Chapter 6
RUNOFF
____________________________________________________________________________
6.1
Factors affecting runoff
Runoff in a stream is affected by two major factors:
(a) Climate
(b) Physical characteristics of the drainage basin.
The influence of climate on runoff is due to the following characteristics/factors:
i.
Precipitation
ii.
Rainfall Intensity
iii.
Duration of rainfall
iv.
Distribution of rainfall on the basin
v.
Direction of storm movement
vi.
Infiltration
6.1.1 Climatic factors
6.1.1.1 Precipitation
Rainfall and snow which are one of the forms of precipitation affect runoff differently. Rainfall
affects runoff hydrograph immediately and produces peak hydrographs depending on the
size of the basin. While snow does not produce runoff immediately and there is a time lag
between snow fall and runoff in the streams and this could be in months.
6.1.1.2 Rainfall intensity
The peak of a runoff hydrograph is a function of increasing rainfall intensity. Flash floods are
usually caused by high intense rain storms of short duration.
6-1
6.1.1.3 Duration of rainfall
Rains of long duration may produce considerable surface runoff though the rainfall intensity
might be relatively mild. High intense rainfall storms of long duration produce serious flood
hazard.
6.1.1.4 Areal distribution of rainfall on basin
For drainage basins of appreciable size, large flood producing storms are seldom uniformly
distributed. For small drainage basins high peak flows are the result of intense rainfall storms
that cover only small areas. For large basins the highest peak flows are usually produced by
general storms of less intensity, long duration and covering much larger areas.
6.1.1.5 Direction of storm movement
The direction in which the storm travels across the basin with respect to the direction of flow of
the drainage system has a great influence upon the resulting peak flow and also upon the duration
of the surface runoff. A rain storm traveling in the downstream direction causes a high peaked
discharge hydrograph. This happens due to the water congestion at the outlet. While a rain storm
traveling in the upstream direction produces a flat runoff hydrograph.
6.1.1.6 Infiltration
Infiltration is the phenomenon of water penetrating from the surface of the ground into the
subjacent soil. As water penetrates the soil, its distribution in space and time varies. The
description of the evolution of the water content in the soil, resulting from the occurrence of a
rain or of a pond of water at the surface, is also sometimes thought to be a part of the
phenomenon of infiltration. Mostly, however, infiltration is thought of as the phenomenon of
water crossing from the air side to the soil side of the air-soil interface.
6.1.2 Physical characteristics of the drainage basin
These are: Land use, type of soil, area of basin, shape of basin, elevation, slope, orientation, the
drainage net, order of streams, length of tributaries, stream density and drainage density.
6-2
6.1.2.1 Land Use
Of all the many physical factors that affect the runoff of any area, one of the most important is
land use. The land use which affects the vegetation has an influence on the rate of infiltration and
therefore on the resulting runoff in the stream. Figure 6.1 shows the effect of land use on the
runoff. Variations in interception indicated by through fall according to age and character of
forest cover at 200 m in the Austrian Tyrol are indicated in A, and the significance of drainage
(B1) and forest removal (B2) upon water levels in an experimental area in Denmark is shown.
The effect of different land use covers upon peak discharge is shown (C) by plotting peak
discharges for the Serven catchment (870 ha, 2/3 forest) against those for the Wye catchment
(1055 ha, sheep grazing) in the Plynlimon study. D shows the increase in runoff according to
years since treatment in the Coweeta watersheds. E indicates possible differences in hydrograph
form according to land use cover, and F indicates sediment yields in the Serra do Mar Brazil.
6.1.2.2 Type of soil
In any drainage basin the runoff characteristics are greatly influenced by the soil type because of
the varying infiltration capacities of different soils. Soils with high infiltration capacity would
produce less runoff and vice versa.
6.1.2.3 Area of basin
The larger the basin the longer it takes for the total runoff to pass a given station. The peak flow
decreases with an increase in the drainage area. Actually for any locality the maximum intensity
of rain that is likely to occur with any given frequency varies inversely with the area covered by
the storm. Consequently, the larger the basin the less will be the intensity of the storm and
therefore the lower will be the flood peak.
6.1.2.4 Shape
The shape of the basin mainly governs the rate at which water is supplied to the main stream as it
proceeds along its course from the source to the mouth (see figure 6.2). It can be seen in Figure
6.2 A, B, C and D that basin shape affects the peak of the resulting runoff hydrograph.
6-3
Figure 6.1 Illustrations of the effect of land use and vegetation on runoff
6.1.2.5 Elevation
The variation in elevation and also the mean elevation of a drainage basin are important factors
in relation to temperature and to precipitation, particularly as to the fraction of the total amount
which falls as snow.
6-4
6.1.2.6 Slope
The slope of a drainage basin has an important but rather complex relation to infiltration, surface
runoff, soil moisture , and ground water contribution to stream flow. It is one of the major factors
controlling the time of overland flow and concentration of rainfall in stream channels and is of
direct importance in relation to flood magnitude (see figure 6.2). It can be seen in Figure 6.2 that,
a catchment with a steep slope produces a high peaked hydrograph and vise versa.
6.1.2.7 Orientation
Orientation of basin affects the transpiration and evaporation losses because of its influence on
the amount of heat received from the sun. Orientation of the basin coupled with storm movement
has an influence on runoff.
Figure 6.2 Basin relief and shape in relation to drainage basin process
6-5
6.2 Hydrometric measurements
The hydrometric measurements that are required and or carried out are, water and sediment
discharge. However, before the measurements are carried out one has to choose the site for the
hydrometric station.
6.2.1 Choice of a site for a hydrometric station
There are a number of factors which, influence the choice of a site for a hydrometric station and
these are:
(a) The channel is straight and uniform for at least 100 m or three times the channel width
upstream and down stream of the location.
(b) No flow can by-pass the site, neither as surface nor as subsurface flow.
(c) The streambed is not scoured or filled by sediment and is free of aquatic growth.
(d) The banks are permanent and the stream does not change course regularly. The banks
should be high enough to contain all floods.
(e) Ideally there should be a permanent hydraulic control giving stable, unique, stagedischarge relationship for the reach. The sensitivity of the relationship dictates the
accuracy of the stage measuring and recording equipment required to produce a discharge
value of specified accuracy.
A natural control is either a section control, which usually involves critical flow
conditions, e.g. at a constriction in the channel or at an increase in longitudinal bed-slope,
or a channel control, in which uniform flow conditions may be approached and which
depends on the channel geometry and roughness. Artificial controls include weirs and
flumes constructed across the river.
(f) A site is available for housing the measuring and recording equipment.
(g) The site should be accessible at all times, even in extreme floods.
(h) The depth of flow and velocity at minimum flows and the velocity and turbulence at
maximum flows should be within the limits of the method envisaged for discharge
measurement.
(i) The site should be selected such that the stage-discharge relationship is not influenced
by variable backwater from downstream confluences, lakes, resorvoirs, locks, intakes
or from tides or seiches.
(j) Reach should be oriented at right-angles to the direction of the prevailing wind.
(k) If possible, a local person should be employed to take the measurements.
6-6
6.2.2 Discharge measurement
Discharge measurements are made for a variety of reasons concerned with the planning and
management of water resource including ....
(i) Studies for occurrences of floods.
(ii) Studies of occurrences of low flows.
(iii) Water-balance studies
In cases (i) and (ii) above, actual values of peak and low flows are required (instantaneous
values). In case (iii) the total quantity of water passing a point of interest in a specified period of
time is required. Thus all of these applications require continuous measurements, regardless of
how frequent.
Water discharge carries with it sediment material load. Sediment deposition affects the water
carrying capacity of rivers and the useful life of reservoirs. Therefore, it is also imperative to
carry sediment measurements at points of interest in the catchment where the construction of a
dam downstream is likely to take place. This information is very important in the determination
of the useful reservoir capacity and the life span of the reservoir.
Stream flow is measured in terms of stage and discharge. River stage is measured using: Staff
gauges and automatic water level recorders while water discharge is measured by current meters;
slope area method, tracer dilution method, floating object method, radio active tracers method
and hydraulic structures. There exists a unique relationship between the river stage and the
discharge at the hydrometric station. This relationship is very useful for the transformation of
river stage into discharge (see Figure 6.12 ).
6.2.2.1 Determination of Stage
The term stage, as used in a streamflow measurement, refers to the water-surface elevation at a
point along a stream measured above an arbitrary datum. Stage is determined by indicators of
various types and these are: staff gauge; chain, tape; and wire gauges; pressure transmitters; and
crest stage indicators. The above are also categorized as manual and automatic water level
indicators:
Manual stage indicators:
1.
Staff Gauge: A staff gauge is a graduated scale set in a stream by fastening it to a pier,
wall, supporting or other structure. It is read by observing the level of the water surface in
contact with it, with proper allowance for the meniscus. The gauge may extend upward
6-7
in one section to cover the expected range in stage; it may be set vertically in several
