Stream Gauging

Stream GaugingStream Gauging

IntroductionIntroduction Stream flow is the largest operation among the Stream flow is the largest operation among the

various hydrologic networks. The necessity for various hydrologic networks. The necessity for stream gauging arises because of many reasons; stream gauging arises because of many reasons; streams provide water supply for men and streams provide water supply for men and animals, irrigation water for plants, dilution and animals, irrigation water for plants, dilution and transport for removal of waste, and energy for transport for removal of waste, and energy for production of power. Records of stream flow are production of power. Records of stream flow are important in each of these uses.important in each of these uses.

Water in streams can also be a hazard. Floods Water in streams can also be a hazard. Floods cause extensive damages and hardships. Records cause extensive damages and hardships. Records of flood events obtained at gauging stations serve of flood events obtained at gauging stations serve as the basis for the design of bridges, culverts, as the basis for the design of bridges, culverts, spillways, reservoirs, etc spillways, reservoirs, etc

River StageRiver Stage River stage is a term used in stream River stage is a term used in stream

gauging. It is the elevation of the water gauging. It is the elevation of the water surface at a specified station above some surface at a specified station above some arbitrary datum.arbitrary datum.

The zero elevation is some times taken as The zero elevation is some times taken as mean sea level but more often it is set mean sea level but more often it is set slightly below the point of zero in the slightly below the point of zero in the stream. stream.

The river stage is denoted by “g”. Fig 1 The river stage is denoted by “g”. Fig 1 shows definition sketch.shows definition sketch.

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River StageRiver Stage

Fig. 1

Channel ControlChannel Control This is another term often used in This is another term often used in

stream gauging. It is the reach of a stream gauging. It is the reach of a channel or a channel section where channel or a channel section where there is a unique relationship there is a unique relationship between stage and discharge. between stage and discharge.

There are two types of channel There are two types of channel control. control.

It may be an It may be an artificialartificial or or naturalnatural one. one.

Artificial ControlArtificial Control It is an amended section or length of stream for It is an amended section or length of stream for

measurement purposes. Examples are weir, measurement purposes. Examples are weir, flumes etc. flumes etc.

The design of an artificial control should be The design of an artificial control should be based on the following considerations.based on the following considerations. The profile of crest should be such that a small change The profile of crest should be such that a small change

in discharge indicates appreciable change in stage.in discharge indicates appreciable change in stage. The structure should not create undesirable The structure should not create undesirable

disturbance in the channel above or below the control.disturbance in the channel above or below the control. The control should have structural stability and should The control should have structural stability and should

be permanent.be permanent.

Selection of a Gauging SiteSelection of a Gauging Site The conditions regarding depth of water are The conditions regarding depth of water are

depending upon the physical features of the depending upon the physical features of the stream on the downstream side. stream on the downstream side.

The relation between stage and discharge is The relation between stage and discharge is controlled by the physical features of the controlled by the physical features of the channel downstream from the gauge site. channel downstream from the gauge site.

Essential requirements for stream gauging Essential requirements for stream gauging are:are: Permanence of controlPermanence of control Opportunity to install an artificial controlOpportunity to install an artificial control Possibility of no backwater effect from downstream Possibility of no backwater effect from downstream

tributaries or other sources.tributaries or other sources.

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Selection of a Gauging SiteSelection of a Gauging Site Availability of a good metering station where Availability of a good metering station where

good discharge measurement can be made.good discharge measurement can be made. Availability of a site for proper placement of Availability of a site for proper placement of

stage gauge to record all fluctuations of water stage gauge to record all fluctuations of water level and free from debris and floating matter level and free from debris and floating matter with respect to the control and the metering with respect to the control and the metering section.section.

Suitability of existing structures for use in Suitability of existing structures for use in making flood discharge measurements, or the making flood discharge measurements, or the availability of a site for the proper placement availability of a site for the proper placement of a cable way for this purpose.of a cable way for this purpose.

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Selection of a Gauging SiteSelection of a Gauging Site There is no possibility of flow bye-There is no possibility of flow bye-

passing the site in ground water or in passing the site in ground water or in flood channels.flood channels.

Availability of power line or telephone Availability of power line or telephone lines, where needed for special lines, where needed for special instrumentation.instrumentation.

Accessibility of the site by roads, Accessibility of the site by roads, particularly during floods.particularly during floods.

Economic construction is possible. Economic construction is possible.

Measurement of River Measurement of River StageStage

The river stage is measured by two The river stage is measured by two types of gauges.types of gauges. Non-recording gaugesNon-recording gauges Recording gauges.Recording gauges.

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Non-Recording Gauges:Non-Recording Gauges: The non-recording gauges are of three The non-recording gauges are of three

typestypes Staff gaugeStaff gauge Float type gaugeFloat type gauge Electric tape gaugeElectric tape gauge

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Staff GaugeStaff Gauge The staff gauges are further of the The staff gauges are further of the

following types.following types. Vertical Staff GaugeVertical Staff Gauge Sectional Staff GaugeSectional Staff Gauge Inclined Staff GaugeInclined Staff Gauge

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Staff GaugeStaff Gauge Vertical Staff GaugeVertical Staff Gauge

The simplest way to measure river The simplest way to measure river stage is by means of staff gauge. A stage is by means of staff gauge. A portion of the vertical staff gauge is portion of the vertical staff gauge is immersed in the water at all times. immersed in the water at all times.

The gauge may consist of a single The gauge may consist of a single vertical scale attached to a bridge pier, vertical scale attached to a bridge pier, or other structure that extends into the or other structure that extends into the low water channel of the stream. Figure low water channel of the stream. Figure 1 shows a typical vertical staff gauge.1 shows a typical vertical staff gauge.

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Fig. 1: Vertical Staff Gauge Continued….


Staff GaugeStaff Gauge Sectional Staff Gauge:Sectional Staff Gauge:

If no suitable structure exists in a If no suitable structure exists in a location, which is accessible at all location, which is accessible at all stages, a sectional staff gauge (as stages, a sectional staff gauge (as shown in figure 2) may be used. shown in figure 2) may be used.

Short sections of staff are mounted on Short sections of staff are mounted on available structures or on specially available structures or on specially constructed supports in such a way constructed supports in such a way that one section is always accessible.that one section is always accessible.

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Fig. 2: Sectional Staff Gauge Continued….


