrunofftoprecipitation?
Solution for determining the losses:
1.Computeforthevolumethatenteredthecatchmentareaduetorainfall/precipitation,�,incubic
meters.
�=�
????????????
�=10.5��×
1�
100��
150ℎ??????�.×
10,000�
2
1ℎ���??????��
�=157,500�
3
2.Calculatethevolumeattributabletodischargeattheoutletofthecatchment,�,incubicmeters.
�=�
??????∆�
�=1.5
�
3
�
10ℎ����×
3600����.
1ℎ���
�=54,000�
3
The rain lasted for 90 minutes and
this is the total amount of rainfall
received by the catchment.

28. The Water Budget Equation
ProblemNo.3:Asmallcatchmentareaof150hectaresreceivedarainfallof10.5cmin90minutesduetoa
storm.Attheoutletofthecatchment,thestreamdrainingthecatchmentwasdrybeforethestormand
experiencedarunofflastingfor10hourswithanaveragedischargeof1.5m
3
/s.Thestreamwasagaindry
aftertherunoffevent.
a.Whatistheamountofwaterincubicmeterswhichwasnotavailabletorunoffduetocombined
effectofinfiltration,evaporation,andtranspiration?
b.Whatistherunoffcoefficientortheratioofrunofftoprecipitation?
Solution for determining the losses:
3.Computeforthelosses,�,incubicmeters.
�=�−�
54,000�
3
=157,500�
3
−�
??????=���,���??????
�

29. The Water Budget Equation
ProblemNo.3:Asmallcatchmentareaof150hectaresreceivedarainfallof10.5cmin90minutesduetoa
storm.Attheoutletofthecatchment,thestreamdrainingthecatchmentwasdrybeforethestormand
experiencedarunofflastingfor10hourswithanaveragedischargeof1.5m
3
/s.Thestreamwasagaindry
aftertherunoffevent.
a.Whatistheamountofwaterincubicmeterswhichwasnotavailabletorunoffduetocombined
effectofinfiltration,evaporation,andtranspiration?
b.Whatistherunoffcoefficientortheratioofrunofftoprecipitation?
Solution for determining the runoff coefficient:
�
�=
�
�
�
�=
54,000�
3
157,500�
3
�
??????=�.���

30. The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?
Given: ??????��??????���ℎ��??????��ℎ����, ??????=140��
2
.
??????��������????????????��??????��, �
??????=120��
A���??????���??????��ℎ??????���, �
1=2.0m
3
/s���∆�
1=3����ℎ�
A���??????���??????��ℎ??????���, �
2=3.0m
3
/s���∆�
2=6����ℎ�
A���??????���??????��ℎ??????���, �
3=5.0m
3
/s���∆�
3=3����ℎ�
Required: a.) Runoff coefficient of the catchment, �
�.
b.) Increase in abstraction, ∆�, if the runoff coefficient is reduced to 0.50.

31. Solution for computing the runoff coefficient of the catchment:
1.Computeforthevolumethatenteredthecatchmentareaduetorainfall/precipitation,�,incubic
meters.
�=�
????????????
�=120��×
1�
100��
140��
2
.×
1000�
1��
2
�=168,000,000�
3
=168��
3
The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?

32. Solution for computing the runoff coefficient of the catchment:
2.Calculatethevolumeattributabletodischargeattheoutletofthecatchment,�,incubicmeters.
�=�
1+�
2+�
3=�
1∆�
1+�
2∆�
2+�
3∆�
3
�
1=2�
3
/�3���.×
365�????????????�
12����ℎ�
×
86,400����
1�????????????
=15,768,000�
3
�
2=3�
3
/�6���.×
365�????????????�
12����ℎ�
×
86,400����
1�????????????
=47,304,000�
3
�
3=5�
3
/�3���.×
365�????????????�
12����ℎ�
×
86,400����
1�????????????
=39,420,000�
3
�=15,768,000�
3
+47,304,000�
3
+39,420,000�
3
�=102,492,000�
3
=102.492��
3
The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?
This conversion factor was used to account
the months with 31 days in a regular year
since in the problem, the period being
specified both for the rainfall and
discharges is one whole year.