sections at different locations (see Fig. 6.3).
2.
Chain, Tape and Wire Gauges: Stage is determined by these devices by lowering a
weight to the water surface.
The chain gauge is read from a reference head moving along a graduated scale. The tape
gauge is read at a pointer in contact with the tape. The wire gauge is read by means of a
mechanical counter attached to the real on which the wire is wound. The advantages of
these gauges is that they can be installed so as to be readily accessible under all
conditions and they are easy to install.
Figure 6.3 A staff gauge. Stage reading at X = 0.585 m (Shaw, 1983)
3.
Pressure Transmitter: The stage in a stream may be converted to pressure by means of
a cylinder and flexible diaphragm. This pressure is transmitted via a light liquid through
a tube to a sensitive gauge. The major disadvantage to this device is that it is very
sensitive to temperature changes,
6-8
4.
Crest-stage Indicator: This indicator is used to delineate the peak stage of a flood at
points other than at a hydrometric station. Such data are valuable in the establishment of
flood profiles and in determining slope for the investigation of formulas for the
computations of flood flows in streams.
A crest stage indicator consists of a pipe set vertically with an open, screened bottom and a
vented top. It contains a graduated wooden staff gauge, held in place by a cap on the pipe. A
small quantity of powdered cork is introduced into the top of the pipe and washed to the bottom
with water. When the stage is visited, the stage is read and the device returned to operating
condition by pouring a little water in to wash the cork back down the pipe.
Automatic water level recorder:
Automatic or continuous water level recorders are float-or probe-actuated type devices.
The most commonly used water-stage recorders is the float actuated device using a stilling well
to exclude wave action. The level can be recorded by a pen on a chart fixed on a rotating drum
(Figure 6.4).
Figure 6.4
Float automatic water level recorder
Nowadays the level is usually transmitted by e.g. telephone line or recorded by an electronic
device. Other recording gauges (e.g. so-called divers) may register the level every 15 min. Some
of these gauges are part of a flood warning system, initiating an alarm when the stage exceeds a
6-9
prescribed level. Divers are steel cylinders (diameter 3 cm, length 15 cm) with a sensor to
measure water pressure. The divers may be programmed to measure the water level at a fixed
time interval. The instrument id battery operated (batteries last 8 – 10 years). Divers may be read
out with a PC or laptop, but the readings may also be transmitted elsewhere.
Another type of recording gauge is known as pressure-actuated gauge, which measures the
pressure by pressing small quantities of air through a pipe that is fixed on the river bed. The
water level in the river is directly proportional to the pressure. The method does not require a
stilling well.
6.2.2.2 Methods of Discharge Measurement
As mentioned earlier, the methods of measuring discharge are: current meters; slope area
method, tracer dilution method; floating object method, radio active tracers method and
hydraulic structures. The flowing velocity of water in a stream varies with depth. That is the
water flow velocity increases from the channel bed and reaches its maximum value at the water
surface. Horizontally, the water velocity increases from the river bank and attains its maximum
value close to the center of the river. Therefore, the velocity distribution of flowing water has an
influence on the accuracy of the measured values. Figure 6.5 shows a vertical velocity profile in
a stream.
A current meter is a simple device which, consists of a precisely formed propeller rotating freely
on a well-lubricated shaft. The is lowered into the water and the rate of revolution of the
impeller is directly proportional to the velocity of the water. A small magnet is usually built into
the shaft of the instrument and a coil detects the passage of the magnet and allows the number of
revolutions of the shaft in the given time to be counted. Once the rate of revolution of the
impeller is known the water velocity can be calculated using the calibration equation for the
instrument, which is expressed as follows:
V
=
a + bn
Where, V is the water velocity
n is the number of revolutions of the impeller per second
a, b are constants for the particular instrument
(6.1)
6-10
Figure 6.5
A typical vertical velocity profile in a stream (Linsley et al, 1975)
Many manufacturers test each current meter separately and calculate a calibration equation for
each one. However, the derived equation for the current meter with normal use should be
recalibrated every three years (WMO). Prolonged use in sediment-laden water damages the
bearings and great care should be taken in cleaning the meter after use and the lubrication oils
should be changed regularly.
Current meter calibration is done in a special calibration tank. Usually the tank is over 100 m
long and 2 m wide and 1.5 – 2 m deep. The tank is filled with water and a small carriage can
move on rails above the water surface. The current meter is attached to the carriage so that the
impeller is beneath the water surface. The carriage is then moved a precisely determined fixed
speed and the rate of revolution of impeller is accurately measured. The test is repeated for a
number of different carriage speeds, varying from 0.025 m/s up to 4 m/s. If a weight is used with
the meter then the meter should also be calibrated with the weight attached. A straight line,
relating rating of impeller revolution to carriage speed, is fitted to the data test data by leastsquares regression to establish the calibration equation. Figure 6.6 shows a typical current meter
fixed on to a wading rod.
6-11
Figure 6.6
A typical current meter
Methods of river crossing while making velocity measurements
A discharge measurement is classified according to manner in which the stream crossing is
made. There are four ways of making discharge measurement by current meters and these are;
wading; cable way, bridge and boat.
Wading measurement are usually carried out for shallow streams. The limit is determined by the
ability of the hydrographer to cross safely and to stand in position while making an observation.
A tag line, usually a tape or small-diameter metal cable with beads marking 10 or 20 cm intervals
is stretched across the stream. The hydrographer notes the width of flow during this procedure,
which enables him to determine the spacing of the verticals. The number of verticals depend
upon the regularity of the cross section and the distribution of flow. The verticals (Fig. 6.7)
are closely spaced through irregular parts of the section or where the velocity is changing rapidly
and are spaced more widely in the center of the stream where the flow is uniform. However, the
flow through the section between any pair of adjacent soundings should not be more than 5 per
cent of the total.
In wading measurements the hydrographer should stand in a position which will least affect
the distribution of flow passing the current meter. With the meter rod at the tag line, the
6-12
hydrographer will face along the line toward the bank, standing 10 to 30 cm downstream from
the tag line and 45 cm or more from the meter rod, supporting the rod with his upstream arm.
A cable way consists of a cable stretched across the stream, supported at the banks by A-frames
and securely anchored at each end. The cable is designed to support safely a gauging car, its
occupants, and the measuring equipment. The cable is marked off in intervals by short stripes
around its circumference. The spacing between stripes is determined by the width of the stream.
Two types of bridge are used for stream flow measurements, those constructed especially for
that purpose and those used by road and rail transportation. The first type serves essentially the
same purpose as the cable way. Railroad and road bridges when used for stream flow
measurements have two disadvantages: they are dangerous, and the stream cross sections
beneath them are usually disrupted by piers or piles. Discharge measurements are made from
bridges by hand line, hand operated reels and booms, powered-operated reels and booms
attached to trucks or trailers, or power operated reels and booms mounted on prime movers
constructed especially for the purpose. Measurements are generally made from the downstream
side. Soundings are made in the same way as from cable ways, except that more sections are
required, particularly around piers and piles. Distances for soundings are determined by marking
on the handrail of the bridge in the same manner as a cable way. 30 or more sections are
recommended with additional observations near piers.
Measurement from a boat is a satisfactory way of determining streamflow if conditions are
favorable for its operation. The requirements are that the stream be safe for boats and that a
suitable cross section be available. A boat measurement is in a sense a combination of wading
and cable way operation, the hydrographer working from just above the water surface but
using meter and sounding weight rather than a rod for depth determination. Cross sections
distances are established from a tagged cable stretched across the stream just above the water
surface. The sounding equipment is operated by a reel, with line passing over a boom
extending ahead of the bow of the boat. The sections should number 30 or more, depending on
the uniformity of depth and velocity distribution.
6.2.2.2.1 Velocity Area Method
Velocity area method estimate discharge by using the relationship
Q
=
VA
(6.2)
6-13
where, Q is the discharge, V is the mean water velocity and A is the cross-sectional area of flow.
The Discharge Q, and cross-sectional area of flow, A, are actual physical quantities and can thus
be measured. However, the mean water velocity, V, is not necessarily the actual velocity at any
given point in the flow. The mean velocity if a function of the velocities at all points in the crosssection. It is a derived quantity.
The actual velocity varies so much in a cross-section that large errors may be expected in any
direct estimate of the average velocity for the cross-section. This difficulty is reduced by
considering the cross-section to be divided into a number of separate areas of flow. The total
discharge trough the cross-section is the sum of the discharges through each sub-division of area.
The sub-divisions are made sufficiently small so that there is justification for using the average
velocity and the above equation applies to the sub-division (Figure 6.4). The total discharge is
thus calculated by the formula:

