Web_CE 372_ Water Resorces Engineering_Lecture Notes_25_02_2.pdf

7/21/2019 Web_CE 372_ Water Resorces Engineering_Lecture Notes_25_02_2.pdf

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CE372 WATER RESOURCES ENGINEERING LECTURE NOTES

1. HYDROLOGY

Hydrology may be broadly defined as the study of the life cycle of water, a simplified diagram of

which is shown in Figure 1.

Figure 1. Hydrologic (Water) Cycle

Of particular importance in this cycle is the section where rainfall occurs and results in stream

flow. The quantity of water which becomes stream flow, as the result of rainfall and snow melt, is

critical to many activities, for example in designing flood protection works for urban areas and

agricultural land, and in assessing how much water may be extracted from a river for water


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supply or irrigation. Generally, that part of rainfall which results in stream flow is referred to as

run-off, and the quantity of rainfall depends on a number of factors. The initial wetness and

permeability to the catchment play a major role. Rain falling on a very dry, permeable catchment

will tend to infiltrate the soil rather than move across the surface of the river, and, conversely,

rain striking a wet, comparatively impermeable surface will result in a high proportion of run-off.The intensity of the rainfall and slope of the catchment will also affect the quantity of run-off to

the response. There will be a lag in time from the start of rainfall to the resulting flow in the river,

which will build up to a peak value. If the catchment has a rapid response, then, for a given

quantity of run-off, the peak flow in the river will be higher than if a slow response had occurred,

with the run-off being more evenly distributed with time. This is illustrated in Figure 2.

Figure 2. Run-off response variation

Precipitation

Precipitation is one of the most important phases in the hydrologic cycle. It represents the process

by which water vapor is removed from the air and distributed over Earths surface in solid or

liquid form. However, it does exhibit tremendous variability in time and space; quantifying this

variability for design purpose is a challenge.

Precipitation is measured by distributing rain gauges throughout a watershed. The three major

types of rain gauges are: (1) weighing, (2) float and siphon, and (3) tripping bucket. If the gauges

are evenly distributed in the watershed, a simple arithmetic mean may suffice for an average

rainfall depth determination. If the areal distribution of gauges is uneven or the precipitation isquite variable, then a weighted average is necessary. The Thiessen method is a method that was

developed before the advent of hydrologic computer models.

The Thiessen method provides a weighting factor for each gauge based on its areal impact. The

gauge stations are located on a watershed map, and straight lines are drawn connecting each

gauge to nearby gauges. Perpendicular bisectors of the connection lines form polygons around

each gauge. This identifies an effective area for each gauge. The polygon areas are determined

and expressed as percentage of the watershed area. A weighted average precipitation is computed

by multiplying the precipitation at each gauge by its associated percentage and summing the

products. This can provide more accurate results than those obtained by simple arithmetic


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averages. However, the Thiessen method assumes a linear variation of precipitation between

stations that may misrepresent localized orographic influences.

Example: Compute the average rainfall depth over the watershed shown in Figures by thearithmetic and Thiessen methods.

Figure. Watershed gauge locations and precipitation amounts. (Distances from the watershed

centroid to the nearest gauge in each quadrant are depicted.)

Figure. Thiessen method for determining average watershed precipitation Arithmetic method:

Average the rainfall depths from the gauges in the watershed:

Arithmetic method: Average the rainfall depths from the gauges in the watershed:

mm3.1193/)110115133(


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Thiessen Method:

Area Gauge Precipitation

(mm)

Area Factor Weighted

Precipitation (mm)

I 110 0.30 33

II 107 0.07 7.5

III 115 0.30 34.5

IV 118 0.09 10.6

V 133 0.16 21.3

VI 121 0.08 9.7

Total - 1 116.6

Rainfall Run-off Relationship

The percentage of rainfall resulting in run-off tends to vary during the period of rainfall,

increasing with time (as the catchment becomes wetter and infiltration reduces) and approachinga constant value. The factors in this dynamic process are the amounts of rainfall going to soil

moisture, interflow, storage in depressions and interception by vegetation. These factors in turn

depend on topography, geology, land use, vegetative cover and degree of urbanization. Figure 3

shows the relative amounts of run-off and infiltration during a storm.