Staff GaugeStaff Gauge Inclined Staff GaugeInclined Staff Gauge

An alternative to the sectional staff gauge is An alternative to the sectional staff gauge is an inclined staff gauge as shown in the an inclined staff gauge as shown in the figure 3. figure 3.

Inclined staff gauge is placed on the slope of Inclined staff gauge is placed on the slope of the stream bank and graduated so that the the stream bank and graduated so that the scale reads directly in the vertical depth. scale reads directly in the vertical depth.

The inclined staff gauges are considered The inclined staff gauges are considered better than the sectional staff gauges due to better than the sectional staff gauges due to better accuracy.better accuracy.

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Fig. 3: Inclined Staff Gauge Continued….


Float Type GaugeFloat Type Gauge This gauge is generally used as an This gauge is generally used as an

inside reference gauge and is installed inside reference gauge and is installed in a stilling well to avoid wave effects. in a stilling well to avoid wave effects.

The stilling well is 1.20 m in diameter The stilling well is 1.20 m in diameter or with inner dimensions 1.20 m x 1.20 or with inner dimensions 1.20 m x 1.20 m. m.

It is built on side of a bank. A pipe It is built on side of a bank. A pipe connects well to river at its lowest level.connects well to river at its lowest level.

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The gauge consists of a float, graduated steel tape, The gauge consists of a float, graduated steel tape, counter weight and a pulley. The pulley is grooved counter weight and a pulley. The pulley is grooved to accommodate the tape and mounted on a stand. to accommodate the tape and mounted on a stand.

An arm extends from the stand to a point slightly An arm extends from the stand to a point slightly beyond the tape to carry an adjustable index, beyond the tape to carry an adjustable index, which shows the gauge reading. which shows the gauge reading.

The index is adjusted at the initial setting of the The index is adjusted at the initial setting of the gauge at the site. If the adjustments to the tape gauge at the site. If the adjustments to the tape readings are too large to be accommodated by the readings are too large to be accommodated by the adjustable index further adjustments can be made adjustable index further adjustments can be made with the help of a clamp connecting the tape to the with the help of a clamp connecting the tape to the float float

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Fig. 4: Float Type GaugeContinued….


Electric Tape GaugeElectric Tape Gauge It consists of a graduated steel tape, a It consists of a graduated steel tape, a

cylindrical weight, a reel for the tape, a cylindrical weight, a reel for the tape, a battery and voltmeter. battery and voltmeter.

One terminal of the battery is attached One terminal of the battery is attached to ground connection and the other to to ground connection and the other to one terminal of the voltmeter. one terminal of the voltmeter.

The other terminal of the voltmeter is The other terminal of the voltmeter is connected through the frame reel, and connected through the frame reel, and tape to the weight. The weight is tape to the weight. The weight is lowered until it touches the water lowered until it touches the water surface. surface. Continued….


This contact completes the electric This contact completes the electric circuit and produces a signal on the circuit and produces a signal on the voltmeter. The tape reading is then voltmeter. The tape reading is then taken at the index provided on the reel taken at the index provided on the reel mounting. mounting.

This gives river stage with respect to a This gives river stage with respect to a datum on the site. To find stage with datum on the site. To find stage with respect to another datum further respect to another datum further addition/subtraction will be required.addition/subtraction will be required.

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Recording Gauges:Recording Gauges: These are similar to the non-recording gauges but These are similar to the non-recording gauges but

have some arrangement to give a continuous have some arrangement to give a continuous record. In recording gauges motion of a float for record. In recording gauges motion of a float for example is recorded on a chart, and in a example is recorded on a chart, and in a continuous recorder, the motion of the float moves continuous recorder, the motion of the float moves a pen across a long strip chart. a pen across a long strip chart.

The chart is usually 25 cm wide and at a scale of The chart is usually 25 cm wide and at a scale of 1:12. When the pen reaches the edge of the chart 1:12. When the pen reaches the edge of the chart it is reverses direction and records the next it is reverses direction and records the next readings in the other directions across the chart. readings in the other directions across the chart.

The chart roll contains enough paper to operate The chart roll contains enough paper to operate for a year at a scale of 6 cm/day.for a year at a scale of 6 cm/day.

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A float type water stage recorder A float type water stage recorder requires a shelter house and stilling requires a shelter house and stilling well as shown in figure 4. well as shown in figure 4.

The stilling well serves to protect the The stilling well serves to protect the float and counter-weight cables from float and counter-weight cables from floating debris and if the intakes are floating debris and if the intakes are properly designed, suppress properly designed, suppress fluctuations resulting from surface fluctuations resulting from surface waves in the stream.waves in the stream.

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Crest - Stage GaugeCrest - Stage Gauge A third type of stage measuring device is the crest A third type of stage measuring device is the crest

gauge, used to obtain a record of flood crests at gauge, used to obtain a record of flood crests at sites where recording gauges are not installed. It sites where recording gauges are not installed. It gives the information about maximum water level in gives the information about maximum water level in the past.the past.

A variety of such gauges have been devised, A variety of such gauges have been devised, including small floats which rise with the increase including small floats which rise with the increase in stage but are restrained at the maximum level. in stage but are restrained at the maximum level. Water-soluble paints on bridge piers where they are Water-soluble paints on bridge piers where they are protected from rain and can indicate a definite high protected from rain and can indicate a definite high water mark are also in use as crest stage gauge. water mark are also in use as crest stage gauge.

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The piers of bridge are repainted after a The piers of bridge are repainted after a flood. The gauge used by U.S. geological flood. The gauge used by U.S. geological survey consists of a length of vertical pipe survey consists of a length of vertical pipe containing a graduated stick and a small containing a graduated stick and a small amount of ground cork. amount of ground cork.

The cork floats, as the water rises and some The cork floats, as the water rises and some adheres to the stick at the highest level adheres to the stick at the highest level reached by water. The stick can be removed, reached by water. The stick can be removed, the crest reading recorded, the cork wiped the crest reading recorded, the cork wiped off and the stick replaced ready for the next off and the stick replaced ready for the next reading. Fig 5 shows crest type staff guage.reading. Fig 5 shows crest type staff guage.

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Fig. 5

Discharge MeasurementDischarge Measurement Stream discharge represents the runoff phase Stream discharge represents the runoff phase

of the hydrologic cycle. Stream discharge can of the hydrologic cycle. Stream discharge can be measured more accurately than other be measured more accurately than other components of hydrologic cycle such as components of hydrologic cycle such as precipitation, evaporation, infiltration etc. precipitation, evaporation, infiltration etc.

