Runoff, Stream flow, Concept of unit

hydrograph and S-curve

Dr. Mohsin Siddique

Assistant Professor

Dept. of Civil & Env. Engg

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Outcome of Lecture

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� After completing this lecture…

� The students should be able to:

� Understand surface runoff and its categories

� Understand the concept stream flow, velocity and discharge

� Understand the concept of hydrograph, unit hydrograph and its application

� Understand the application of rational formula and its application

Surface Runoff and Stream flow

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Surface Runoff and stream flow

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� On hard or frozen ground, most of the precipitation is unable to seep below ground. This precipitation then flows down slopes and hills, eventually stopping in rivers, lakes, streams, and oceans.

� Some of this water will then evaporate and rejoin the hydrologic cycle, while other water will remain in the body of water.

� This process of water traveling over the ground and collecting in a body of water is called surface runoff.

Stream

Surface Runoff and Stream flow

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� Stream flow, or channel runoff, is the flow of water in streams, rivers, and other channels, and is a major element of the water cycle.

� Importance:

� Stream flow is one of the most important topics in engineering hydrology because it directly relate to water supply, flood control, reservoir design, navigation, irrigation, drainage, water quality, and others.

Point of interest1. Discharge1.1 Velocity1.2 Cross-sectional area

2. Stage (water depth),

Stream Flow Measurements (Discharge)

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� Serves as the basis for many water resources engineering designs

� Measurement of Discharge;

� Measurement of flow area

� Measurement of flow velocity

Devices for Flow Velocity Measurement

� Floats: Suitable for straight channel, V = L/T

� PitotTubes: Suitable only for clean water

� Current Meters

� Cups

� Propellers

V = a + b×N

where V = flow velocity; a = starting velocity to overcome mechanical friction; b = equipment calibration constant; N = revolutions/sec.

Floats

8

� Surface velocity of flow= = L/T

Current Meters

Mean Flow Velocity Estimation

� Velocity Profile

Deph < 0.6m 0.6d

VV = ; 0.6 water depth from the water surface

2mDepth0.6m ≤≤ 2

0.8dV

0.2dV

V+

=

2mDepth ≥ 4

0.8dV

0.6d2V

0.2dV

V++

=

Current Meters

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Measurement of Stream Flow Discharge

� 1. Mid-Section Method

iA

iV

ii

QQ

iA

iV

iQ

ibd

iA

∑=∑=

=

=

∑=

=

+=

++=

+

ii

QQ

iA

iV

iQ

)Vi

V(2

1

iV

)1i

di

(d2

b

iA

1i

� 2. Mean-Section Method

Example

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� Estimate the discharge in stream as shown. Current meter measurements are also given in table

Distance from left edge depth Current meter

m m No. of Rev Time (s)

3 1.4 12 50

6 3.3

38 52

23 55

9 5

40 58

30 54

12 9

48 60

34 58

15 5.4

34 52

30 50

18 3.8

35 52

30 54

21 0 18 50

0 3 6 9 12 15 18 21

Velocity equation by current meter is given byV=2.3N+0.05Where N is revolution per second.

Example:

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Distance from left edge depth Area Current meter N V Vavg. Q

m m sq.m No. of Rev time RPS m/s m/s cu.m/s

3 1.4 2.1 12 50 0.24 0.602 0.602 1.2642

6 3.3 7.05

38 52 0.73 1.73

1.37 9.6723 55 0.42 1.01

9 5 12.45

40 58 0.69 1.64

1.48 18.4530 54 0.56 1.33

12 9 21

48 60 0.80 1.89

1.64 34.5334 58 0.59 1.40

15 5.4 21.6

34 52 0.65 1.55

1.49 32.2330 50 0.60 1.43

18 3.8 13.8

35 52 0.67 1.60

1.46 20.1930 54 0.56 1.33

21 0 5.7 18 50 0.36 0.88 0.88 5.00

Total. Q= 121.331

Example

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� Estimate the discharge in stream as shown. Current meter measurements are also given in table

0 4 8 12 16 20 24 28

Velocity equation by current meter is given byV=2.3N+0.05

Where N is revolution per second.

Example:

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Distance from left edge depth Area Current meter N V Vavg. Q

m m sq.m No. of Rev time RPS m/s m/s cu.m/s

4 1.68 18 50

8 33

57 52

34.5 55

12 6

60 58

45 54

16 10.8

72 60

51 58

20 6.48

51 52

45 50

24 4.56

52.5 52

45 54

28 0 18 50

Total. Q=

Measurement of Stream Flow Discharge

(3) Area-Slope Method

2/13/21SAR

nQ =

A= cross-sectional areaR=hydraulic radiusS= channel slopen= Manning’s roughness coefficient

Measurement of Stream Flow Discharge

(4) Chemical dilution method

(5) Hydraulic structures

Hydraulic Structures for Discharge

Measurement

Measurement of Water Stage

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� Measurement of Water Stage

� Water stage: the elevation above some arbitrary datum of water surface at a station.

