-

-

.. :

1. Engineering Hydrology by Subramanya

2. Advanced Hydrology by V.T. Chow

3. Engineering Hydrology by Linsley :

:

: ( Introduction) : ( Precipitation) : ( Abstraction from Precipitation) : ( Run-Off) :

: (Hydrograph)

: (Floods) : (Flood Routing)

: (Ground Water)

( Introduction)

1 .1. Hydrology : ( ) .

:

1. : .2. ( ) : :

. . .1. 2. Hydrological Cycle :

( ) () .1 .3 . Hydrological cycle Paths: :1. 2. 3. 4. 5. :

. . 1. 4. Hydrological Budget Equation :

(t) :

=

S = Vi - Vo / 15 2 : 1. ( ) 8*104 3 6.5*104 3

2. 107 3

:

1. S = Vi - Vo m3 8 * 104 6.5 * 104 = 1.5 * 104 = S 2. Average Depth = 107 / 15*106 = 0.667 m. = 66.7 cm.1. 5. Engineering Aplications of Hydrology: :

1. 2. 3. 4. 5. :

( ). ( Spillway ). ( ) .1. 6 . :

:

1. ( Spillway).2. .3. ( ).1. 7. Sources of Data :

1. : .2. .3. .4. . 5. .6. .7. . ( Precipitation)

.1.2 : :1. .

2. .3. .4. . . 2.2 Forms of Precipitation : ( ) 0.5 6 :

2.5 /

2.5 7.5 /

7.5 /

.3.2 : :

EMBED Equation.3

: N m (%) : Cv ith : Pi : m___________________________________________________________________________ (1) / (6) :

ABCDEF

(cm)82.6102.9180.3110.398.8136.7

10%

/

; m = 6 ; m-1 = 35.04 ; = 10%

Cv = 100 * 35.04 / 118.6 = 29.54

N = 8.7 = 9 stations

3 4.2 . Preparation of Data :

. (30) .

.5.2 Estimating of Missing Data : :1 . :

Px = 1/m [P1+P2++Pm] m : Px : 10% X . ,.. , P2 , P1 Pm , 1 , 2 , . m .

_____________________________________________________________

2 . :

Px=Nx/m[P1/N1+P2/N2++Pm/Nm]

: ( Nm / Nx > 1.1) 10 % ( 30 ) N1 , N2 , , Nm ( 30 ) Nx (2) / A B C D 80.97 , 67.59 , 76.28 , 92.01 1975 D A B C 91.11 , 72.23 , 79.89 , D

/ 10 % , PD = 92.01/3 (91.11/80.97 + 72.23/67.59 + 79.89/76.28) = 99.41 cm.

.6.2 Test for Consistency of Records : , , , :

1 . .

2 . .

3 . .

4 . .

Double Mass Curve Technique :

1. X (Px) (Pav) .

2. (Px) (Pav) X X :

Pcx = Px * Mc / MaPcx : t1 x Px : t1 x : Mc Ma :

(3) / D 1996 .1997

A B C D

199679.777.278.4140.15

199669.466.567.9125.2

199665.361.360123

199671.768.162.3116.9

19968380.181.8155.1

199682.785.687.3168.1

199689.490.189.988.6

199691.593.794.793.7

199792.491.592.893.5

199790.190.389.990.2

199782.383.684.983.5

199780.783.487.182.4

/PavPavPxPcx

199783.7383.7382.482.4

199783.6167.33165.983.5

199790.1257.43256.190.2

199792.23349.66349.693.5

199693.3442.96443.393.7

199689.8532.76531.988.6

199685.2617.9670094.14

199681.63699.59855.186.86

199667.37766.9697265.46

199662.2829.16109568.88

199667.93897.091220.270.11

199678.43975.521360.3578.48

1996

2 . 7 . Rainfall Data-show Methods :1. Accumulated Rainfall Curve: :

: 1 . (cm) 2 .

3 . (cm/hr.)__________________________________________________________________________

2. ( ) Hyetograph: (Bar Chart). :

( 8 10 / )

2. 8 . Average Precipitation over Area : :

1. Arithmatic Mean Method:

P1 P2 .... Pi ....PN

N :

.

2 . Thiessen Average Method:

.

___________________________________________________________________________

3 . Isohyetal LineMethod: .

a1 a2 a3 .....an .

.

(4) / 100 1980

12345

(100,100)(30,80)(70,100)(100,140)(130,100)(100,70)

()-85135.295.3146.4102.2

/

Weighted P

(cm)RainfallFraction of Total AreaArea (Km2)Boundary of AreaStation

-85---1

36.86135.20.27262141Abcd2

19.5395.30.20491609Dce3

39.91146.40.27262141Ecbf4

25.54102.20.24991963fba5

Total 7854 1.0000 121.84

Mean Precipitation = 121.84 cm (5) / :

/12Area (Km2) (3) (4Fraction of Area %( 5 = 2 * 4

1212300.06670.8

10 -12111400.31113.422

8 109800.17781.6

6 871800.40002.8

4 - 65200.04440.222

8.84 cm 450

2. 9 . : 24 . (24) .

( ) X P recurrence interval ( ) :

T = 1/P ..(1)

(20) (24) (10) A (20) (24) (10) (10) (100) (10) A : P = 1/T (2) P :

q = 1-P (3) r n :

. (4) :

1. P n :

.(4-a)

2. n :

P0,n = qn = (1-P)n (4-b)

. n :

P1 = 1-qn = 1- (1-P)n ..(4-c)

(6)/ 280 50 280 :

1. 20

2. 15

. 20

/

.

n = 20 , r = 1 , T = 50 , P = 1/50 = 0.02 P1,20 = (20 !)/(19! * 1!) * 0.02 * (0.98)19 = 0.272

.

n = 15 , r = 2

P2,15 = (15!)/(13!*2!)*(0,02)2 * (0.98)13 = 0.0323

.