In this section methods of measurement of In this section methods of measurement of discharge are described. Methods for discharge are described. Methods for determining discharge can be classified as.determining discharge can be classified as. Velocity area method (free flow method).Velocity area method (free flow method). Measurement by permanent structures.Measurement by permanent structures. Chemical gauging method Chemical gauging method

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Free Flow Method (Velocity Free Flow Method (Velocity Area Method)Area Method)

In these methods certain In these methods certain instruments are used to observe, the instruments are used to observe, the velocity in the stream, and the velocity in the stream, and the discharge is calculated from the data discharge is calculated from the data thus obtained. In this method the thus obtained. In this method the regime of the channel is not regime of the channel is not affected. i.e. for example depth affected. i.e. for example depth remains unaffected when instrument remains unaffected when instrument is inserted in stream is inserted in stream

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Also free flow method can be Also free flow method can be employed at any suitable section. employed at any suitable section.

The basic principle that Q =AV is The basic principle that Q =AV is used in this method.used in this method.

WhereWhereQ = Discharge Q = Discharge A = Area of cross-section of flow and A = Area of cross-section of flow and V = mean flow velocity. V = mean flow velocity.

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This needs measurement of mean velocity of This needs measurement of mean velocity of flow and the flow cross-sectional area. The flow and the flow cross-sectional area. The channel is divided in to sub-sections, the channel is divided in to sub-sections, the mean velocity and the area of flow is mean velocity and the area of flow is measured at each sub-section and finally the measured at each sub-section and finally the total discharge is the sum of the discharges total discharge is the sum of the discharges through these sub-sections.through these sub-sections.Q=qQ=q11+q+q22+q+q33+………………..+ q+………………..+ qnn - - - 1 - - - 1

Where Q is total discharge and qWhere Q is total discharge and qi i is discharge is discharge through a sub-section ‘i’ of stream.through a sub-section ‘i’ of stream.

Finding Mean Velocity:-Finding Mean Velocity:- The velocity in the free flow method The velocity in the free flow method

is found byis found by Current meter Current meter Pitot tubePitot tube Floats.Floats.

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Current MeterCurrent Meter A current meter is an instrument used to A current meter is an instrument used to

measure velocity of water in open channels or measure velocity of water in open channels or streams. One of the most commonly used streams. One of the most commonly used current meter is the Price Meter. current meter is the Price Meter.

This type of current meter is used by U.S. This type of current meter is used by U.S. geological survey. It consists of six conical geological survey. It consists of six conical cups rotating about a vertical axis. cups rotating about a vertical axis.

Electric contacts driven by the cups close a Electric contacts driven by the cups close a circuit through a battery and a wire of circuit through a battery and a wire of supporting cable, causes a click in supporting cable, causes a click in headphones worn by the operator for each 5 headphones worn by the operator for each 5 or 10 revolutions of cups. or 10 revolutions of cups.

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Current MeterCurrent Meter

For shallow depths wadding (depth measurement For shallow depths wadding (depth measurement by rods) is done and for measurements in deep by rods) is done and for measurements in deep water the meter is suspended from a cable. water the meter is suspended from a cable.

The meter reader is either in a boat or on a bridge. The meter reader is either in a boat or on a bridge. There is a heavy weight suspended at the bottom There is a heavy weight suspended at the bottom of this cable to keep the whole family vertical. of this cable to keep the whole family vertical.

The velocity of water is given asThe velocity of water is given asV = a + bN - - - - - - - - - - 2 V = a + bN - - - - - - - - - - 2

Where N is the number of revolutions per second Where N is the number of revolutions per second of cups and a , b are the coefficients for a given of cups and a , b are the coefficients for a given current meter current meter

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Current MeterCurrent Meter Following steps are adopted to take Following steps are adopted to take

measurements by the current meter.measurements by the current meter. Measuring depth of flow (sounding)Measuring depth of flow (sounding) Taking reading for “N”, the revolutions per second.Taking reading for “N”, the revolutions per second.

Figure 5 shows a photograph of current meter.Figure 5 shows a photograph of current meter.

Fig. 5. Price Current Meter Continued….


Measuring depth of flow (sounding)Measuring depth of flow (sounding) The depth is measured by a rigid rod called The depth is measured by a rigid rod called

wading rod or by a sounding weight wading rod or by a sounding weight suspended from a cable. The cable is suspended from a cable. The cable is controlled either by a reel fixed on a pulley controlled either by a reel fixed on a pulley or by hand line of a bridge. or by hand line of a bridge.

The wadding rod is placed in the stream so The wadding rod is placed in the stream so that the base plate rests on the stream bed that the base plate rests on the stream bed and the depth of water is read on the and the depth of water is read on the graduated main rod.graduated main rod.

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A sounding weight (Coulomb’s Weight) is A sounding weight (Coulomb’s Weight) is suspended below the current meter to keep it suspended below the current meter to keep it stationary in the water. stationary in the water.

The weights offer minimum resistance to The weights offer minimum resistance to flowing water and have sufficient weight not to flowing water and have sufficient weight not to be taken away by the water. be taken away by the water.

Reading is taken when the weights just touch Reading is taken when the weights just touch the water surface. These are further lowered the water surface. These are further lowered till these touch the base of the channel. The till these touch the base of the channel. The reading of reel is taken again. The difference of reading of reel is taken again. The difference of these readings gives the depth of flow.these readings gives the depth of flow.

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Current MeterCurrent Meter Methods of Measuring Average Velocity:-Methods of Measuring Average Velocity:-

There are four alternatives for current meter There are four alternatives for current meter readings. readings.

Single point MethodSingle point Method Two point MethodTwo point Method Multiple Point MethodMultiple Point Method Direct Integration MethodDirect Integration Method

To decide which method should be used, the To decide which method should be used, the governing factors aregoverning factors are

How much accuracy is required?How much accuracy is required? The time availableThe time available The behavior of streamThe behavior of stream

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Methods of Measuring Average VelocityMethods of Measuring Average Velocity Single Point Method:Single Point Method:

The current meter is placed at 0.6 of depth to find The current meter is placed at 0.6 of depth to find mean velocity. This is least time consuming method. mean velocity. This is least time consuming method. This is done when the depth of flow is less than 1 m. This is done when the depth of flow is less than 1 m.

The average velocity is denoted as V=VThe average velocity is denoted as V=V0.6d0.6d, Where V, Where V0.6d0.6d represents velocity at 0.6 of depth.represents velocity at 0.6 of depth.