Measurement of water stage

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� Types of Gages Measuring River Stage:� Staff gage – vertical or inclined

� Suspended – weight gage

� Recording gage

� Crest – stage gage ( used to indicate high water mark)

Measurement of Water Stage

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Stage-Discharge Relation

� Rating curve is a graph of discharge versus stage for a given point on a stream, usually at gaging stations, where the stream discharge is measured across the stream channel with a flow meter

Q

HH Q

t t

Stage Hydrograph

Stage-Discharge Curve

or Rating Curve

Discharge Hydrograph

Stage-Discharge Relation

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� During the event of large flood, it is impossible or impractical to measure discharge directly. More often, the flood stage goes beyond the range of the data range used to define the rating curve. Therefore, extrapolation of the ration curve is needed when water level is recorded below the lowest or above the highest level.

Q

H

Stage-Discharge Curve

or Rating Curve

Q

H

Extension of Rating Curve

Methods for extension(1). Logarithmic method(2). Chezy’s method

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Part II

Hydrograph

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� A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, or other channel or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second (cms or cfs).

Hydrograph

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� Time to Peak, tp: Time from the beginning of the rising limb to the occurrence of the peak discharge.

� Time of Concentration, tc: Time required for water to travel from the most hydraulically remote point in the basin to the basin outlet

� Lag Time, tl: Time between the center of mass of the effective rainfall hyetograph and the center of mass of the direct runoff hydrograph

� Time Base, tb: Duration of the direct runoff hydrograph.

Essential Components of Hydrograph

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Essential components of a hydrograph are:

(i) the rising limb,

(ii) the crest segment, and

(iii) the recession limb.

(iv) Direct run off

(v) BaseflowD.R.O

baseflow

Falling limb

crest

Rising

limb

Q (m3/s)

Concentration curve

Recession curve

Inflection Point

t

D.R.O=Direct run-off

Separation of Base flow

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N (days)=0.83A0.2

A= area of catchment

Separation of Base flow

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� Hydrograph-Baseflow=Direct runoff

Hydrograph Direct runoff

Unit Hydrograph

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� The hydrograph that results from 1-inch (or 1 cm) of excess precipitation (or runoff) spread uniformly in space and time over a watershed for a given duration.

� The key points :

� 1-inch (or 1cm) of EXCESS precipitation

� Spread uniformly over space -evenly over the watershed

� Uniformly in time - the excess rate is constant over the time interval

� There is a given duration

Unit Hydrographs of Different Duration

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� In practice the unit hydrographs of different duration are needed. e.g., 1h- unit hydrograph, 2h-unit hydrograph, etc

� Two methods are available to generate hydrograph of different durations

1. Method of Superposition

2. the S-Curve

1. Method of Superposition

� T-H unit duration is available and it is needed to make UH of nT-H, where n is and integer

� Superposing n UH with each graph separated from the previous one by

T-H

2- The S-Curve

0.00

10000.00

20000.00

30000.00

40000.00

50000.00

60000.00

0 6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

96

10

2

10

8

11

4

12

0

Time (hrs.)

Flo

w (

cfs

)

The S-curve method involves continually lagging a T-h unit hydrograph by its duration and adding the ordinates.

Solution of Example 6.9 by S-curve method

Problem

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Time from start

Ordinate of 4h-UH (cu. m/s)

(Hours) cu.m/s

Col.1 Col. 2

0 0

2 8

4 20

6 43

8 80

10 110

12 130

14 146

16 150

18 142

20 130

22 112

24 90

26 70

28 52

30 38

32 27

34 20

36 15

38 10

40 5

42 2

44 0

Ordinate of 4h-Unit Hydrograph are given, Determine

(1). Ordinate of S-Curve(2). Ordinates of 2-h Unit Hydrograph

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Time from start

ordinate of 4h-UH

(cu.m/s)

S Curve addition

S Curve ordinatesS-Curve

lagged by 2 h

D.R.O Hydro. of (2/4) cm of

precipitation

Ordinate of 2-H UH

Col.1 Col. 2 Col.3 Col.4=Col.2+Col.3 Col.5 Col.6=Col.4-Col.5 Col.7=Col.6/(2/4)

0 0 0 0 0

2 8 8 0 8 16

4 20 0 20 8 12 24

6 43 8 51 20 31 62

8 80 20 100 51 49 98

10 110 51 161 100 61 122

12 130 100 230 161 69 138

14 146 161 307 230 77 154

16 150 230 380 307 73 146

18 142 307 449 380 69 138

20 130 380 510 449 61 122

22 112 449 561 510 51 102

24 90 510 600 561 39 78

26 70 561 631 600 31 62

28 52 600 652 631 21 42

30 38 631 669 652 17 34

32 27 652 679 669 10 20

34 20 669 689 679 10 20

36 15 679 694 689 5 10

38 10 689 699 694 5 10

40 5 694 699 699 0 0

42 2 699 701 699 2 (0) 4 (0)

44 0 699 699 701 -2 (0) -4 (0)

Thank you

� Questions….

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