Q
q1  q2  .... qn
(6.3)
Where n is the number of the sub-divisions.
Mathematically, the above equation can be considered to be a numerical approximation to the
exact integral relationship:
B y( x)
Q

  v( x, y)dydx
0
where, x
y
v(x,y)
B
y(x)
(6.4)
0
is distance from a particular bank.
is distance below the water surface.
is the velocity at a depth y and a horizontal distance, x from the bank
is the width of the river.
is the depth of the river at a distance x from the reference bank.
On any given vertical line, the water velocity varies with depth. The lowest velocity is usually at
the bed of the river, while the highest velocity is either at or near the water surface. Very many
individual velocity measurements are required to establish the exact variation at a given vertical.
If the exact variation of velocity with depth is known then the average velocity for the vertical
can be calculated by integration as follows:
6-14
y( x)
v( x)

 v( x, y)dy
0
(6.5)
Since this method is time consuming, a number of approximations have been developed for
practical use. There is the one point method (0.6 of depth), the two point method (0.2 and 0.8 of
the depth) and the three point method ( 0.2, 0.6. and 0.8 of the depth). A velocity measuring
instrument which is lowered and raised at a constant speed through the vertical section of water
integrates the velocity and provides a means of measuring the average velocity of the section. A
current meter with a blade impeller is often used, but a cup-type current meter cannot be used for
this method.
Current meters can be grouped into two groups namely: rotating meter and dynamometer. The
rotating meter converts a part of the stream momentum into angular momentum while
dynamometer converts momentum into force. Rotating current meters fall into two general
groups according to the orientation of the revolving axle; that is the axle may be vertical or
may be horizontal and parallel to the direction of flow. Rotating about the vertical axle is
accomplished by means of cups or vanes, that about the horizontal axle by means of screw-or
propellor shaped blades. The dynamometer translates the momentum force of stream velocity
into either deflection or stress. This is measured and calibrated against velocity or discharge.
Rotating horizontal axle current meters are commonly used in the region. The current meter give
the stream velocity in a vertical cross section. In shallow streams, it is general practice to set the
current meter at 0.6 of the depth. The general practice in deeper streams is to take the
average of readings at 0.2 and 0.8 of the depth. The minimum depth at which the two-point
setting can be made is determined by the meter suspension. If a rod is used, the minimum is
1.5ft and if the meter is suspended or a hanger above a weight, the minimum depth for two-point
settings is 5 times the distance from the center of the meter to the bottom of the weight.
Occasionally, observations in very deep streams/rivers are made at 0.2, 0.6 and 0.8 depths, and
the velocity at 0.6 depth averaged with that determined from the average of the observations at
0.2 and 0.8 depth.
A velocity observation is made by timing the number of revolutions which the meter makes
during a selected period of time, usually for about one minute. The number of revolutions are
obtained by use of a counter which makes use of a make-and-break electrical contact. If the
current meter is suspended on a rod, current from a battery in the counter flows through a wire
6-15
to the contact chamber of the current meter and returns through the rod. If the current meter is
suspended on a hanger above a weight, the connecting wire from the counter is carried to the
current meter as the insulated core of the cable, and the cable provides the return path.
There are several ways of measuring depth and these include; graduations on the wading rod,
tags on the cable which supports the current meter and weight assembly, or by a mechanical
indicator attached to the reel on which the supporting cable is wound and electrical depth
sounders.
The wading rod is graduated in tenths of a meter with the zero at the bottom of the base plate.
The depth is read by estimating the point at which the level surface of the water intersects
the rod.
The current meter and sounding assembly is supported on a steel cable. This is fastened to a
rubber covered two-conductor cable which serves as a hand line for making measurements
with 7-kg and 14-kg sounding weights. The sounding reel is equipped with a mechanical
counter so that the depth may be read directly.
6.2.2.2.1.1 Data recording and discharge computation
During stream discharge measurement by current meters, the data to be recorded are: distance
from the initial point, depth, depths of observation, revolutions of the current meter and time in
seconds. In addition, if the direction of flow is not perpendicular to the section, the cosine
of the angle of departure is indicated
A discharge measurement is computed by determining the discharge per unit width for each
sounding, multiplying it by the width corresponding to one-half the distance to each adjacent
sounding to determine the partial discharge. The partial discharges are added to obtain the total.
The stage is also recorded at the time of discharge measurement.
In any given vertical line, the water velocity varies with depth. The lowest velocity is usually at
the bed of the river, while the highest velocity is either at or near the water surface. Very many
individual velocity measurements are required to establish the exact variation at a given vertical.
If the exact variation of velocity depth is known then the average velocity for the vertical can be
calculated by integration i.e.