Two point Method: Two point Method: The current meter is placed at two points. First the The current meter is placed at two points. First the

reading is taken at 0.2 of depth and then at 0.8 of the reading is taken at 0.2 of depth and then at 0.8 of the depth. This is more accurate than one point method. depth. This is more accurate than one point method.

The average velocity is mean of the velocity at 0.2 The average velocity is mean of the velocity at 0.2 depth and that at 0.8 depth. V= (Vdepth and that at 0.8 depth. V= (V0.2d0.2d +V +V0.8d0.8d)/2)/2

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Current MeterCurrent Meter Multiple Point Method: Multiple Point Method:

In this method current meter is placed at In this method current meter is placed at different points. Velocity at each point is different points. Velocity at each point is measured and then mean of these velocities measured and then mean of these velocities is taken. is taken.

This method is although accurate but is This method is although accurate but is very time consuming. very time consuming.

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Direct Integration Method:Direct Integration Method: This method is same as that at No. (3). In this method it This method is same as that at No. (3). In this method it

is essential that the worker should be an experienced is essential that the worker should be an experienced person. person.

The current meter is lowered from the surface to the The current meter is lowered from the surface to the bed of stream with the uniform velocity and from bed of bed of stream with the uniform velocity and from bed of channel to the surface with the same velocity. channel to the surface with the same velocity.

The number of revolutions made by the propeller is The number of revolutions made by the propeller is recorded and the dividing by time consumed in this recorded and the dividing by time consumed in this operation gives the mean velocity directly. operation gives the mean velocity directly.

The behavior of flow in channel is also an important The behavior of flow in channel is also an important factor. i.e. in case of unsteady flow where the discharge factor. i.e. in case of unsteady flow where the discharge is changing during the measurements as that in floods is changing during the measurements as that in floods etc, we have to use the quickest method.etc, we have to use the quickest method.

Methods of Holding Current Methods of Holding Current MeterMeter

Measurement By Wading Rods:Measurement By Wading Rods: The wading rod is placed in the stream so that The wading rod is placed in the stream so that

the base of the rod rests on the stream bed the base of the rod rests on the stream bed and the depth of water is read on the and the depth of water is read on the graduated main rod.graduated main rod.

The wading rod is used to hold the current The wading rod is used to hold the current meter when the depth of stream is not high meter when the depth of stream is not high and the stream section is known to be safe. and the stream section is known to be safe. For deep streams which are dangerous for For deep streams which are dangerous for wading the current meter is held by cable wading the current meter is held by cable having sounding weights.having sounding weights.

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When the depth is 0.45 to 0.75 m., then When the depth is 0.45 to 0.75 m., then the top setting rod (the position of the top setting rod (the position of Current meter should be at 0.6d and Current meter should be at 0.6d and velocity is then found and if depth is velocity is then found and if depth is more than 0.75 m, then at 0.2d and 0.8d more than 0.75 m, then at 0.2d and 0.8d the two velocities are found and the the two velocities are found and the mean velocity mean velocity

V=( V0.2d +V0.8d) ÷ 2V=( V0.2d +V0.8d) ÷ 2

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Measurement From Bridge:Measurement From Bridge: We can measure the depth of water from upstream We can measure the depth of water from upstream

as well as down stream side of the bridge. as well as down stream side of the bridge. On the upstream side the hydraulic characteristics On the upstream side the hydraulic characteristics

are usually more favorable, the approaching drift are usually more favorable, the approaching drift can be seen and avoided and the stream bed is less can be seen and avoided and the stream bed is less likely to scour. likely to scour.

On the other hand, on the down steam side On the other hand, on the down steam side vertical angles are more easily measured in case vertical angles are more easily measured in case the cable is not exactly vertical because of the the cable is not exactly vertical because of the sounding lines moving away from the bridge. sounding lines moving away from the bridge. Moreover, the flow lines may be straight.Moreover, the flow lines may be straight.

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The meter is suspended from a handrail The meter is suspended from a handrail of the bridge or a sounding reel of the bridge or a sounding reel supported by a bridge board or a supported by a bridge board or a portable crane, the latter is most portable crane, the latter is most commonly used. commonly used.

The method of measurement of depth The method of measurement of depth and velocity is same as discussed and velocity is same as discussed earlier. However the current meter is earlier. However the current meter is not used near the bridge piers and not used near the bridge piers and abutments.abutments.

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Measurements from a Cable-Way:Measurements from a Cable-Way: The cable way provides a track for the operation of The cable way provides a track for the operation of

a cable from which an observer takes measurement a cable from which an observer takes measurement on current meter. Cable also supports the sounding on current meter. Cable also supports the sounding reel and other necessary equipment. reel and other necessary equipment.

The car is moved from one point to another on the The car is moved from one point to another on the cable-way by means of rollers. As a rule of thumb cable-way by means of rollers. As a rule of thumb the size of the sounding weight in pounds should be the size of the sounding weight in pounds should be greater than the maximum product of velocity and greater than the maximum product of velocity and depth in the cross-section. depth in the cross-section.

The depth is measured by sounding reel and the The depth is measured by sounding reel and the velocity is measured by current meter.velocity is measured by current meter.

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Measurement From Boat:Measurement From Boat: If the cable- way and bridge are not available and the If the cable- way and bridge are not available and the

water depth is too deep to be waded, a boat is used. water depth is too deep to be waded, a boat is used. The measurement is made by first stretching the tag The measurement is made by first stretching the tag

line across the steam and then moving the boat at line across the steam and then moving the boat at each tag to take depth and velocity measurements. each tag to take depth and velocity measurements.

When the stream is very wide and the tag line can not When the stream is very wide and the tag line can not be used the boat can be kept in position at the cross-be used the boat can be kept in position at the cross-section by lining up with flags position on each end of section by lining up with flags position on each end of the cross - section. the cross - section.

The position of the boat is determined by a transit on The position of the boat is determined by a transit on the stand and a standard rod held in the boat.the stand and a standard rod held in the boat.

Pitot TubePitot Tube A pitot tube can also be used for measurement A pitot tube can also be used for measurement

of velocity in order to calculate discharge in of velocity in order to calculate discharge in laboratory flumes or very small streams. laboratory flumes or very small streams.

However the use of pitot tube may not be However the use of pitot tube may not be recommended for rivers due to following recommended for rivers due to following reason. Supporting the pitot tube is very reason. Supporting the pitot tube is very difficult when the channel is very wide and difficult when the channel is very wide and deep. deep.