P1 = 1- (0.98)20 = 0.332

2. 10. Plotting Position Criterea : () . m ( m = 1 m = 2 N = m ).

P (Weibull Formula)

P = m / (N+1) and T = 1 / P

___________________________________________________________________________

(6) / A - 24 :1. - 24 13 50

2. 10 24 A .6059585756555453525150Year

8.98.911.212.589.61614.37.61213Rainfall (cm)

7170696867666564636261Year

9.58.310.610.88.467.58.510.297.8Rainfall (cm)

/mRainfall (cm)P= m/(N+1)T=1/PmRainfall (cm)P= m/(N+1)T=1/P

1160.04323.261290.5221.92

214.30.08711.5138.9--

3130.137.67148.90.6091.64

412.50.1745.75158.50.6521.53

5120.2174.6168.40.6961.44

611.20.2613.83178.30.7391.35

710.80.3043.291880.7831.28

810.60.3482.88197.80.8261.21

910.20.3912.56207.60.871.15

109.60.4352.3217.50.9131.1

119.50.4782.092260.9571.05

( Y (Rainfall) X (Return Period (T) ) ) :. () ()

14.5513

1850

. = 10 T = 2.4 P = 0.417 (Abstraction from Precipitation)3. 1. Evaporation : .

( 585 / ) .

:1. .2. .3. .4. .5. .6. .1. Vapor Pressure : ew ea

EL = C( ew ea ) ( ) EL : (/) , C : , ew , ea ea = ew ea > ew . 2 . Temperature: .

3 . Wind : .

4 . Atmospheric Pressure : .

5 . : Soluble Salts .3. 2. Evaporimeter : :

1.

2. 3. ____________________________________________________________________3. 3. Evaporation Measurement Stations : WMO :

1. : 30000 2.

2. : 50000 2.3. : 100000 2.___________________________________________________________________ 3. 4. Empirical Evaporation Eqs. : :

EL = k f(u) (ew ea) k : f(u) : 3 4.1. . : Meyer Eq.

EL = km (ew ea) (1+ U9/16) U9 : (/) 9 Km : (0.36 0.5 )3 4. 2 . : Rohwer Eq.

EL = 0.771 (1.465 0.000732 Pa) (0.44 + 0.0733 Vo) (ew ea) Pa : ( ) Vo : (/) 0.6

/ ew (3 3 ) 103 .

(Uh) (U) : Uh = U ( h )1/7 (1) / 250 = 200 = 40 % 1 = 16 /

/ ( 3-3) : ew = 17.54

ea = 0.4 * 17.54 = 7.02 mmHg U9 = U1 * (9)1/7 = 16 * (9)1/7 = 21.9 km/hr.

:

EL = 0.36 (17.54 7.02) (1 + 21.9/16) = 8.97 mm/day

7 ( 3 ) :

7 * (8.97/1000) *250*10-4 = 157000 m3

3. 5. Analytical methods for estimating Evaporation : :

1. 2. 3. ______________________________________________________________________1 . Water Budget Method :

P + Vig + Vis = Vog + Vos + EL + S + TL

Or : EL = P + (Vis Vso) + (Vig vog) TL S

P : Vig : Vog : (Seepage)

Vis : ( ) EL : Vos : TL :

S :

/ (m3) () .

3. 6. Evapotranspiration Eqs.: 3 .6 .1. Penman Equation :

PET : (mm/day)A : (mmHg/Co) (3-3) 103 Y : = 0.49 (mmHg/Co)

Hn : ()

Ea :

Hn = Ha(1- r) (a+b(n/N)) - Ta4 (0.56 - 0.092) (0.1 + 0.9 (n/N))

a = 0.29 cos Ha : (mm/day) ( (3-4) 104 )

r : = 0.25

= b 0.52 n = ()N = (3-5) 104

= - = 2* 10 -9 /

Ta = 273 + Co

Ea = 0.35 (1 + (U2 /160)) (ew ea)U2 : 2 (/)______________________________________________________________________

(2) / ( ) :

28o 4 19 75%

(n) = 9 2 = 85 /

/ (3-3) A = 1 / Co ew = 16.5

(3-4) Ha = 9.5 /

(3-5) N = 10.716

n / N = 9 / 10.716 = 0.84

ea = 0.75 * 16.5 = 12.38 mmHg

a = 0.29 cos 28o 4 = 0.2559 , b = 0.52 , = 2*10-9

Ta = 273 + 19 = 292 k , Ta4 = 14.613 , r = 0.25

Hn = 9.506(1 - 0.25) (0.2559 + 0.52*0.84) 14.613(0.56 0.092)(0.1 + 0.9 (0.84))

Hn = 1.99

Ea = 0.35 (1 + (85/100)) ( 16.5 12.38) = 2.208 , Y = 0.49

mm / day 3 .6 .2. Blaney Criddle formula : PET = 2.54 K F

F = Ph Tf / 100

K : ( 3-7 109 )

F :

Ph : ( 3-6 109 )Tf : ()

(3) / PET 300 :

2 1 2

(0)16.5131114.5

/ (3-7) 109 K = 0.65

Ph Tf / 100PhTf (Fo)Month

4.447.1961.7 2

3.967.1555.4 1

3.787.351.8 2

4.087.0358.1

Total = 16.26

PET = 2.54 * 0.65 * 16.26 = 26.85 cm.3. 8. Infiltration : () () () . :

1. Soil Properties : .

2. Surface of Entry : .3. Fluid Characteristics : . .3. 9. Infiltration Capacity : ( ) ( f c) ( / ) . ( f ) :

f = f c if i > f c

f = i if i < f c i :

3. 10. Infiltration Capacity Values : :

(Horton) 1930 :

fct = fcf + (fco fcf) e k h t 0 t t d fct : fco : t = 0 fcf : td : kh : 3. 11. Infiltration Indices : ( ) :

1. 2. W

1 . : . (i) (i) :

(4) / 10 5.8

(hr)12345678

(cm)0.40.91.52.31.81.610.5

/ = 10 5.8 = 4.2

tc = = 8 ( )

= 4.2 / 8 = 0.525 / ( (0.4) (0.5) tc = 6 ) = 10-5.8 0.4 0.5 = 3.3

= 3.3 / 6 = 0.55 / (O.K)

(hr)12345678

(cm)00.350.951.751.251.050.450

2 . W : (W) :

( cm / hr )

P : () R : () Ia : () tc : i > w

( Run Off )1.4. : .