Figure 3. Rainfall run-off relationship


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This pattern is reflected in the resulting plot of a river flow against time, known as hydrograph and

shown in Figure 4. There is, of course, a base flow component to the hydrograph, which is the dry

weather flow. The area under the hydrograph gives the volume of run-off, which can be divided by the

catchment are to give a value in, sayi milimeters, which can be compared to the total rainfall. In

attempting to predict the likely quantity to run-off and hydrograph shape from a given rainfall, there is

no purely theoretical means based on physical parameters which can be measured in the field. All

methods are semi-emprical in nature, and many comlex (mathematical) models are used, with rainfall as

input and run-off as the output.

Figure 4. Hydrograph

Where little or no records exist, a simple emprical formula may be used:

AiCQ

Q: Peak discharge

C: Coefficient of run-off

I: Mean rainfall intensity

A: Catchment area

Hydrologic Design

Many hydraulic projects require a hydrologic study to establish the design discharge. Indeed, the

design discharge is critical in establishing appropriate size and design of many hydraulic

structures.

Water is constantly being cycled between the sea, the air, and the land. This phenomenon is

called the hydrologic cycle. If the precipitation occurs over land, the water can take a number of

paths. Rainfall is either stored in depression, infiltrated into ground, or runs off the land driven by


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gravitational forces. The depression storage water either infiltrates or evaporates. Infiltration

water is either held in the soil pores or moves downward to the water table. Water held in soil

pores can be used by plants and released back to the atmosphere through the process of

transpiration. Water that drains down the groundwater aquifer often ends up in rivers and

eventually the sea. This is also the ultimate destination of surface runoff water. Figure 11.1 is asimple depiction of the process. Measurement of rainfall and stream flow is a prerequisite for

understanding the complex rainfall-runoff process.

Figure 5. Hydrologic budget for a reservoir

In equation form, the hydrologic budget is defined as

STEIQQP oi

where P represents precipitation, Qi represents inflow, Qo represents outflow, I represents

infiltration, E represents evaporation, T represents transpiration, and S represents the change in

storage over time period of interest. A hydrologic budget represents a quantitative accounting of

the water within a system. Accounting for the stream flow entering and leaving the reservoir is

necessary. It may also be necessary to account for infiltration of water at the lake bottom and

evaporation from the lake surface. Note that the water in the reservoir represents the control

volume and is bounded by a control surface.

An accurate topographic map is necessary to properly deliante a watershed boundary. The

watershed is delineated in two steps:

1. Identify the design point with a circle on the topographic map and designate all peak

elevations with Xs close to design point and upstream to the headwaters of the watershed.

2. Circumscribe the stream with a watershed boundary that passes through the peak points

and the design point.

Any significant precipitation that occurs within the watershed boundary will produce

surface runoff that eventually flows through the design point.


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Design Storm

A designed event is used as basis for designing a hydraulic structure. It is presumed that the

structure will function properly if it can accommodate the design event at full capacity. However,

the structure would fail to function as intended if the magnitude of the design event is exceeded.Example 1: A rainfall event occurs over the Nelson Brook watershed. The average Rainfall

Intensity and average stream flows at the design point for 1-hr time increments were measured

during each hour of the 7-hour storm and are shown in the following table. Determine the

quantity of water in acre-feet that was added to the ground water table during the event if the

watershed is 350 acres. Assume that small pond and wetlands in the watershed have negligible

storage capacity.

Parameter Hour

1 2 3 4 5 6 7

Stream Flow (cfs) 30 90 200 120 80 40 20

Rainfall Intensity

(in./hr)

0.5 2.5 1 0.5 0 0 0

STEIQQP oi

ftacacresinfthrhrinP 131)350)(12/1)(1(/)5.00.15.25.0(

0iQ

ftachrhrcfsQo 9.47)1sec/3600)(1()2040801202009030(

0E Assume that evaporation during the 7-hr storm is negligible

0T Assume that transpiration is also negligible

0S No change in storage in the control volume during the storm.

ftacI 1.839.47131 is added to the groundwater table.

Example 2: A storm occurs over the Pierre Creek watershed. Measurements of rainfall and

stream flow are listed in the following table. The drainage area that contributes stream flow to the

gauge site is 1,150 km2. Determine the unit hydrograph from this rainfall event for this

watershed.