1
(6-6)
V  d V ( y)dy
6-16
6.2.2.2.1.2
Mean-Section Method:
The discharge between two verticals is calculated by determining (i) the mean of the average
velocities for the verticals on either side of the sub-division, (ii) the mean of the depths of the
verticals on either side of the sub-division and (iii) multiplying these by the width of the subdivision (see Figure 6.7). Mathematically the above explanation is expressed as follows:
qj

 V j  V j 1   Yj  Yj 1 


b
2 
2  j

(6.7)
jn
Q

q
j0
j
Figure 6.7 Mean-section method of discharge calculation
6-17
6.2.2.2.1.3
Mid-Section Method:
The depth and average velocity calculated for each vertical is assumed to apply to an area which
extends half way to the next vertical on either side. The discharge through this area is calculated
by multiplying the depth by the average velocity and by the width of the area involved (see
Figure 6.8). The above explanation is expressed mathematically as follows:
qj

 B j  B j 1 
V j Yj 

2


(6.8)
n
Q

Q
j0
Figure 6.8
j
Mid-section method of discharge calculation
6-18
6.2.2.2.2 Slope area method
The most commonly used formula in the slope area method is Manning’s
equation which is expressed as follows:
Q

2
1
1
3
AR S 2
n
(6.9)
where Q is the discharge; n is the Manning's roughness coefficient; A is the cross-sectional
area, R is the hydraulic radius which is determined as the ratio (A/P) (refer the sketch below,
Figure 6.9) , and S is the slope of the energy gradient line (for uniform flow, this is equal to the
slope of the channel bed). The mean depth may be substituted for hydraulic radius for very wide
rivers.
Figure 6.9 Sketch to define the hydraulic radius
The field work for making a slope-area discharge measurement includes careful marking of the
high-water profile of the flood through the reach, precise levels to determine the elevations of
the marks, and careful selection and surveying of the cross sections that will be utilized for the
determination. It must be remembered that the surface of a stream during flood is a markedly
warped surface and the trace of its passage along the stream banks provides at best only an
approximation of the true slope of the water surface.
6.2.2.2.3 Salt dilution method
In the salt dilution method a concentrated salt solution is introduced at a constant and measured
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rate q. The concentration of the salt is determined a priori while the constant rate is achieved by a
special metering pump or by an orifice connected to a constant head, Marriot etc. At a point
some distance downstream, after complete mixing has taken place, water samples from the
stream are drawn and analysed. The weight of the salt passing the sampling point per second
must equal the sum of the weight of salt ordinarily carried by the stream and the weight of the
concentrated solution added per second. A simple calculation will give the volume of water per
second passing the sampling point. This method is suitable for turbulent mountain streams
and for cross sections where the flow is so rough that no other method is feasible.
Q

 C1  C2 

q
 C2  C0 
(6.10)
where C0 is the background concentration already present in the water, C1, is the known salt
concentration added to the stream at a constant rate q, and C2 is a sustained final concentration of
the salt in the well mixed flow at the sampling point.
It is recommended that the salt/chemical used should have a high solubility, be stable in water
and be capable of accurate quantitative analysis in dilute concentrations. The chemical/salt
should be non-toxic to fish and other forms of river life, and be unaffected itself by sediment
and other natural chemicals in the water.
Careful preparations are needed and the required mixing length, dependent on the state of the
stream, must be assessed first, usually by visual testing with fluorescein. The salt dilution
equipment is easily made portable for one or two operators and thus the method is recommended
for survey work in remote areas.
6.2.2.2.4 Floating object method
The simplest approach to this method is by timing the velocity of floating objects i.e. orange to
pass a certain point. This will give the indication of the velocity of the water at the surface. The
other approach uses the principle of moving floats by releasing compressed air bubbles at regular
intervals from special nozzles in a pipe laid across the stream, bed (Figure 6.10). The bubbles
rising to the surface with a constant terminal speed V, are displaced downstream a distance L
at the surface by the effects of the velocity of the flow as the bubbles rise. The discharge per unit
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width is expressed as:
q

Vr L
(6.11)
where L is the mean surface displacement of the bubbles at that point. The total discharge of the
stream is expressed as:
n
Q

q b
i 1
i
i
(6.12)
where n is the number of points across the stream and b is the width of a segment. The area A
is obtained in the field by taking photos of the bubble pattern and then using a micro computer
technique to compute A from the photographic points.
Figure 6.10 Integrated float technique (from Shaw 1983)
6.2.2.2.5 Radio-Active tracers method
A variation of the salt-velocity method utilizes radioactive tracers. Radioactive material are, not
stable and thus not suitable. While the concentrations used do not pose a serious health hazard
for water users, the measuring personnel may be affected over a long period of time. Therefore,
the increased cost and the care needed to avoid danger of radiation exposure make the method
somewhat disadvantageous. However, this method is appropriate for very wide rivers.
6-21
6.2.2.2.6 Weirs
There is a wide variety of weir types which can be used for the measurement of discharges
ranging from a few litres per second to many hundreds of cubic meters per second. Weirs are
hydraulic structures which provide restriction to the depth of flow in a river or stream. A
distinct sharp break in the bed profile is constructed which creates a raised upstream sub-critical
flow, a critical flow over the weir and a super-critical flow downstream. The upstream head is
uniquely related to the discharge over the crest of weir where the flow passes through Sharpcrested or thin plate weirs are commonly used for gauging small streams and man-made
channels. These give highly accurate discharge measurements but to ensure the accuracy of the
stage-discharge relationship, there must be atmospheric pressure underneath the nappe of the
flow over the weir. Thin plate weirs can extend across the total width of a rectangular approach
channel or contracted (Figure 6.11 ).
The shape of the weir may be rectangular or trapezoidal or triangular cross-section (i.e. a Vnotch). The angle of the V-notch may have various values, the most common being 90 o, 60o
and 45o .The basic discharge equation for a rectangular sharp crested weir is expressed as
follows:
1.5
(6.13)
Q

kBH
where Q, is the discharge, B is the width of the stream, H is the depth of flow over the crest of
the weir and k is a coefficient which is a function of the channel geometry, nature of the
constriction etc. For V-notch weirs, the discharge is expressed as follows:
Q


k tan( 2 ) H 2.5
(6.14)
Where  is the angle of the v - notch
6-22
Figure 6.11: Thin plate weirs (from Shaw, 1983)
For larger channels the recommended gauging stations using weirs are usually constructed in
concrete. One of the simplest to build is the broad-crested rectangular weir. The discharge in
6-23
terms of gauge height H is expressed as in the equation for the sharp crested weir. The length L
of the weir, related to H and to P the weir height is very important since critical flow should be
well established over the weir. However, separation flow may occur at the upstream end, and
with increase in flow depth H, the pattern of flow and the coefficient, k may change (see Figure
6.12).
Figure 6.12 Rectangular profile weir (from shaw, 1983)
6-24
6.2.3 Rating curves
6.2.3.1 Stage-Discharge relationship
In the measurement of river flow, the computed total discharge corresponds to a certain stage in
the river. The stage-discharge relationship is defined by the complex interaction of channel
characteristics, (i.e. cross-sectional area, shape, slope and channel roughness). The
combination of these effects has been the disignation control. A control is permanent if the stage
discharge relationship which it defines does not change with time; otherwise it is not permanent,
and is defined as a shifting control. The shifting control and its effects on the stage-discharge
relationship are of great importance in the operation of the hydrometric station and the
computation of runoff.
The rating curve is an equation which relates discharge to water level (stage). An often-used
equation has the form:

Q
kH
n
(6.15)
where Q is the discharge
H is the water stage
k and n are constants to be determined
If the zero of the water stage readings does not coincide with the bottom of the channel (i.e. zero
discharge) then the equation is written in the form:
Q
k  H  a

n
(6.16)
where a is the stage reading corresponding to zero discharge. However, this does not add any
extra complication since a will always be known in advance or has to be optimized.
Taking logarithms of both sides of the above equation gives:
Log (Q)