( ) (Subsurface Runoff). (Ground Water Runoff). :

1. Direct Runoff : .

2. Base Flow : . (Virgin Flow) :

Rv = Vs + Vd - Vr

Rv : (3) Vs : (3) Vd : Vr : (3) (1) / . (Upstream) (Weir) 3 0.5 (Mm3 ) (Upstream) 0.8 0.3 120 2 185 123456789101112

Mm321.50.80.62.18182214973

/Vr = 0.8 + 0.3 = 1.1 Mm3Vd = 3 + 0.5 = 3.5 Mm3 Rv :

123456789101112

Vs 21.50.80.62.18182214973

Vd3.53.53.53.53.53.53.53.53.53.53.53.5

Vr1.11.11.11.11.11.11.11.11.11.11.11.1

Rv4.43.93.234.510.420.424.416.411.49.45.4

Rv = 116.8 Mm3 Annual Runoff = 116.8 * 106 / 120 *106 = 0.973 m. = 97.3 cm.

Runoff Coefficient = Runoff / Rainfall = 97.3 / 185 = 0.526

2.4. : Runoff Characteristics of Streams :1. : .

2 . : .

3. : .

:

1. : .

2. : .3. : .3.4. ( ) : :

= x

:

1. .

2. .3. .1. :

R = a P + b . (1)

. (2)

(3)

N : R , P

.. (4) / r 1 0 R P r < 1 0.6 < R P

R P :

R = Pm .. (5)

ln R = m ln P + ln (6) (2) / P R 18 . P R .P(cm)R(cm)P(cm)R(cm)

150.510308

2351011102.3

34013.81281.6

4308.21320

5153.114226.5

6103.215309.4

750.116257.6

831121781.5

936161860.5

/ N = 18 , P = 348 , R = 104.3 , P2 = 9534 , R2 = 1040.51 , PR = 3083.3

(P)2 = 121104 , (R)2 = 10878.49

a = 0.38 , b = - 1.55 , R = 0.38 P 1.55r = 0.964 P 3.4. Empirical Equation : ( 1960) ().

Rm = Pm Lm

Lm = 0.48 Tm Tm > 4.5o C

Rm : () ( Rm 0 )

Pm : () Lm : () Tm : ( ) Tm 4.5 (Lm) :

- 6.5 -1 4.5T(oC)

1.521.782.77Lm (cm)

______________________________________________________________________ (3) / . 2 1 2 1

T(oC)121621273134312928291914

(cm)4420212322916212

/

Tm 4.5

Lm = 0.48 Tm

2 1 2 1

Lm5.767.6810.0812.9614.8816.3214.8813.9213.4413.929.126.72

Rm00000017.1215.082.56000

= 17.12 + 15.08 + 2.56 = 34.76 = 34.8 / 106 = 0.328 4.4. - :Flow Duration Curve . N (Plotting Position) Q :

m : Pp :

______________________________________________________________________

5.4. - :Flow Duration Curve Characteristics 1. ( ).

2. .3. .4. . :

1. .

2. (HydroPower ) .3. .4. .5. . (4) /

(m3/s)

1961 - 19621962 - 19631963 - 1964

140 - 120.1 015

120 - 100.12710

100 - 80.1121815

80 - 60.1153215

60 - 50.1302945

50 - 40.1706064

40 - 30.1847576

30 - 25.1615061

25 - 20.1434538

20 - 15.1283025

15 - 10.1151812

10 - 5.1500

50% 75% . / Pp ( X) :

( Y ). (m3/s)

1961-1964 (m)

1961 - 19621962 - 19631963 - 1964

140-120.1015660.55

120-100.1271019252.28

100-80.112181545706.38

80-60.11532156213212.03

60-50.130294510423621.51

50-40.170606419443039.19

40-30.184757623566560.62

30-25.161506117283776.3

25-20.143453812696387.78

20-15.128302583104695.35

15-10.115181245109199.45

10-5.15005109699.91

1096 :N = 1096 Q50 = 35 3 / Q75 = 26 3 /

_________________________________________________________________ 6.4. ():Flow Mass Curve (V) .

( ) to : Q :

/

1. (Q = dv / dt ) .

2. AB . 7.4. :Storage Volume Evaluation : S = Vs - VD

S : Vs :

VD : S (Accumulated Volume) S .

(5) / 40 3 / 123456789101112

m3/s6045352515225080105908070

/ m3/s m3/s. day m3/s. day

16018601860

24512603120

33510854205

4257504955

5154655420

6226606080

75015507630

880248010110

9105315013260

1090279016050

1180240018450

1270217020620

: For Qd = 40 m3/s. S1 = 2100 m3/s. day

(6) / / m3/s m3/s. day

m3/s (cumec.day) Col(3)-col(5) (cumec day) (cumec day)

1601860401240620620

2451260401120140760

3351085401240-155-155

425750401200-450-605

515465401240-755-1380

622660401200-540-1920

7501550401240310310

88024804012401240

9105315040120019503500

1090279040124015506050

1180240040120012007250

127021704012409308180

( 7) = 1920 m3/s. day

/ 8 .

__________________________________________________________________________ 8.4. :Calculation of Maintainable Demand .

:

1. ( V1 U2 ) .

2. .________________________________________________________________________

(7) / 3600 3 /.