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Day Hour Rainfall

(cm)

Stream

Flow

(m3/s)

Base

Flow

(m3/s)

Direct

Runoff

(m3/s)

Unit

Hydrograph

(m3/s)

Hour

After

Start

22 00:00 170 170 0

06:00 1.7 150 150 0 0 0

12:00 5.1 400 157 243 38 6

18:00 4.7 750 165 585 91 12

00:00 0.8 980 172 808 125 18

06:00 890 180 710 110 24

12:00 690 187 503 78 30

18:00 480 195 285 44 36

00:00 370 202 168 26 42

06:00 300 210 90 14 48

12:00 260 217 43 7 54

18:00 225 225 0 0 60

00:00 200 200

06:00 180 180

12:00 =12.3 170 170 =3,435

With the data provided, the six-step computation procedure is employed to obtain the coordinates

of the unit hydrograph. The values in each column of the solution table just presented are

explained as follows:

Day and Hour: time of rainfall and discharge measurementsRainfall: depth of rainfall that occurred within a six hour increment (for example, 1.7 cm of

rainfall between hour 00:00 and 06:00 on day 22.

Stream Flow: Instantaneous discharge measurements on Pierre Creek

Base Flow: Base-flow estimates taken from the depicted hydrograph

Direct Runoff: Portion of the rainfall that runs off the land surface and contributes the stream

flow (found by subtracting base-flow column from the stream flow column)

Unit Hydrograph: Ordinates found by dividing the direct runoff column by the volume of direct

runoff expressed in centimeters over the drainage area (i.e., the depth of runoff, which is found by


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summing the direct runoff column, multiplying by the time increment-6 hr- and dividing by

drainage area):

Hrs After Start: hours after start of effective (runoff-producing) rainfall (establishing this time

frame is important for using the unit hydrograph as a design tool).

cm

km

cmkm

m

cm

hr

shrssm

45.610

)150,1(

100)

600,3)(6)(/435,3(

RunoffofDepth2

52

3

3

Note that 12.3 cm of rainfall is that was measured, only 6.45 cm produced runoff. The rest of the

rainfall was lost as infiltration and depression storage.


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2. GROUNDWATER FLOW

When water is pumped from a well, drawdown of the water table occurs. The resulting shape of the

water table is called the cone of depression. Consider Figure 5 which shows this situation.

Figure 6. UnConfined Aquifer: flow to a well

The flow towards the well is on a cylindrical surface and at some point r from the well, may be stated

from Darcys law:

AikQ

Q: discharge

k: Coefficient of permeability

I: Hydraulic gradient

A: Flow area

which becomes:

hrdr

dhkQ

2

Thus, the flow between r2 an r1 may be written as:

r

dr

k

Qdhh

2

2

1

2

1

2

r

r

h

h

r

dr

k

Qdhh


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)/(

)(

12

2

1

2

2

rrLn

hhkQ

This equation applies to unconfined conditions.

Confined Aquifer

Where an acqufier is confined under an impermeable material, as illustrated in Figure 7, flow

occurs radically towards the well thought the whole depth of the aquifer. If the piezometer tube is

inserted into the aquifer, the water will rise in it to what is called piezometric level or head, and

the locus of all these points defines the piozometric surfaces as shown in Figure 7.

Figure 7. Confined Aquifer

When pumping occurs, the piozemetric surface is drawn down towards the well in a similar

manner to the cone of depression for an unconfined acquifer. Now from Equation

AikQ

Therefore:

brdr

dhkQ

2

At radius r. the flow between r2 and r1 my be written:

2

1

2

1

2 r

r

h

h r

drdh

Q

k


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)/()(2

1212 rrLnhhQ

T

)/(

)(2

12

12

rrLn

khhQ

Table 1. Typical Coefficient of Permeability Ranges for Some Natural Soil Formations

Figure 8. Laboratory determination of coefficient of permeability


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Figure 9. Field determination of permeability coefficient in unconfined aquifers

Example 1: For an unconfined aquifer, the following data are gathered from the laboratory.

Calculate the coefficient of permeability of the test conditions: Q= 0.5 L/min, h1=53 mm at r1=40

mm, and h2=67 mm at r2=640 mm.

smQ /1033.860

105.0 363

)/(

)(

12

2

1

2

2

rrLn

hhkQ

)(

)/(2

1

2

2

12

hh

rrLnQk

, smLn

k /1038.410)5367(

)40/640(1033.8 3622

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Web_CE 372_ Water Resorces Engineering_Lecture Notes_25_02_2.pdf