Log ( k )  nLog ( H )
(6.17)
which implies a linear relationship between the logarithms of Q and H. The constants, k and n
can be determined either
6-25
(a) Graphically, by plotting a graph of the log(Q) against Log(H) and fitting, by
the eye, a straight line to the points, or,
(b) Numerically, by using numerical optimization algorithm to find the values of
k and n which give the best fit to the given data. The least-squares method is often
used for this as it is the simplest to compute.
If the flow occasionally overtops the banks, a break is noticed in the stage-discharge relationship.
This may often be treated by fitting one equation to the data corresponding to flows within banks
and another equation to the flows above the bank full levels. Figure 6.13 shows the Q-H
relationship (rating curve).
Gauge Height (cm)
600
Discharge Rating curve
500
400
300
200
100
0
0
50
100
150
200
250
300
3
Discharge (m /s)
Figure 6.13 Discharge stage relationship (rating curve)
6.2..3.2 Factors affecting the rating curve
The factors affecting the rating curve are: unsteady flow, floods which overtop the banks,
backwater effects, aquatic growth and change in cross-section.
1.
A flow is unsteady if it changes with time so, by definition, most natural flows can be
considered to be unsteady. In some cases the flow changes so slowly that, for the purpose
of certain analyses, it can be considered approximately steady/uniform. In the case of
6-26
2.
3.
4.
unsteady flow, there may not be a unique relationship between discharge and stage. A
given value of stage, for example, may correspond to a certain discharge when the water
level is rising, at the beginning of a flood, and to a different, lower, discharge when the
water level is falling, after a flood. If a sufficient variety of flow conditions are included
in the measured data, this effect produces a “looped” curve when the data is plotted.
Please note that during the passage of a flood wave, the maximum discharge at any given
point occurs before the maximum stage.
When a flood discharge overtops the river banks, the relatively greater increase in crosssectional area of flow changes the relationship between stage and discharge. In this case a
separate stage-discharge relationship may be derived for within-banks flows and a
different relationship derived for the out-of-bank flows.
If the gauging station is affected by backwater from a lake, the level of which changes
more slowly than flows in the river, then the rating data may suggest a series of parallel
rating curves rather than a single unique relationship. If on the other hand, the backwater
effect changes as rapidly as the flows in the river, i.e. caused by a small lake, or reservoir,
or by a downstream river confluence, then it may be difficult to see any pattern in the
rating curve.
Weeds and mosses can change the stage-discharge relationship at a cross-section. These
usually have cyclical growth patterns and their effects may be seen in a greater variation
in the rating data fore low flows. This is because their influence is greatest for the
shallower flows. The change in river cross-section may be due to erosion, or deposition,
at either the channel bed of banks. It should cause a systematic change in the stagedischarge relationship. Infrequent measurements are required at every gauging station to
detect this type of change (check survey of gauging stations).
6.2.4 Sediment discharge measurement
6.2.4.1 Introduction
Sediment particles are transported by the flow in one or more of the following ways:Surface
creep
(a)
Saltation
(b)
Suspension
Surface creep is the rolling or sliding of particles along the channel bed. Saltation is the cycle of
motion above the bed with resting periods on the bed. Suspension involves the sediment particle
being supported by the water during its entire motion. Sediments transported by surface creep
6-27
and saltation are referred to as BED LOAD, and those transported by suspension are called
SUSPENDED LOAD. The suspended load consists of sands, silts and clays. The bed - material
load is the sum of bed load and suspended bed material load. Generally, the amount of bed load
transported by a large river is of the order of 5 to 25 percent of the suspended load.
The total sediment load in a channel is the sum of bed - material load and wash load. The bed material load is that part of the total sediment discharge which is composed of grain sizes found
in the bed. The wash load is that part composed of particle sizes finer than those found in
appreciable quantities in the bed. Engineers assume that bed material load size is equal to or
greater than 0.0625mm which is the division point between sand and silt. It is also assumed
that, most of the wash load is transported through the system by stream flow and little wash load
is deposited on or in the stream bed.
Sediment transport in overland flow occurs by sheet flow and through development of rills and
gullies. The eroding and transporting power of sheet flow is a function of flow depth and
velocity for a given size, shape and density of soil particles. The combined action of sheet flow
and raindrop splash contributes to total erosion.
The settling velocity of suspended particles in still water is approximated by stoke’s law:
vs