/ 1. 3600 3 /. 2. (C) (Y) (D) .

3. CYD (50 m3/s. ) . 9.4. :Variable Demand .

/ A B .

_________________________________________________________________________

(8) / . 20 2 . 0.5 m3/s Mm3 cm)) (cm)

12525122

22026132

31527171

41029181

5429201

69291613

7100191224

8108191219

980191219

104019121

113021116

12302572

/

= E/100X 20 X 106 = 0.2 EMm3

= P/100 (1-0.5) X 20 X 106 = 0.1 PMm3

Mm3 (3+4+5) Mm3 Mm3 Mm3 Mm3

Mm3 Mm3 Mm3

123456789

267252.4-0.227.239.8-39.8

48.8262.6-0.228.420.4-60.2

40.2273.4-0.130.39.9-70.1

25.9293.6-0.132.5-6.6-6.6-

10.7294-0.132.9-22.2-28.8-

23.3293.2-1.330.9-7.6-36.4-

267.8192.4-2.419248.8-248.8

289.3192.4-1.919.5269.8-518.6

207.4192.4-1.919.5187.9-706.5

1107.1192.4-0.121.385.8-792.3

277.8212.2-0.622.655.2-847.5

180.4253.4-0.228.252.2-899.7

= 36.4

( Hydrograph)1.5. : .

:

1. AB (Rising Limb) : . .

2. BC (Crest Segment) : .3. P(Peak) : B C .

4. ( )CD (Recession Limb): . ( ) . 5. tp (Peak Time) : A P .6. tB (Base Time) :

1. Surface Runoff 2. Inter Flow 3. Base Flow

.

.

______________________________________________________________________

2.5. : :

: : 1.

1. : .

2. : . .. : (depletion of storage) .

. : .

.

. 2. :

1. : 150 2 .2. .

3. : .

: : 1.

.

2.

3. 3.5. Recession Curve Eq. :

( 1940( :

Qt = Qo Krt (1)

Qt : t Qo : Kr : ( Kr < 1)

:

Qt = Qo e at ....... (2)

a = - ln Kr

Kr = krs . kri . krb

krs = = 0.05 0.2 , kri = = 1

krb = 0.99 =

_________________________________________________________________

(1) / . .

(day) (m3/s) (day) (m3/s)

09043.8

0.5664.53

13452.6

1.5205.52.2

21361.8

2.596.51.6

36.771.5

3.55

/

. AB . B 5 .

(1) :

Qt / Qo = Krbt log Krb =

log (Qt / Qo)

:

Qo = 6.6 m3/s. , t = 2 days , Qt = 4 m3/s.

log Krb = log (4 / 6.6) Krb = 0.78

Qo = 26 m3/s. , t = 2 days , Qt = 2.25 m3/s.

log Krs = log (2.25 / 26) Krs = 0.29

Kr = 0.29 * 0.78 * 1 = 0.226

4.5. Base Flow Separation :

( ) . : : :

A . B N () Pi B :

N = 0.83 A0.2

A : (2) A B

: ( C) B AC BC .

: Pi ( EF ) A F .

5.5. Effective Rain :

(ERH).

/ (DRH ERH) (ERH) (cm/hr) (DRH)._______________________________________________________________________________________

(2) / 3.8 2.8 4 27 2

(hr)-60612182430364248546066

(m3/ s)65132621161297554.54.5

/ index = 0.135 cm /hr

Rainfall index = 5.52 cm.

N = 0.83 (27) 0.2 = 1.6 day = 38 hr.

(t = 0) (DRH) (t = 0) (t = 48) N :

Time of N = 48 16 = 32 hr.

(N = 38) DRH t = 0 t = 48

5 3/

DRH = 6*60*60[0.5*8+0.5(8+21)+0.5(21+16)+0.5(16+11)+0.5(11+7)+0.5(7+4)+0.5(4+2)+0.5(2)] = 1.4904*106 m3 Depth of Runoff = Runoff vol./ Area = 1.4904*106 / 27*106 = 5.52 cm. ( )

Total Rainfall = 2.8 + 3.8 = 6.6 cm.

Time of Duration = 8 hr.

index = (6.6 5.52) / 8 = 0.135 cm/hr.

6.5. Unit Hydrograph :

(1) (D ) . :

1. D . 1 1 .

2. / .3. . DRH UH :

DRH = UH * ER

_________________________________________________________________________

7.5. Unit Hydrograph Assumptions : 1. .

2 . UH .

___________________________________________________________________________

(3) / 6 3.5 6 (hr.)03691215182430364248546066

UH (m3/s)02550851251601851601106036251680

/ (hr.)03691215182430364248546066

UH (m3/s)02550851251601851601106036251680

DRH (m3/s)087.5175297.5437.5560647.556038521012687.556280

(4) / 6 3 2 2 3 . 6 . DRH .

/ () UH (m3/s)DRH 3 cm (m3/s) DRH 2 cm (m3/s) DRH 5 cm (m3/s)

00000

32575075

6501500150

98525550305

12125375100475

15160480170650

18185555250805

(21)(172.5)(517.5)(320)(837.5)

24160480370850

30110330320550

3660180220400

4236108120228

48257572147

5416485098

608243256

(66)(2.7)(8.1)(16)(24.1)

6900(10.6)(10.6)

750000

(5) / 6 3.5 7.5 5.5 . ( ) 0.25 / . 6 . 15 3/ 2 3/ 12 . .

/ : 6 6 6

()3.57.55.5

6 ()1.51.51.5

()264

UH 2 * 2 2 *6

6 2 *4

12 DRH (3+4+5) (6+7)

12345678

0000001515

3255000501565

6501000010015115

985170150032015335

12125250300055017567

1516032051010093017947

181853707502001320171337

(21)(172.5)(345)(960)(340)(1645)(17)(1662)

2416032011105001930191949

(27)(135)(270)(1035)(640)(1945)(19)(1964)

301102209607401920191939

36601206606401420211441

42367236044087221893

48255021624050623529

54163215014432623349

608169610021225237

66(2.7)(5.4)(48)(64)(117)(25)(142)

69-------

72001632482775

75-------

78000(10.8)(11)2738

81000002727

84000002727

8.5. Unit Hydrograph Derivation : DRH DRH .

:

1. .