The head generated by a pitot tube in open The head generated by a pitot tube in open channel is generally very small due to very low channel is generally very small due to very low velocities, and therefore discharge can not be velocities, and therefore discharge can not be accurately measured. accurately measured.

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Pitot TubePitot Tube

The use of pitot tube may however be The use of pitot tube may however be recommended for estimating discharge in recommended for estimating discharge in laboratory flumes and small channels. laboratory flumes and small channels.

The formula for calculating velocity is The formula for calculating velocity is V=(2gh)0.5 - - - - - - - - - 3V=(2gh)0.5 - - - - - - - - - 3

Where h is water height in tube above Where h is water height in tube above surface of water. It is the velocity head. surface of water. It is the velocity head. Fig 6 shows method of velocity Fig 6 shows method of velocity measurement by a pitot tube. measurement by a pitot tube.

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Pitot TubePitot Tube

FloatsFloats

This method consists of putting a float in This method consists of putting a float in the channel and noting the time and the channel and noting the time and distance covered by the float. distance covered by the float.

The velocity will be equal to the distance The velocity will be equal to the distance traveled in a unit time. i.e.traveled in a unit time. i.e.

V=S/t - - - - - 4V=S/t - - - - - 4 Where S is distance covered by float in Where S is distance covered by float in

time t.time t. A straight reach of the channel is to be A straight reach of the channel is to be

selected where the depth is nearly uniform. selected where the depth is nearly uniform. Following alternatives can be used to find Following alternatives can be used to find

average velocity average velocity Continued….

FloatsFloats Type-1 floats:Type-1 floats: The float is kept on the surface The float is kept on the surface

of water, specific distance and time is noted as of water, specific distance and time is noted as mentioned earlier. The velocity of float is mentioned earlier. The velocity of float is determined which is the velocity at the surface determined which is the velocity at the surface of water. The mean velocity then is about 0.85 of water. The mean velocity then is about 0.85 of surface velocity.of surface velocity.

Type-2 floats:Type-2 floats: Some weight is put in the water Some weight is put in the water attached with a flag kept above water surface, attached with a flag kept above water surface, the string length is so adjusted so that the the string length is so adjusted so that the weight is at a depth of 0.60 of total depth. This weight is at a depth of 0.60 of total depth. This directly gives the mean velocity.directly gives the mean velocity.

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FloatsFloats Type-3 floats:Type-3 floats: A hollow box is provided A hollow box is provided

at top. Canvas skirts are connected at top. Canvas skirts are connected with stiffening rings. The mean with stiffening rings. The mean velocity is found by the formula.velocity is found by the formula.

Vm = Vo (1.012 - 0.116 d/d1) - - - - - - - 5 Vm = Vo (1.012 - 0.116 d/d1) - - - - - - - 5 Vm = Mean velocity, Vm = Mean velocity, Vo = Observed velocity, d=Total depthVo = Observed velocity, d=Total depth d1= Clearance of lower edge of float from the d1= Clearance of lower edge of float from the

bed of channel bed of channel

Processing field data & Processing field data & calculation of dischargecalculation of discharge

Mid-Section Method of Estimating Mid-Section Method of Estimating DischargeDischarge The following data is required for The following data is required for

estimation of discharge by mid-section estimation of discharge by mid-section method:method:

Location of sampling points 1, 2, 3,...., n across Location of sampling points 1, 2, 3,...., n across the stream in reference to the distance from the stream in reference to the distance from an initial point on one of the banks. Say ban initial point on one of the banks. Say b11, b, b22, , bb33,.........,b,.........,bnn are the distances from the initial are the distances from the initial point to the observation points 1, 2, 3,...., n point to the observation points 1, 2, 3,...., n

Continued….

Processing field data & Processing field data & calculation of dischargecalculation of discharge Stream depth d, at each observation point. Stream depth d, at each observation point.

Say dSay d11, d, d22, d, d33,.........,d,.........,dnn represent depths of represent depths of water at observation point to the water at observation point to the observation points 1, 2, 3,...., n observation points 1, 2, 3,...., n

Mean stream velocity perpendicular to the Mean stream velocity perpendicular to the cross-section at each observation point.1, cross-section at each observation point.1, 2, 3,......, n (observation points)2, 3,......, n (observation points)

Continued….


With the above information being known, the With the above information being known, the partial discharge can be computed for any partial partial discharge can be computed for any partial section at location ‘i’ as qsection at location ‘i’ as qii= d= dii V Vii ( b ( bii -1 +b -1 +b ii+1 )/2 +1 )/2 WhereWhere q q ii = = discharge through partial discharge through partial section isection i

VVii = = Mean velocity at location “i”Mean velocity at location “i”bbii = = distance from initial point to location “i”distance from initial point to location “i”bbii-1=-1= distance from initial point to location i-1 .distance from initial point to location i-1 .bbii+1=+1= distance from initial point to location i+1.distance from initial point to location i+1.ddii = = depth of water at location “i”.depth of water at location “i”.

Continued….


The discharge at first section 1 and The discharge at first section 1 and last section n are calculated last section n are calculated separately as follows separately as follows qq11= d= d11 V V11 ( b ( b11 +b +b 22 )/2 - - - - - - - 6 )/2 - - - - - - - 6 qqnn= d= dnn V Vnn ( b ( bnn +b +b nn+1 )/2 - - - - - 7+1 )/2 - - - - - 7

The total dischargeThe total discharge Q = qQ = q11+ q+ q22+ q+ q33+………+ q+………+ qnn - - - 8 - - - 8

Essential Requirements for Essential Requirements for Good Discharge MeasurementGood Discharge Measurement

The essential requirements for good The essential requirements for good discharge measurement are;discharge measurement are; Keep the current meter clean and properly oiled Keep the current meter clean and properly oiled

to reduce the friction losses.to reduce the friction losses. The stream cross-section should be sub-divided The stream cross-section should be sub-divided

into as small sub-sectors as possible (15-20 sub-into as small sub-sectors as possible (15-20 sub-stations). If this requirement causes verticals to stations). If this requirement causes verticals to be less than 0.15 m. then increase the spacing be less than 0.15 m. then increase the spacing accordingly. accordingly.

Use the average of velocities at 0.2 and 0.8 of Use the average of velocities at 0.2 and 0.8 of the depth when the depth is greater than 0.60 m the depth when the depth is greater than 0.60 m otherwise take a single measurement at 0.6 otherwise take a single measurement at 0.6 times the depth.times the depth.