   w 

2 gr 2  s
9



(6.18)
Where s and w are densities of the particle and the liquid/water respectively, r is the radius of
the particle, g is the gravitational acceleration and  is the absolute viscosity of water. Generally
considered applicable to particles from 0.0002 to 0.2 mm in diameter.
In turbulent flow the gravitational settling of particles is counteracted by upward transport in
turbulent eddies. Since the concentration of suspended material is greatest near the bottom of
the stream, upward moving eddies carry more suspended sediment than downward moving
eddies. The system is in equilibrium if gravity movement and turbulent transport are in balance
and the amount of suspended sediment remains constant.
6.2.4.2 Methods of sediment measurement
Sediment is measured at the hydrometric station using sediment samplers. A good sediment
6-28
sampler must cause minimum disturbance of streamflow, avoid errors from short-period
fluctuations in sediment concentration and give results which can be related to velocity
measurements. Sediment samplers consist of a streamlined shield enclosing a glass bottle as a
sample container. A vent permits escape of air as water enters the bottle and controls the inlet
velocity so that it is approximately equal to the local stream velocity. Nozzle tips of various
sizes are available to control the rate at which the bottle fills. Large sediment sampler models
have the bottle fully enclosed and are fitted with tail vanes to keep it headed into the current
when cable-supported.
The sediment sampler is lowered through the stream at constant vertical speed until the bottom is
reached and is then raised to surface the at constant speed. The result is an integrated sample
with the relative quantity collected at any depth in proportion to the velocity at that depth. The
duration of the transverse is determined by the time required to nearly fill the sample bottle and
can be computed from the filling - rate curves for the particular nozzle when the stream velocity
is known. A number of transverse are made at intervals (similar to the discharge measurement
procedure) across the stream to determine the total suspended - sediment load for the section.
Point samplers are used only where it is impossible to use the depth - integrating type because of
great depths, high velocity or for studies of sediment distribution in streams. Since the nozzle of
the sediment sampler cannot be lowered to the streambed, this may represent a large error in
shallow streams. Figure 6.14 shows suspended sediment samplers.
The collected samples are filtered and the sediment dried. The ratio of dry weight of sediment to
total weight of the sample is the sediment concentration, usually expressed in parts per million or
milligram per liter. Other analyses that are performed include determination of grain-size
distribution, fall velocity and occasionally heavy-mineral or chemical analysis. Sediment
discharge measurements are given in tons/day.
Bed-load samplers are designed to rest on the streambed and thus trap the moving bed load
without disturbing the flow. Bed load samplers consist of boxes or bags of wire mesh with
supporting frame and a tail vane to keep the entrance pointed into the current. Permeable fabric
bags are used when the bed material consists of fine particles which would otherwise pass
through the wire mesh. Figure 6.15 shows the types of bedload samplers.
Devices which have been developed for continuous monitoring of sediment load in streams are:
pumping samplers, photocell probes etc. A significant limitation to much devices is that they
sample only one point in the cross section.
6-29
Figure 6.14 Suspended sediment samplers
6-30
Figure 6.15 Bed-load sediment samplers
6.2.4.3 Sediment water discharge relationship
Sediment measurements, like discharge measurements by current meters, give only occasional
samples of the sediment discharge. Since sediment is transported by water, there exists a
relationship between sediment discharge and water discharge. This relationship is unique for
each stream and is called a sediment-rating curve, relating suspended-sediment discharge and
water discharge. This relationship is commonly used to estimate load on days when no
measurements were taken. Figure 6. 16 shows the sediment rating curve for the Ruvu river at
Morogoro road bridge (Tanzania). The scatter of points in this figure shows that such relations
are only approximate. This is because a given river discharge may result from vegetation covers
and land uses occurring in different seasons. Rainfall storms of differing intensity, and thus a
different sediment load would result from each case. Rainfall storms occurring in different
seasons also produce different sediment load due to the different vegetation covers and land uses
occurring in different seasons. Therefore, sediment-rating curves should be used with caution
6-31
and where possible applied only to small and relatively homogeneous basins. However, when
they are used to estimate mean annual sediment yield, the errors in the sediment rating will tend
to compensate and the resulting answer should be reasonably satisfactory if a sufficiently long
record is used.
Figure 6.16 Water sediment discharge relationship (Ruvu river, Tanzania)
6.3 Hydrograph analysis
A runoff hydrograph is a response of a catchment due to rainfall. As soon as rainfall begins
there is an initial period of interception and infiltration before any measurable runoff reaches the
stream channel. During the period of rainfall these losses continue in a reduced form.
When the initial losses are met, surface runoff begins and continues to a peak value which occurs
at the time tp (measured from the centre of gravity of the rain graph of net rain). There after it
declines along the recession limb until it completely disappears. Meanwhile the infiltration and
percolation which have been continuing during the gross rainfall period elevates the groundwater
table which therefore contributes more at the end of the storm flow than at the beginning. But,
6-32
thereafter it again declines along its depletion.
Surface runoff is convenient assumed to contain two other components namely: Channel
precipitation and interflow.
The time to peak or lag time is defined as follows: from start of rainfall to peak flow center or
from center of rainfall to peak flow or from center of rainfall to center of runoff.
The time of concentration tc is the time required for a rainfall drop to travel from the remotest
part of the drainage basin to the gauging station or basin outlet. The time of concentration is not
necessarily equal to the lag time or time of peak.
For a given rainfall intensity (I) the proportion of rainfall which contributes to runoff increases
with time. Rising limb of a runoff hydrograph is influenced by:
a)
Area characteristics
b)
The effect of valley storage
c)
Infiltration capacity of catchment
d)
Pattern of rainfall intensity (I) which is normally non-linear and time variant.
The falling limb is influenced by: Storage characteristics in the basin which are made up of
surface and sub-surface storage. Since groundwater contribution to flood flow is quite different
in character from surface runoff it is normally analysed separately. The first requirement in
hydrograph analysis is to separate these two. In baseflow analysis, there are two cases to be
known.
1.
2.
Influent streams:
In Influent streams the channel bed is above the ground water table and therefore, the
river recharges the groundwater and thus the baseflow is negative i.e. the stream feeds the
under groundwater.
Effluent streams:
In Effluent streams the channel bed is below the groundwater table and therefore, the
groundwater contributes to the flow in the river and thus the groundwater contribution is
positive.
Rivers which dry up completely from time to time are called Emphemeral streams. Intermittent
streams are those which are both Influent and Effluent streams according to seasons contributing
6-33
baseflow during rainless periods in the wet season of the year but drying up completely in the
dry season. Perennial streams are mainly Effluent streams i.e. they never dry up and the flow
during the dry season is mainly due to baseflow.
6.3.1 Baseflow separation
Separation of baseflow can vary very widely. Detailed knowledge of geo-hydrology of the
catchment including areal extent of transmissibility of the aquifers is necessary to analyze its
precise position. It is more practical to use consistent baseflow separation technique. Figure 6.17
shows the baseflow separation techniques.
Figure 6. 17 Methods of baseflow separation
6-34
(a) Project the pre-storm baseflow under the peak. Draw the separation line rising from
beneath the peak to a point on the recession limb that is N days after the peak, where
N(days) = A0.2 (sq. Miles).
(b) Plot the hydrograph on a semi-logarithmic paper with discharge on the logarithmic
scale. Fit a straight line to the lower part of the recession limb on this paper and project it
backward under the peak. Transfer the values on this line to arithmetic graph paper.
Sketch a rising limb for the baseflow to meet the projected curve.
(c) Connect the discharge from the start of the rainstorm causing the flood hydrograph to
the start of the depletion curve. The depletion curve is the lower part of the recession
limps, which plots a straight line on semi-logarithmic paper.
6.3.2 Unit hydrograph
The theory of the unit hydrograph was introduced by Sherman in 1932. The method is based on
the assumption that the physical characteristics within a river basin (such as slope, size, drainage
network, etc.) do not change significantly, and consequently there should be a great similarity in
the shape of the hydrographs resulting from similar high intensity rainfalls. The unit hydrograph
is defined as the runoff of a catchment to a unit depth of effective rainfall (e.g. 1 cm) falling
uniformly in space and time during a period T (minute, hour, day). It should be noted that the
intensity of the rainfall during this period T is equal to 1/T in order to obtain unit depth. The
requirement of an effective precipitation falling uniformly in space limits the application of the
unit hydrograph theory to catchments smaller than 100 - 500 km2, since for larger basins the
assumption of a uniform distribution of the rainfall is hardly ever valid.
The specific period of time for the excess rainfall T is known as the ‘unit storm period’. For
small to medium sized drainage basins there is a certain unit storm period for which the shape of
the hydrograph is not significantly affected by changes in the time distribution of the excess
rainfall over this unit storm period. This means that equal depths of excess rainfall with different
time-intensity patterns produce hydrographs of direct runoff which are the same when the
duration of this excess rainfall is equal to or shorter than the unit storm period.
An example of a unit hydrograph is given in Figure 6.18, where the effective rainfall, Pe and the
unit hydrograph, DUH (Distribution Unit Hydrograph) are expressed in the same units: cm/d.
6-35
Figure 6.18 Unit hydrograph
Figure 6.19 Convolution hydrograph
6-36
The unit hydrograph has a length of 4 days. The memory of the rainfall-runoff system is 3 days,
since 3 days after the rain has stopped, the last rainfall excess comes to runoff. If the ordinates of
the DUH are expressed in the same unit as the rainfall excess, they should sum to one. This will
not be so if the ordinates convert unites from e.g. cm/d to m3/s.
The unit hydrograph theory is based on the following assumptions:
1. The rainfall-runoff system is linear: This means that the duration of the surface runoff is
constant for a given unit storm period, and the runoff is proportional to the effective rainfall
depth. Thus, for a rainfall intensity twice the unit depth, the ordinates of the unit hydrograph
have to be multiplied by two in order to obtain the corresponding surface runoff.
2. The principle of superposition applies: This is demonstrated with an example in Figure
6.19 for a rainstorm that lasts 3 days. The effective rainfall on these three days is 1, 3 and 2 mm,
respectively. The rainfall of the first day produces a runoff Q1 equal to the unit hydrograph
(DUH in figure 6.18). The rain of 3 mm on the second day produces a runoff Q2 starting on the
second day and with ordinates three times the unit hydrograph (principle of linearity above).
Finally the 2 mm rain on the third day results in a hydrograph Q3 with ordinates twice as large as
the DUH and starting on day 3. The principle of superposition means that the rainfall-runoff
relation of each day is independent of events on other days, so that the combined effect of the
three day rainstorm may be found by adding the runoff (Q1 + Q2 + Q3) produced by each single
day as shown on the bottom of figure 6.19. This process of computing the runoff for each time
step and the subsequent shifting and adding is known as convolution. The process of convolution
shown in Figure 6.19 is numerically worked out in Table 6.1
3: Time-invariance: This means that the unit hydrograph does not change with time. So, in
summer and winter, dry or wet season, the same direct runoff response to rainfall excess
applies.Thus if the rainfall-runoff system may be assumed linear and time-invariant, the unit
hydrograph may be convoluted with the effective rainfall to yield the direct runoff or surface
hydrograph, as demonstrated with an example in Table 6.1.
6-37
Derivation of the unit hydrograph
Graphically the derivation of the unit hydrograph would involve the following steps:
1.
Draw the full runoff hydrograph and separate the base flow
2
Determine the ordinates of the base flow and surface runoff
3.
Draw the hydrograph of surface runoff and calculate the volume/depth
4.
Calculate the runoff coefficient which, is usually expressed as follows:
k
5.