2. .3. 1 4 .______________________________________________________________________ (6) / 432 2 6 . 6

(hr)-60612182430364248

(m3/s)10103087.5115.5102.585715947.5

(hr)5460667278849096102

(m3/s)3931.52621.517.51512.51212

/A = DRH t = 0 B = DRH t = 90

Pi = t = 24 N = 90 24 = 66 = 2.75

N = 0.83 * (423)0.2 = 2.78 (2.75 )

(hr) (m3/s) (m3/s) DRH (m3/s) 6 (m3/s)

3 4

12345

6-101000

0101000

63010206.7

1287.510.57725.7

18111.510.510133.7

24102.510.59230.7

3085117424.7

3671116020

4259114816

4847.511.53612

543911.527.59.2

6031.511.5206.6

662612144.6

7221.5129.53.2

7817.5125.51.8

841512.52.50.8

9012.512.500

96121200

102121200

m3/s 587

= (587*6*3600) / (423*106) = 3

______________________________________________________________

(7) / 3 3 270 3/ 5.9 0.3 / 20 3 /

/ = 5.9 3*0.3 =5

DRH = 270 20 = 250 3/

UH 3 = 250 / 5 = 50 3 /

__________________________________________________________________________

9.5. Unit Hydrograph for Different Duration :

nD D :

1. 2. S

1. Super Position Method :

D nD - n n D :

______________________________________________________________ (8) / 4 12 . ()AB 4 C 8 2+3+4 UH 12 ( 5 3)

123456

00--00

4200-206.7

88020010033.3

12130802023076.7

1615013080360120

20130150130410136.7

2490130150370123.3

28529013027290.7

3227529016956.3

361527529431.3

40515274715.7

440515206.7

48-0551.7

52--000

2. S S - Curve Method :

mD m S ( S) .

___________________________________________________________________

(9) / S .

() UH-4 hr S S (2+3) S 12 4 5 6 (12/4)

1234567

0000-00

420020-206.7

88020100-10033.3

12130100230023076.7

1615023038020360120

20130380510100410136.7

2490510600230370123.3

285260065238027290.7

322765267951016956.3

36156796946009431.3

4056946996524715.7

440699699679206.7

48-69969969451.7

52--69969900

_____________________________________________________________________

(10) / 4 . 2 ./

() UH-4 hr S S (2+3) S 2 4 5 6 (2/4)

( UH 2hr)

1234567

00-0-00

28-80816

42002081224

643851203162

88020100514998

101105116110061122

1213010023016169138

1414616130723077154

1615023038030773146

1814230744938069138

2013038051044961122

2211244956151051102

24905106005613978

26705616316003162

28526006526312142

30386316696521734

32276526796691020

34206696896791020

3615679694689510

3810689699694510

4056946996990(0) 3

422699701699(2)(4) 0

440699699701(-2)(-4) 0

_____________________________________________________________________10.5. :

. :1. .

2. .

3. .

.

5000 2 .

. :1. .

2. .

3. .

20 % 10 % .

____________________________________________________________________ (11) / 200 7.5 2 5 . 2.5 / 6 5 15 40 25 10 5 . . /

(day) (cm) (cm/day)ER (cm) % (cm)

502.5cmm3 / s

0 -17.52.5550.250.255.79

1 -222.50150.7500.7517.36

2 352.52.540200.1252.12549.19

3 4251.2500.3751.62537.62

4 5100.5011.534.72

5 650.2500.6250.87520.25

6 70000.250.255.79

7 80.1250.1252.89

8 - 9000

* (200*104 / 86400) = * 23.148 3 /

( Floods )1.7. Flood : . () ( 100 ) :

1. Rational Method

2. () Empirical Method 3. Hydrograph Method 4. Flood Frequency Studies :

. . .

_____________________________________________________________________

1 . Rational Method :

:

(0utlet) (tc) ( ) (tc) (QP):

QP = C A i t t c C = Runoff / Rainfall , A : , i :

:

QP = C ( itcp) A

QP : (m3/s) , C : , itcp : P tc ( / ) A : (2) __________________________________________________________________________ (tc) Time of Concentration :

:

1. U.S.A. Practice : :

tc = tP = CtL ()n

tc : () , n = 0.38 , s : CtL= constant

= 0.83 = 0.5 = 0.24 L : ()Lca : () 2. : Kirpich Equation

tc = 0.01947 L0.77 S-0.385

tc : (min)

L : (m) S = H / L : H : _______________________________________________________________________ Rainfall Intensity :

tc P ( T = 1 / P ) :

K , a , x , m

________________________________________________________________________ (1) / 0.3 0.85 2 0.006 950 25 : (min)51020304060

(mm)172640505762

(QP) 25 .

/

tc = 0.01947 * (950)0.77 * (0.006)-0.385 = 27.4 min.

27.4 () :

mm

itcp ( / ) :

mm/hr.

m3 /s.

2. () : Empirical Formulas . . .

Flood Peak Area Relationships : QP A :

QP = f (A)

____________________________________________________________________

. Dickens Formula :

QP = CD A3/4 QP : (m3/s)

A : (2)

CD : (6 30) . Ryves Formula :

QP = CR A2/3 QP : (m3/s)

A : (2)

CR :

= 6.8 (80)

= 8.5 (80 - 160) = 10.2 . Inglis Formula : QP =

QP : (m3/s)

A : (2)

. Fuller's Formula :

QTP = Cf A0.8 (1+ 0.8 log T) QTP : (m3/s) T 24 Cf : (0.18 1.88 ) . Bird McWarn Formula : QMP = (2) / 40.5 2

/1. (CD = 6)QP = 6 * (40.5)0.75 = 96.3 m3/s

2. (CR = 6.8)QP = 6.8 (40.5)2/3 = 80.2 m3/s

3.