Continued….

Essential Requirements for Essential Requirements for Good Discharge MeasurementGood Discharge Measurement Keeping the meter clean of floating materials by raising Keeping the meter clean of floating materials by raising

the meter out of water to let the debris pass by.the meter out of water to let the debris pass by. When using the wading rod keep it vertical and keep When using the wading rod keep it vertical and keep

your feet 0.45 – 0.60 meters down stream from the your feet 0.45 – 0.60 meters down stream from the meter.meter.

Read and record the river stage from an auxiliary staff Read and record the river stage from an auxiliary staff gauge periodically during the discharge measurement. gauge periodically during the discharge measurement.

If the stage begins to change by greater than 5% the If the stage begins to change by greater than 5% the procedure may be speeded up by procedure may be speeded up by

Decreasing the sounding time. Decreasing the sounding time. Reducing the number of verticals.Reducing the number of verticals.

Continued….


Example 1Example 1 Compute the stream flow for the measurement data Compute the stream flow for the measurement data

given below columns 1 to 5 of table 1 below. Take given below columns 1 to 5 of table 1 below. Take the meter rating from equation. V= a+bN with the meter rating from equation. V= a+bN with a=0.03 and b=0.66 a=0.03 and b=0.66

SolutionSolution AsAs V = a + bNV = a + bN So V = 0.03 + 0.66 NSo V = 0.03 + 0.66 N V is in m/s and N is in revolutions/s. Using this the V is in m/s and N is in revolutions/s. Using this the

following calculations in columns 6 to 11 of Table 1 following calculations in columns 6 to 11 of Table 1 below are made. Find the discharge using Mid-below are made. Find the discharge using Mid-Section method.Section method.

Continued….

Essential Requirements for Essential Requirements for Good Discharge Good Discharge MeasurementMeasurement

Distance Distance from bankfrom bank

Depth Depth (m)(m)

Meter Meter DepthDepth

Revol-Revol-utions.utions. TimeTime NN Velocity at Velocity at

pointpointMean in Mean in verticalvertical

Width of Width of sub-sub-

sectionsectionAreaArea Disc-hargeDisc-harge

(m)(m) (m)(m) (m)(m) (Sec)(Sec) (Rev./s)(Rev./s) (m/s)(m/s) (m/s)(m/s) (m)(m) (m²)(m²) (m³/s)(m³/s)

(1)(1) (2)(2) (3)(3) (4)(4) (5)(5) (6)(6) (7)= a+bN(7)= a+bN (8)(8) (9)(9) (10)=(2)(10)=(2)x(9)x(9)

(11)= (8) x (11)= (8) x (10)(10)

0.600.60 0.300.30 0.180.18 1010 5050 0.200.20 0.1620.162 0.1620.162 0.600.60 0.180.18 0.030.03

1.201.20 1.051.05 0.840.84 2222 5555 0.400.40 0.2940.294 0.3840.384 0.600.60 0.630.63 0.2420.242

0.210.21 3535 5252 0.670.67 0.4740.474

1.801.80 1.561.56 1.261.26 2828 5353 0.530.53 0.3790.379 0.4320.432 0.600.60 0.940.94 0.4040.404

0.30.3 4040 5858 0.690.69 0.4850.485

2.702.70 1.891.89 1.51.5 3232 5858 0.550.55 0.3940.394 0.4600.460 0.600.60 1.1341.134 0.5210.521

0.390.39 4545 6060 0.750.75 0.5250.525

3.303.30 1.321.32 1.151.15 2828 4545 0.620.62 0.4410.441 0.4720.472 0.600.60 0.7920.792 0.3740.374

0.270.27 3333 4646 0.720.72 0.5030.503

3.903.90 0.660.66 0.390.39 2222 5050 0.440.44 0.3200.320 0.3200.320 0.600.60 0.3960.396 0.1270.127

4.504.50 0.240.24 0.150.15 1212 4949 0.240.24 0.1920.192 0.1920.192 0.600.60 0.1440.144 0.0280.028

5.105.10

TotalTotal 4.2124.212 1.7261.726

Table 1: Computations for Current Meter Observations


Q = 1.726 m³/sQ = 1.726 m³/s Total area, A= 4.212 m²Total area, A= 4.212 m² Average velocity = V = (Q/A) Average velocity = V = (Q/A) = (1.726/4.212) = (1.726/4.212) = 0.41 m/sec= 0.41 m/sec Average depth (hydraulic depth) “D” Average depth (hydraulic depth) “D” = AREA / TOP = AREA / TOP

WIDTH WIDTH = 4.212/5.10= 4.212/5.10 = 0.826 m= 0.826 m

Continued….

Essential Requirements for Essential Requirements for Good Discharge MeasurementGood Discharge Measurement Example 2 Example 2

From the data given in columns 1 to 4 of the table 2 below find From the data given in columns 1 to 4 of the table 2 below find discharge.discharge.

Table 2 Calculation of DischargeTable 2 Calculation of DischargeDistance Distance

from bankfrom bank Depth (m)Depth (m) Mean Mean VelocityVelocity

Width of Width of sub-sectionsub-section AreaArea DischargeDischarge

(m)(m) (m)(m) (m/s)(m/s) (m)(m) (m²)(m²) (m³/s)(m³/s)

0.000.00 0.000.00 1.001.00 0.000.00 0.000.00 0.000.00

2.002.00 0.500.50 2.502.50 2.002.00 1.001.00 2.502.50

5.005.00 2.002.00 3.003.00 4.504.50 9.009.00 27.0027.00

8.008.00 2.502.50 3.003.00 6.006.00 15.0015.00 45.0045.00

11.0011.00 2.402.40 3.003.00 6.006.00 14.4014.40 43.2043.20

14.0014.00 1.501.50 3.003.00 4.004.00 6.006.00 18.0018.00

17.0017.00 1.001.00 3.503.50 2.002.00 2.002.00 7.007.00

21.0021.00 0.500.50 2.002.00 1.001.00 0.500.50 1.001.00

TotalTotal 47.9047.90 143.70143.70

Q = 143.7 m³/s

Chemical Gauging Method Chemical Gauging Method (Dilution Method)(Dilution Method)

This method is particularly useful when plenty of This method is particularly useful when plenty of turbulence exist in the flow and the measurement turbulence exist in the flow and the measurement of discharge by current-meter is not feasible. of discharge by current-meter is not feasible.