total
surface
runoff
total ra inf all
(6.19)
Let us say that the resulting runoff coefficient is 0.5 and that the total rainfall was 10 cm.
Therefore, the effective rainfall is equal to 5 cm. But the unit hydrograph is one which,
has a surface runoff contribution due to a unit of effective rainfall (i.e. 1cm) and not due
to 5 cm of effective rainfall.
6.
Therefore, we divide the ordinates of the surface runoff hydrograph by 5 to obtain the
respective ordinates of the unit hydrograph we require, for the duration of our interest or
specified duration.
Numerically the ordinates of the Unit Hydrograph can be solved from the set of of equations
presented in matrix form as show below:
The general expression for the set of equations relating the runoff ordinates (Q), unit hydrograph
ordinates (U) and effective rainfall ordinates (P) may be written as
Qn = ni-1UiPn-(i-1)
(6.20)
Where n is the total number of runoff ordinates which is determined from the expression
n = M + J –1
(6.21)
where M is the total number of rainfall ordinates and J is the total number of unit hydrograph
ordinates. It should be noted that Ui = 0 for i > J and Pi = 0 for i > M.
6-38
The set of equations may also be written in matrix form
Q=PU
(6.22)
from which U could be solved as QP-1. However, the inverse of matrix P can only be obtained if
P is a square matrix. Multiplying both sides of equation ?? by the transpose PT yields a square
matrix (PTP) for which the inverse exists. Hence
PT Q = PT P U
(6.23)
and the unknown vector U is found from
U = (PT P)-1 PT Q
(6.24)
The matrix inversion method is one of the methods to solve the unit hydrograph from a set of
rainfall-runoff data. Using a spreadsheet the matrix inversion method is available in the form of a
multiple linear regression. The above problem is considered to consist of 6 linear equations of
the type
Y = c1X1 + c2X2 + c3X3 + c4X4
(6.25)
where the dependent Y-variable is the discharge, the X-coefficients the ordinates of the unit
hydrograph and the independent X-variables the precipitation values.
Application of Unit hydrograph
Consider a rain storm lasting three 3 time steps (say days) for which the effective rainfall is
given by P1, P2 and P3. The unit hydrograph consists of 4 ordinates, U1, U2, U3 and U4. The
convolution procedure as explained in Table 6.1 may be written as follows.
6-39
Q1 = P1U1
Q2 = P2U1 + P1U2
Q3 = P3U1 + P2U2 + P1U3
Q4 = 0
+ P3U2 + P2U3 + P1U4
Q5 = 0
+0
+ P3U3 + P2U4
Q6 = 0
+0
+0
+ P3U4
(6.26)
Since Ui = 1 it follows that Qi = Pi thus the total of effective rainfall equals the surface
runoff. (The convolution procedure does not account for losses).
Table 6.1
Numerical example of the convolution procedure
Time
1
2
3
4
DUH
0.1
0.5
0.3
0.1
P
1
3
2
Q1
0.1
0.5
0.3
0.1
0.3
1.5
0.9
0.3
0.2
1.0
0.6
0.2
2.0
2.0
0.9
0.2
Q2
Q3
Q
0.1
0.8
5
6
7
0.0
It should also be noted that there are unit synthetic hydrographs which are derived from basin
characteristics.
6.4 Reservoir storage analysis
The major aim of evaluating the water resource is for planning purposes for the different water
uses. In summary, water resources evaluation is carried out for the purpose of, to name a few;
estimation of water requirements for hydro power generation, water supply for municipal and
industrial supply and for the operation of water resource schemes. The methods that are applied
in water resources evaluation are flow duration curve, mass curve analysis and the hydrologic
mass balance approach.
The yield of a basin is determined without storage and with storage. The water use in the basin is
first quantified and this can be for water supply, irrigation, hydro power generation or a
combination of the above uses. A major output of the river basin is a quantity of water per year
W delivered according to some seasonal schedule. If at is the fraction of W to be delivered in
month t, . then atW is the amount to be delivered in any month t and W is a single scalar
6-40
variable characterising the yield of the basin, at represents the fractional total yearly water
demand W required for month t (water use coefficients). In a river basin, the water demand
which can be provided with zero storage is:
at
I 
Min  t a 
t