QP = = 704 m3/s

4. : QMP = = 1367 m3/s3. ( ) Unit Hydrograph :

.

_____________________________________________________________________

4. Flood Frequency Studies :

.

Plotting Position :

P = m / (N+1) and T = 1 / P (r) n :

:

XT = X + k

XT : T X

X : : k : T

:

1. .

2. .3. .2.7. Real Gumbel's Equation :

XT = X + k n-1

XT : T

YT = - [ ln . ln ] k =

/ Yn ( ) 7 3 317 Sn ( ) 7 4 318 (N).

______________________________________________________________________

(3) / 1951 1977 :

1. 100 2. 150

5152535455565758596061626364

(m3/s)29473521239941243496294750604903375747984290465250506900

65666768697071727374757677

(m3/s)4366338078263320659937004175298827093873459367611971

/

TP = (N+1)/m = 28 / m

(x) (m3/s)T (year)

1782028

2690014

367619.33

465997

550605.6

650504.67

749034

847983.5

946523.11

1045932.8

1143662.55

1242902.33

1341752.15

1441242

1538731.87

1637571.75

1737001.65

1835211.56

1934961.47

2033801.4

2133201.33

2229881.27

2329471.21

2427471.17

2527091.12

2623991.08

2719711.04

T = 5 years : X = 4263 , n-1 = 1432.6

YT = - [ ln.ln (5/4)] = 1.5

K = (1.5 0.5332)/1.1004 = 0.88 , X5 = 4263 + ( 0.88 * 1432.6) = 5522 m3/s.

T = 10 years : X10 = 6499 m3/s. , X20 = 7436 m3/s.

XT T :

T = 100 year XT = 9600 m3/s.

T = 150 year XT = 10700 m3/s.

:

X100 = 9558 m3/s. & X150 = 10088 m3/s.

/ T = 2.33 (Mean Annual Flood).

(4) / :

T () 50 100

(3/) 40809 46300

500 .

/

X100= X + k100 n-1

X50= X + k50 n-1

(k100 - k50) n-1 = X100 X50

= 46300 40809 (k100 k50) n-1 = 5491

kT =

Y100 = - [ln . ln (100/99)] = 4.6 , Y50 = 3.9

n-1/ Sn = 5491 / (4.6 3.9) = 7864

T = 500 :

Y500 = - [ln . ln (500/499)] = 6.21

(Y500 - Y100) * ( n-1/ Sn ) = X500 X100

( 6.21 4.6) * 7864 = X500 46300

X500 = 59000 m3/s. 3.7. Confidence Limits : X . C X1 X2 :

X1/ 2 = XT f(c) Se f(c) : C C %506880909599

f(c)0.67411.2821.6451.962.58

Se : Se = and b =

k = ( ( , N : ___________________________________________________________________

(5) / 92 6437 2951 3/ 500 . :

. 95% .80% .

/ 7 3 N = 92 Yn = 0.5589

7 4 N = 92 Sn = 1.202

Y500 = - [ln .ln (500 / 499)] = 6.21

K500 = (6.21 0.5589) / 1.202 = 4.7

X500 = 6437 + 4.7 * 2951 = 20320 m3 /s.

b = = 5.61 , Se = = 1726

. C = 95 % f ( c ) = 1.96

X1 / 2 = 20320 (1.96 * 1726) X1 = 23703 m3/s , X2 = 16937 m3/s

. C = 80 % f ( c ) = 1.282

X1 / 2 = 20320 (1.282 * 1726) X1 = 22533 m3/s , X2 = 18110 m3/s

_____________________________________________________________________

4.7. : X :

Z = log X ZT = Z + kz z kz : (Cs)

z : Z z =

Cs =

Z : Z N : Where kz ( Cs , T ) (7 6 ) 327 (6) / (3) :

) 100 ) 200 .

/5152535455565758596061626364

(X) (m3/s)29473521239941243496294750604903375747984290465250506900

Z = log X3.46943.54673.383.61533.54363.46943.70423.69053.57483.68113.63253.66763.70333.8388

65666768697071727374757677

(X) (m3/s)4366338078263320659937004175298827093873459367611971

Z = log X3.64013.52893.89353.52113.81953.56823.62073.47543.43283.5883.66213.833.2947

z = 0.1427 , Z = 3.607

Cs = = 0.043

T (year)KzKz zZTXT ( m3/ s)

1002.330.33253.948709

2002.5840.3693.9759440

( Flood Routing )1.8. : . . :

1. 2.

:

1. .

2. . . .

_____________________________________________________________________

2.8. Hydrologic Storage Routing : :

1. Modified Paul's Method :

Q1 , Q2 : (t) I1 , I2 : (t) S1 , S2 : (t) :

1. (S + Qt / 2) 20% - 40% .

2. .3. t (S1 Q1t / 2 ) (S2 + Q2t / 2 ) .4. (S2 + Q2t / 2 ) (1) Q2 (2).5. Q2 t (S2 + Q2t / 2 ) (S1 Q1t / 2 ) .6. .

(1) / :

(m ) ( *106 m3 ) (m3/s)

1003.350

100.53.47210

1013.8826

101.54.38346

1024.88272

102.55.37100

102.755.527116

1035.856130

100.5 :

()061218243036424854606672

(m3/s)10205580735846365520151311

:

1. .

2. . / 6 - S + Qt / 2 .

t = 6 * 60 * 60 = 0.0216 * 106 sec.