33. Solution for computing the runoff coefficient of the catchment:
3.Computefortherunoffcoefficientofthecatchment,�
�.
�
�=�/�
�
�=
102.492��
3
168.000��
3
�
�=0.610
The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?

34. Solution for computing the increase in abstraction, ∆??????, if the runoff coefficient is reduced to 0.50.:
1.Calculatetheinitialabstraction,�
??????,consideringinitialvaluesintheproblem.
�
??????=�−�
�
??????=168.000��
3
−102.492��
3
�
??????=65.508��
3
2.Computeforthenewvolumeattributabletorunoffconsideringthenewvalueoftherunoff
coefficient,�
�??????
,andthevolumeduetoannualrainfallof120cm.
�
�??????
=
�
�
�
�
�=�
�??????
�
�
�=(0.50)×(168.000��
3
)
�
�=84.000��
3
The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?
Take note of the preposition “to” in the
phrase “If the afforestation of the
catchment reduces the runoff coefficient to
0.50…”. It means that the runoff coefficient
was reduced tothe said value and has not
decreased bythat value.

35. Solution for computing the increase in abstraction, ∆??????, if the runoff coefficient is reduced to 0.50.:
3.Determinetheabstraction,�
�,duetothereductionofrunoffcoefficient.
�
�=�−�
�
�
�=168.000��
3
−84.000��
3
�
�=84.000��
3
4.Solvefortheincreaseinabstraction,∆�,consideringthetwoconditions.
∆�=�
�−�
??????
∆�=84.000��
3
−65.508��
3
∆�=18.492��
3
The Water Budget Equation
ProblemNo.4:Acatchmentareaof140km
2
received120cmofrainfallinayear.Attheoutletofthe
catchment,theflowinthestreamdrainingthecatchmentwasfoundtohaveanaveragerateof2.0m
3
/sfor3
months,3.0m
3
/sfor6months,and5.0m
3
/sfor3months.
a.Whatistherunoffcoefficientofthecatchment?
b.Iftheafforestationofthecatchmentreducestherunoffcoefficientto0.50,whatistheincreaseinthe
abstraction(inMm
3
)fromprecipitationduetoinfiltration,evaporation,andtranspiration,forthe
sameannualrainfallof120cm?
Observe that due to the reduction of runoff
coefficient, the volume of water that drains
the catchment has also decreased from
102.492 Mm
3
to 84.000 Mm
3
.It can thereby
be inferred that afforestation which is the
opposite of deforestation helps impede the
water that drains from a certain area as
trees or plants absorb some amount of
water that don’t go to runoff.

36. The World Water Balance

37. The World Water Balance
These three volumes
account for the Polar Ice
in Table 1.1. that’s
previously shown.
These two volumes
account for Other Ice and
Snowin Table 1.1. that’s
previously shown.

38. (35,029,210 km
3
)
(24,064,100 km
3
)
(10,530,000 km
3
)
(300,000 km
3
)
(135,110 km
3
)
(91,000 km
3
)
(16,500 km
3
)
(2,120 km
3
)
(1,120 km
3
)
(12,900 km
3
)
(11,470 km
3
)
1,338,000,000 km
3
is the
estimated volume for the
world oceans whereas
12,955,400 km
3
accounts
for other saline waters
(1,385,984,610 km
3
)

39. The World Water Balance

40. The World Water Balance

41. The World Water Balance

42. The World Water Balance

43. Applications of Hydrology

44. Applications of Hydrology

45. Sources of Hydrological Data

46. References
•KSubramanya,EngineeringHydrology,Third
Edition,2008.
•http://water.usgs.gov
•https://www.slideshare.net/DurgeshPratapSIngh8/hy
drology-88363294?from_action=save
•https://www.wikiwand.com/en/Planimeter
•http://www.ams.org/publicoutreach/feature-
column/fcarc-surveying-two
•https://www.backpacker.com/gear-item/reading-
topo-maps-understanding-map-symbols-and-colors/
•https://www.youtube.com/watch?v=eAf3VjQTV44