W

 1,2,...12
(6.27)
12
Dt
12
D
t 1
t
and
a
t 1
t
1
(6.28)
t
where It is the river flow in month t. This is the diversion flow that could be diverted from the
river all year round without the need for a water storage facility.
6.4.1 Flow duration curve
Another approach of determining the diversion flow is to use the flow duration curve for that
basin. The most basic form of flow characteristics particularly for low flow investigation is the
flow duration curve. A flow duration curve shows graphically the relationship between any given
discharge and the percentage of time that discharge is equalled or exceeded. Flow duration
curves are constructed by counting the number of days, months or years with flows in various
class intervals. The selection of the time unit depends on the purpose of the curve.
If a project is for the diversion of water from a river without storage (say you want to pump
water daily to a town directly from the river), then the unit should be a day. This will indicate the
absolute minimum flows of the river. But for reservoir designs the month or even the year may
be sufficient , depending upon the size of the reservoir in relation to the inflow. Flow duration
curves are mostly used in preliminary water resource studies (determination of the diversion flow
and preliminary reservoir capacity) and for comparison of different rivers. Figure 6.20 shows the
flow duration curves for Zambezi and Rufiji rivers.
6-41
Flow Duration curves for Zam bezi and Rufiji rivers
4500
Discharge (m 3/s)
4000
3500
3000
2500
2000
1500
1000
500
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 10
% Time flow is exceeded or equalled
Rufiji river
Zambezi river
Figure 6.20 Flow duration curves for Zambezi and Rufiji Rivers
6.4.2 Mass Curve Analysis
A mass curve is constructed by plotting the accumulative monthly or yearly flows against time.
Figure 6.21 shows a diagram for a 4 year period. The slope of the mass curve at any time is a
measure of the inflow rate at that time. Demand curves are straight lines having a slope equal to
the demand rate which is uniform. Demand lines drawn tangent to the high points of the mass
curve (A,B) represent rates of withdrawal from the reservoir. Assuming the reservoir to be
full whenever a demand line intersects the mass curve, the maximum departure between the
demand line and the mass curve represents the reservoir capacity required to satisfy the
demand. It should be noted that the accumulative inflows have to be adjusted for evaporation
loss and required releases for downstream users. If the demand is not uniform, the demand line
becomes a curve i.e. a mass curve of demand, but the analysis remains the same. It is essential,
however that the demand line for non-uniform demand coincide chronologically with the mass
curve, i.e., June demand must coincide with June inflow. It should also be noted that a demand
line must intersect the mass curve when extended forward. If it does not, the reservoir will not
refill. Figure 6.22 shows a mass curve where the demand is non-uniform.
6-42
Figure 6.21 Mass curve for constant water demand
Figure 6.22 Mass curve diagram for non-uniform water demand.
6-43
REFERENCE
1.
2.
3.
4.
5.
Linsley, R.K., Kohler, M.A., and Paulhus, J.L.H. 1982. Hydrology for Engineers. 3 rd
edition McGraw-Hill Book Company, New York.
Musgrave, G.W. and Holtan, H.N. 1964. Infiltration. Section 12 in Handbook of Applied
Hydrology: Ven Te Chow editor, McGrwa-Hill Book Company, New York.
Shaw, E.M. 1983. Hydrology in practice. Van Nostrand Reinhold (U.K.).
Sherman, L.K. 1932. Streamflow from rainfall by the Unit-Graph method> Eng. NewsRec., Vol. 108.
Chow, V.T. Editor, 1964. Handbook of Applied Hydrology. McGraw-Hill Book
Company New York.
6-44
CHAPTER 6
EXERCISE
Question 1
Table 1 shows the current meter velocity measurements that were carried out for a certain river in
Tanzania. Calculate the discharge for the river at that particular time using the mean and the mid
section and compare the results.
Table 1. Current meter flow velocity measurements for a certain river in Tanzania
Vertical
Number
1
Distance from
bank (m)
1.22
Depth
(m)
0.29
V0.2
M/s
V0.6
(m)
0.095
V0.8
(m)
2
2.134
0.43
0.122
3
3.049
0.61
0.101
4
3.963
0.64
0.128
5
4.878
0.70
0.134
6
5.793
0.69
0.140
7
6.707
0.67
0.152
8
7.317
0.76
0.213
0.146
9
7.927
0.85
0.239
0.152
10
8.537
0.92
0.25
0.159
11
9.146
0.899
0.274
0.180
12
9.756
0.945
0.284
0.174
13
10.366
0.976
0.296
0.159
14
10.976
0.930
0.274
0.195
15
11.585
0.945
0.253
0.159
6-45
Question 2.
The stage-discharge data for a river has been collected and are presented in Table 2. The river
flow overtops the banks at a gauge height of 340.00 cm.
(a)
Establish the rating curve for the river (use linear and/or logarithms plots) and
comment on the suitability of the curves in the conversion of river stage into
discharge.
(b)
Use the least squares method to establish the rating equation which has the form:
Log(Q)
=
a + KlogH
Table 2. River discharge and corresponding river stage
Gauge height (cm)
Discharge (m3/s)
116
7.0
112
9.0
120
10.0
144
15.2
157
16.9
205
27.2
244
38.4
279
49.6
308
62.7
336
72.9
348
76.4
348
80.2
380
104.0
388
105.0
413
118.0
420
121.0
468
186.0
488
241.0
6-46
Question 3.
Use the information given in Table 3. to construct the flow duration curve and estimate the flow
that is available 50% of the time.
Table 3. Discharge values (m3/s) for a certain river in Swaziland
02/10/1959
03/10/1959
04/10/1959
05/10/1959
06/10/1959
07/10/1959
08/10/1959
09/10/1959
10/10/1959
11/10/1959
12/10/1959
13/10/1959
14/10/1959
15/10/1959
16/10/1959
17/10/1959
18/10/1959
19/10/1959
20/10/1959
21/10/1959
22/10/1959
23/10/1959
24/10/1959
25/10/1959
26/10/1959
27/10/1959
28/10/1959
29/10/1959
30/10/1959
31/10/1959
01/11/1959
02/11/1959
03/11/1959
04/11/1959
05/11/1959
06/11/1959
07/11/1959
08/11/1959
09/11/1959
10/11/1959
11/11/1959
2.89
2.92
4.02
4.96
3.74
3.26
3.26
3.26
3.11
3.00
2.94
3.00
3.03
3.06
3.03
2.83
2.66
3.26
5.95
6.23
7.08
5.66
5.27
4.96
4.73
4.19
3.82
3.23
3.11
3.11
3.03
3.40
3.96
4.25
3.82
3.45
3.43
3.45
4.96
5.10
4.59
02/01/1960
03/01/1960
04/01/1960
05/01/1960
06/01/1960
07/01/1960
08/01/1960
09/01/1960
10/01/1960
11/01/1960
12/01/1960
13/01/1960
14/01/1960
15/01/1960
16/01/1960
17/01/1960
18/01/1960
19/01/1960
20/01/1960
21/01/1960
22/01/1960
23/01/1960
24/01/1960
25/01/1960
26/01/1960
27/01/1960
28/01/1960
29/01/1960
30/01/1960
31/01/1960
01/02/1960
02/02/1960
03/02/1960
04/02/1960
05/02/1960
06/02/1960
07/02/1960
08/02/1960
09/02/1960
10/02/1960
11/02/1960
7.16
6.71
6.46
6.12
5.89
5.92
5.97
7.39
6.26
5.89
6.46
6.43
6.26
5.89
5.58
5.30
5.07
6.54
8.66
8.33
6.57
6.09
6.20
14.22
11.36
11.21
9.71
8.41
7.53
6.97
6.54
6.65
18.55
22.51
20.73
15.49
12.20
13.56
14.13
12.74
14.24
21/02/1960
22/02/1960
23/02/1960
24/02/1960
25/02/1960
26/02/1960
27/02/1960
28/02/1960
29/02/1960
01/03/1960
02/03/1960
03/03/1960
04/03/1960
05/03/1960
06/03/1960
07/03/1960
08/03/1960
09/03/1960
10/03/1960
11/03/1960
12/03/1960
13/03/1960
14/03/1960
15/03/1960
16/03/1960
17/03/1960
18/03/1960
19/03/1960
20/03/1960
21/03/1960
22/03/1960
23/03/1960
24/03/1960
25/03/1960
26/03/1960
27/03/1960
28/03/1960
29/03/1960
30/03/1960
31/03/1960
01/04/1960
14.53
13.93
14.70
14.22
13.51
13.65
12.88
11.38
10.79
10.42
9.91
9.26
8.86
8.64
8.41
8.10
7.96
7.79
7.50
7.31
7.02
6.77
6.74
6.97
14.78
15.69
13.37
10.56
9.09
10.56
8.78
8.35
8.07
7.87
7.59
7.45
7.19
7.14
7.05
6.91
6.80
6-47
12/11/1959
13/11/1959
14/11/1959
15/11/1959
16/11/1959
17/11/1959
5.10
5.66
8.78
9.06
10.99
10.19
12/02/1960
13/02/1960
14/02/1960
15/02/1960
16/02/1960
17/02/1960
15.74
16.74
16.48
14.36
12.54
11.47
02/04/1960
03/04/1960
04/04/1960
05/04/1960
06/04/1960
07/04/1960
8.66
7.84
7.67
6.97
6.71
6.46
Question 4.
Table 4 presents the monthly flows for a certain river in the USA (m3/s)
(a)
(b)
Draw the mass curve
Using the answer in (a) estimate the reservoir capacity for a constant demand rate
of 4.5x106 m3 per month
Table 4. Discharge values for a certain river in the USA (m3/s)
1961
1962
January
32.5
7.5
February
32.0
14.0
March
7.0
27.0
April
1.0
10.8
May
0.5
4.0
June
0.0
1.4
July
0.0
0.0
August
0.0
0.0
September
0.0
0.0
October
0.0
6.6
November
2.0
2.1
December
7.5
24.1
6-48