(m ) (m3/s)S + Qt / 2) (Mm3))

10003.35

100.5103.58

101264.16

101.5464.88

102725.66

102.51006.45

102.751166.78

1031307.26

Q S + Qt / 2)) 100.5 Q = 10 m3/s S - Qt / 2)) = 3.36 3 S - Qt / 2)) (S + Qt / 2) 6 :

= (10+20) * (0.0216 /2) + (3.362) = 3.686

(S + Qt / 2) = 3.686 3 100.62 Q 13 3 / (S - Qt / 2) = (S + Qt / 2) :

13 * 0.0216 = 3.405 Mm3 :

(hr) (m3/s)I (m3/s)It (Mm3)(S - Qt / 2) (Mm3)(S + Qt / 2) (Mm3) (m)Q (m3/s)

010150.3243.3623.686100.510

62037.50.813.4054.215100.6213

125567.51.4583.6325.09101.0427

188076.51.6523.9455.597101.6453

247365.51.4154.1075.522101.9669

3058521.1234.0965.219101.9166

3646410.8863.9884.874101.7257

423631.750.6863.9024.588101.4845

485537.50.5133.7894.302101.337

542017.50.3783.6764.054100.129

6015140.3023.5573.859100.9323

6613120.2593.473.729100.7718

72113.427100.6514

1 7 8 :

2. Goodrich's Method :

______________________________________________________________________

(2) / t = 100.6 .

()0612182430364248546066

(m3/s)10308514012596756046352520

/ t = 6 * 60 * 60 = 0.0216 * 106 sec.

(m ) (m3/s)2S/t + Q) (Mm3))

1000310.2

100.510331.5

10126385.3

101.546451.8

10272524

102.5100597.2

102.75116627.8

103130672.2

:

1. (Q) .

2. 2S/t + Q)) . t = 100.6 :

Q = 12 m3/s ( 2S/t + Q) = 340 m3/s ( 2S/t - Q) = 340 2 * Q = 340 2*12 = 316 m3/s

(2S/t +Q)2 = (10 + 30) + 316 = 356

2(2S/t + Q) = 356 = 100.74 Q = 17 3 /

( (2S/t - Q)1 = 356 2*17 = 322 m3 / s

______________________________________________________________________

3.8. Hydrologic Channel Routing : S = f(Q) S = f (I,Q) .

Muskingum's Method for Routing :

Q2 = Co I2 + C1 I1 + C2 Q1

Co + C1 + C2 = 1

k : , x : ___________________________________________________________________ (3) / k = 12 x = 0.2 10 3 /

/ ()061218243036424854

(m3/s)10205060554535272015

I1 = 10 C1 I1 = 4.29

I2 = 20 Co I2 = 0.96

Q1 = 10 C2 Q1 = 5.23

Q = 10.48 m3/s

()(m3/s) I0.048 I20.429 I10.523 Q1Q

123456

0100.964.295.2310

6202.48.585.4810.48

12502.8821.458.6116.46

18602.6425.7417.2332.49

24552.1623.623.8545.61

30451.6819.325.9549.61

36351.315.0224.5546.93

42270.9611.5821.3840.87

48200.728.5817.7433.92

541527.04

t 6 12 Q1 = 10.48 3 / . . attenuation lag time 10 3/ 12 .

( Ground Water ) 8. 1. : :

1. Saturated Zone .

2. Aeration Zone .1. Saturated Zone : water table .

2. Aeration Zone : :1. Soil Water Zone : .

2. Capillary Fringe : .. Intermediate Zone : .

:

1. Aquifer: unconsolidated .2. Aquitard : .3. Aquiclude : .4. Aquifuge : .______________________________________________________________________

8. 2. Ground Water Budget :

. inflow outflow :

I t - Q t = S

I t : Q t : . S : (t) ( Safe Yield) :

1. .

2. .3. .8. 3. Wells : . . cone of depression draw down area of influence radius of influence .

. . recuperation of recovery .

1.3.8. Steady Flow into a Well :1. Confined Flow :

B Q H hw Sw :

, if S1 = H h1 , S2 = H h2 ,

T = k B ( transportation factor m2/s.)

( H = h2 , R = r2 , S = 0 ) ( r1 = rw , h1 = hw , S1 = Sw ) :

(1) 30 45 / = 20 3 300

:

R = 300 m. , rw = 0.15 m. , Sw = 3 m. , B = 20 m.

k = 45 / (3600 * 24) = 5.208 * 10-4 m/s.

T = 5.208 * 10-4 * 20 = 10.416*10-3 m2/s.

Q = 2 * * 10.416*10-3 * 3 / ln (300/0.15) = 0.02583 m3/s. = 1550 liter/min.

----------------------------------------------------------------------------------------------------------------

(2) :

1. 45 .2. 4.5 .

:

1. Q = 1637 m3/s.

2. Q = 2325 m3/s.

1. () Unonfined Flow :

( H = h2 , R = r2 ) ( r1 = rw , h1 = hw ) :

Or :

(3) 30 40 1500 / 25 75 3.5 2 :

1. Q = 1500*10-3/ 60 = 0.025 m3/s.

h2 = 40 2 = 38 m. , h1 = 40 3.5 = 36.5 m.

r2 = 75 m. , r1 = 25 m.

0.025 = ( * k * (382 36.52)) / ln (75/25)

k = 7.823 * 10-5 m/s.

T = k H = 7.823 * 10-5 * 40 = 3.13 * 10-3 m2 / s.2.

0.025 = ( * 7.823 * 10-5 * (36.52 hw2)) / ln (25/0.15)hw = 28.49 m.

Sw = 40 28.49 = 11.51 m

( )a

c

Accumulated Annual Rainfull at multi station (Pav)

Accumulated Annual Rainfull at X station (Px)

Correction Ratio = Mc / Ma = c / a

Pcx = Px * Mc / Ma

Accumulated Annual Rainfull at X station (Px)

Accumulated Annual Rainfull at multi station (Pav)

Ma = 12.5 / 7 = 1.79

Mc = 11/11 = 1

Ma

Mc

Accumulated

Precipitation

(cm)

Time (days)

1st. storm (10 cm)

2nd. storm (4 cm)

Rainfall Intensity

Cm/hr.