The situation may include a weir, or a fall, a sharp The situation may include a weir, or a fall, a sharp bent or turbine. A reach in which hydraulic jump bent or turbine. A reach in which hydraulic jump is taking place, is most appropriate. is taking place, is most appropriate.

In this method one section is selected upstream In this method one section is selected upstream and other at down stream end of the reach of and other at down stream end of the reach of channel. channel.

The upstream section is called the “dosing The upstream section is called the “dosing section” and down-stream end is called sampling section” and down-stream end is called sampling section. section.

Continued….


At the dosing section some soluble chemical At the dosing section some soluble chemical salt made up to a known concentration is fed salt made up to a known concentration is fed into the stream at a measured rate. into the stream at a measured rate.

By the time the flow reaches the sampling By the time the flow reaches the sampling section the salt solution is properly mixed section the salt solution is properly mixed with the whole flow. with the whole flow.

Samples of water are drawn from the Samples of water are drawn from the sampling section from the down-stream sampling section from the down-stream section and are analyzed for the quantity of section and are analyzed for the quantity of salt. salt.

There are two alternatives for injection;There are two alternatives for injection; Sudden injection Sudden injection Injection at constant rate.Injection at constant rate.

Continued….


Sudden Injection.Sudden Injection. In this method a know volume “V” of the In this method a know volume “V” of the

dosing solution or tracer is added to the dosing solution or tracer is added to the stream as rapidly as possible. stream as rapidly as possible.

The concentration at the sampling point The concentration at the sampling point rises rapidly to a peak and then slowly rises rapidly to a peak and then slowly diminishes. diminishes.

Samples are then taken at regular intervals Samples are then taken at regular intervals of time and chemical concentration is of time and chemical concentration is determined in laboratory. determined in laboratory.

Continued….


A concentration-time curve is then drawn. Discharge ‘Q’ is A concentration-time curve is then drawn. Discharge ‘Q’ is

dtV

Q t

toCC

C

2

12

1

dtt

toCC

2

12

= area under the concentration-time curve

V = Volume of injected solutionC1 = Concentration of chemical in dozing solution.Co = Conc. of chemical already existing in stream water C2 = Conc. of chemical in water at sampling point.

Continued….


Constant rate of Injection.Constant rate of Injection. In this method the dosing of the In this method the dosing of the

chemical or any other tracer has to be chemical or any other tracer has to be continued at a constant, pre-determined continued at a constant, pre-determined rate say q until the concentration of the rate say q until the concentration of the chemical is constant at the sampling chemical is constant at the sampling point down stream where mixing is point down stream where mixing is adequate adequate

Continued….


The discharge is given asThe discharge is given asQ = q (CQ = q (C11 – C – C22 ) / (C ) / (C22 – C – Coo ) - - - - - - - 10 ) - - - - - - - 10

Where Co = Concentration of chemical already Where Co = Concentration of chemical already existing in flowing fluid of streamexisting in flowing fluid of stream

Q = Q = NCNC3q3q - - - -- - - - - - - - - - - - - - - 11 - - - -- - - - - - - - - - - - - - - 11 CC22

q = Constant rate of injection of chemicalq = Constant rate of injection of chemicalCC22 = Concentration of chemical in water at sampling point = Concentration of chemical in water at sampling pointCC3 3 = Difference in concentration at dozing and sampling = Difference in concentration at dozing and sampling

pointpoint The sampling point is determined on the basis of The sampling point is determined on the basis of

mixing length. Formulae have been given by mixing length. Formulae have been given by various researchers for mixing length.various researchers for mixing length.

Continued….


Example 3: Example 3: A 30 g/l solution of a chemical was discharged into a A 30 g/l solution of a chemical was discharged into a

stream at a constant rate of 10x10-6 m3/sec. The same stream at a constant rate of 10x10-6 m3/sec. The same chemical was not found in stream water at all. The chemical was not found in stream water at all. The concentration of chemical at sampling section was found to concentration of chemical at sampling section was found to be 5000 parts per million. Estimate the stream discharge.be 5000 parts per million. Estimate the stream discharge.

SolutionSolutionFrom Equation 10, we haveFrom Equation 10, we haveQ = q(C1 – C2 )/ (C2 – Co )Q = q(C1 – C2 )/ (C2 – Co )q = 10x10-6 m3/sec.q = 10x10-6 m3/sec.C1 = 30g/l=0.030 g/mlC1 = 30g/l=0.030 g/mlC2 = 5000 parts per million = 0.005x10-6 g/ml C2 = 5000 parts per million = 0.005x10-6 g/ml Co = 0 Co = 0 Q = [10x10-6 x (0.03-5x10-9)]÷( 5x10-9 )= 60 m3/sec. Q = [10x10-6 x (0.03-5x10-9)]÷( 5x10-9 )= 60 m3/sec.

Discharge Measurement By Discharge Measurement By Permanent StructuresPermanent Structures

Permanent structures for the measurement of Permanent structures for the measurement of discharge are built at the sites where regular discharge are built at the sites where regular discharge measurements are required. discharge measurements are required.

Structures built for other purposes may also Structures built for other purposes may also be used. i.e. spillways of dam, or a fall, or a be used. i.e. spillways of dam, or a fall, or a barrage. barrage.

This may be a masonry structure built in the This may be a masonry structure built in the bed of the channel across the flow. The bed of the channel across the flow. The height is so designed that for all possible height is so designed that for all possible discharges in the channel. discharges in the channel.

The depth over the sill remains the critical The depth over the sill remains the critical depth, as such a hydraulic jump must form depth, as such a hydraulic jump must form down stream of the structure say weir.down stream of the structure say weir.

Continued….


If “H” is the head over the weir just If “H” is the head over the weir just upstream of the weir, “V”, is the critical upstream of the weir, “V”, is the critical velocity “yvelocity “ycc” is the critical depth, on ” is the critical depth, on neglecting the approach velocity and neglecting the approach velocity and applying energy equation. (In MKS applying energy equation. (In MKS system)system)Q = CQ = Cd d 1.7BH1.7BH1.5 1.5 - - - - - - - - - - - 12 - - - - - - - - - - - 12

Where Where B = width of weir, B = width of weir, CCdd = Co-efficient of discharge = Co-efficient of discharge

Continued….