Time (hr.)

3

a

1

5

c

b

D

e

2

4

f

A

B

F

C

E

12

10

10

9.2

9.1

8

8

7.2

7

6

6

4

Annual Max. Precipitation (cm)

Time (year)

Dry Sandy Loam

Wet Sandy Loam

Dry Clay Loam

Wet Clay Loam

Infiltration Rate (mm/ hr)

Time from start of infiltration (hr.)

Time (hr.)

Rainfall Intensity (cm/ hr)

index

Losses

Runoff

Discharge m3/s.

Time (month)

Time (month)

Discharge m3/s.

Time (month)

Discharge m3/s.

x

y

m

y = mx + b

b

b

Runoff (R)

R = aP+ b

a

Precipitation (P)

Percentage time indicated discharge is equalled or exceeded (Pp)

Daily Discharge m3/s.

50

75

(Pp)

Q

m3/s.

26

35

D

E

tm

tn

Time (m,w,d)

Accumulated Flow Volume (V)

Mm3

tc

C

B

A

D

E

C

M

N

S2

S1

S1

S1

D

Demand Line = slope = 40 m3/s

C

C

D

V1

U2

C

D

D

Time (month)

A

B

Time (month)

Accumulated Flow Volume (V)

Mm3

U1

V2

10.6

S2

S2

C

Time (month)

Accumulated Flow Volume (V)

Mm3

Accumulated Flow Volume *103

Mm3

Y

7

Discharge Q (m3/s.)

Time (hr)

Mass curve of demand

Storage

Mass curve of flow

D

A

B

Time (month)

Accumulated Flow Volume *103

Mm3

C

P

B

A

tB

tp

Discharge Q (m3/s)

Time (days)

A

B

M

P

Observed Runoff

Base Flow

Surface Runoff

A

Pi

B

Time

Discharge Q (m3/s.)

N

Surface Runoff

Base Flow

A

B

Time

Discharge Q (m3/s.)

Surface Runoff

Base Flow

A

Pi

E

Time

Discharge Q (m3/s.)

Surface Runoff

Base Flow

B

F

Rainfall Intensity (cm/ hr)

Time (hr.)

Excess Rainfall

Losses

A

Pi

B

Time

Discharge Q (m3/s.)

N = 1.6 day

Surface Runoff

Base Flow

Time (hr)

Discharge Q (m3/s.)

A

B

A +

B = 5 cm DRH

C =

Composite DRH

Time (hr)

Discharge Q (m3/s.)

6hr unit hyd.

Storm hyd.

Pi

Pi

Pi

Base Flow

End of DRH

Time (hr)

Q

(m3/s.)

= DRH of 3 cm.

A +

B +

C

F =

Q

(m3/s.)

Time (hr)

12 hr UH =( 0rd. of F) / 3

QP

Runoff

tc

Recession

End of Rainfall

Runoff & Rainfall

Rainfall

Computed

Plotting Position

Mean

N = 27 years

Discharge m3/s

Log T (years)

5

10

20

2.33

Elevation (m)

Out flow Q (m3 / s)

(S + Qt / 2 (Mm3

Q VS Elevation

(S + Qt / 2 (VS Elevation

3.686

3.58

100.5

10

13

Discharge Q (m3/s.)

Inflow

Outflow

Time (hr.)

Peak lag 7.2 hr.

Peak Attenuation = 10 m3/s.

Elevation (m)

Out flow Q (m3 / s)

(2S/t +Q (m3/s

Q VS Elevation

(2S /t + Q (VS Elevation

3.686

3.58

100.5

B

= 2 rw

Flow

H

S1

S2

h1

h2

Original Piezometric surface

Confined

Aquifer

Piezometric surface under pumping

Sw

hw

r 1

r 2

R

Q from pumping well

= 2 rw

Flow

H

S1

S2

h1

h2

Original Piezometric surface

Unonfined

Aquifer

Piezometric surface under pumping

Sw

hw

r 1

r 2

R

Q from pumping well

PAGE 1

_1250019038.unknown

_1250942333.unknown

_1250971042.unknown

_1251030978.unknown

_1251136588.unknown

_1335804910.unknown

_1335805420.unknown

_1335809504.unknown

_1336675244.unknown

_1336675245.unknown

_1335809515.unknown

_1335805660.unknown

_1335805212.unknown

_1251200659.unknown

_1324798496.unknown

_1251137527.unknown

_1251198246.unknown

_1251050304.unknown

_1251054502.unknown

_1251049483.unknown

_1251028233.unknown

_1251029215.unknown

_1251029417.unknown

_1251028326.unknown

_1251027536.unknown

_1251027543.unknown

_1251027352.unknown

_1251027382.unknown

_1250963044.unknown

_1250965820.unknown

_1250970773.unknown

_1250963189.unknown

_1250960702.unknown

_1250962421.unknown

_1250942358.unknown

_1250675904.unknown

_1250792897.unknown

_1250941253.unknown

_1250942322.unknown

_1250940393.unknown

_1250688470.unknown

_1250791806.unknown

_1250677292.unknown

_1250341328.unknown

_1250424761.unknown

_1250427185.unknown

_1250362337.unknown

_1250340739.unknown

_1250340781.unknown

_1250106705.unknown

_1249903101.unknown

_1249914219.unknown

_1250016687.unknown

_1250018805.unknown

_1250014913.unknown

_1249913363.unknown

_1249913506.unknown

_1249903624.unknown

_1239696694.unknown

_1249901892.unknown

_1249901943.unknown

_1239697442.unknown

_1239569488.unknown

_1239696251.unknown

_1239568550.unknown

_1239569388.unknown

_1229755637.unknown