Example 4: Example 4: Depth of water just upstream of a broad crested Depth of water just upstream of a broad crested

weir was measured to be 0.5 m in a 10m wide weir was measured to be 0.5 m in a 10m wide channel. Find discharge. The height of weir was channel. Find discharge. The height of weir was 0.2 m0.2 m

SolutionSolution Given DataGiven Data

Head avove weir crest = H =0.5-0.2 = 0.3 mHead avove weir crest = H =0.5-0.2 = 0.3 mCd = Co-efficient of discharge = 0.60Cd = Co-efficient of discharge = 0.60B = Width of weir = 10 mB = Width of weir = 10 mQ = 0.6x1.7x10x(0.3)1.5 = 1.676 m³/sQ = 0.6x1.7x10x(0.3)1.5 = 1.676 m³/s

The coefficient of discharge depends on type The coefficient of discharge depends on type of weir structure.of weir structure.

Stage & Discharge Stage & Discharge Relationship (Rating Curve)Relationship (Rating Curve)

The graphical curve between stage and The graphical curve between stage and discharge is called the stage-discharge discharge is called the stage-discharge curve or rating curve. curve or rating curve.

The rating curve is nothing but the graph The rating curve is nothing but the graph giving the relation between stage and giving the relation between stage and discharge. discharge.

Stage is plotted along y-axis and discharge Stage is plotted along y-axis and discharge is plotted along x-axis.is plotted along x-axis.

The shape of rating curve looks like The shape of rating curve looks like parabola.parabola.

Continued….


The stage discharge rating depends upon The stage discharge rating depends upon the channel control. For a permanent the channel control. For a permanent control this relation may be applicable for control this relation may be applicable for years.years.

It may be necessary to take at least three It may be necessary to take at least three discharge measurements in a week to discharge measurements in a week to check the rating curve because of random check the rating curve because of random shifting of the stream channel particularly shifting of the stream channel particularly during flood season during flood season

Continued….


There may be three types of rating curve There may be three types of rating curve for any type of river.for any type of river. Low Flow Rating Curve:-Low Flow Rating Curve:-

It is the most frequently occurring. It is the most frequently occurring. Intermediate Flow Rating Curve:-Intermediate Flow Rating Curve:-

It is the stage between a flood and low flows.It is the stage between a flood and low flows. High flow Rating Curve:High flow Rating Curve:

This occurs in high flood days, so is for rarely This occurs in high flood days, so is for rarely occurring situation. Because of this, it is often occurring situation. Because of this, it is often represented by dotted lines and is obtained by represented by dotted lines and is obtained by extension of low flow rating curve.extension of low flow rating curve.

Not all rating curves are divided into three Not all rating curves are divided into three segments. This division is purely artificial.segments. This division is purely artificial.

Extension of Rating CurveExtension of Rating Curve The most important use of the stage discharge The most important use of the stage discharge

rating curve is obtaining discharge for any rating curve is obtaining discharge for any measured stage. measured stage.

Because of infrequency of floods it may seldom be Because of infrequency of floods it may seldom be practicable to obtain correct rating curve for high practicable to obtain correct rating curve for high flows.flows.

Some times due to unprecedented floods the stage Some times due to unprecedented floods the stage may be so high that it may not be possible to get may be so high that it may not be possible to get the discharge from the original rating curve.the discharge from the original rating curve.

So we need an extension of the rating curve to So we need an extension of the rating curve to obtain discharge during high stage floods. obtain discharge during high stage floods.

Continued….

Extension of Rating CurveExtension of Rating Curve Special methods have to be used to extend Special methods have to be used to extend

the original rating curve to extrapolate the the original rating curve to extrapolate the discharge corresponding to the measured discharge corresponding to the measured high stage.high stage.

The most reliable method would be the one The most reliable method would be the one which straightens the approximated which straightens the approximated parabolic rating curve for the convenience parabolic rating curve for the convenience of its extension.of its extension.

The most commonly used methods which The most commonly used methods which comply with this condition arecomply with this condition are The Logarithmic Method The Logarithmic Method A√D Method A√D Method Slope area Method.Slope area Method.

Continued….

Extension of Rating CurveExtension of Rating Curve

The Logarithmic Method:The Logarithmic Method: This method is used if the cross section of This method is used if the cross section of

the stream at the gauging station is of a the stream at the gauging station is of a regular shape and there is no possibility of regular shape and there is no possibility of getting a number of straight lines of getting a number of straight lines of varying slopes. varying slopes.

In general In general Q = C (g-a) n - - - - - - 13Q = C (g-a) n - - - - - - 13

where (g-a) is the actual water depth and where (g-a) is the actual water depth and “a” is the vertical distance between the “a” is the vertical distance between the zero flow and zero datum. C and n are any zero flow and zero datum. C and n are any constants.constants. Continued….


Now taking “log” on both sidesNow taking “log” on both sideslog Q = log C(g-a)n = log C+ log (g-a)nlog Q = log C(g-a)n = log C+ log (g-a)nlog Q = log C + n log (g-a) - - - - - - - 14log Q = log C + n log (g-a) - - - - - - - 14

The equation (14) is the equation of a straight line The equation (14) is the equation of a straight line with Log C being the intercept and “n” the slope.with Log C being the intercept and “n” the slope.

In this equation the zero gauge height “a” is In this equation the zero gauge height “a” is determined by assuming the various values of ‘a” determined by assuming the various values of ‘a” until log Q” when plotted against log (g-a), forms a until log Q” when plotted against log (g-a), forms a straight line. straight line.

This straight line can then be extended to This straight line can then be extended to extrapolate discharge corresponding to the extrapolate discharge corresponding to the measured gauge height.measured gauge height.

Continued….

Extension of Rating CurveExtension of Rating Curve A√D MethodA√D Method

This method is based on the Chezy’s This method is based on the Chezy’s formulaformula

Q = AC√RS - - - - - - - - 15Q = AC√RS - - - - - - - - 15wherewhere

C =C = roughness coefficient (Chezy’s roughness coefficient (Chezy’s Constant)Constant)

S =S = Slope of energy lineSlope of energy lineA =A = Cross sectional areaCross sectional areaR =R = Hydraulic radius Hydraulic radius

Continued….

Extension of Rating CurveExtension of Rating Curve If C√S is assumed to be constant for the If C√S is assumed to be constant for the

station and “D” the mean depth is station and “D” the mean depth is substituted for “R”, only when the substituted for “R”, only when the section is wide, thensection is wide, then

Q = K A √D - - - - - - - - - 16Q = K A √D - - - - - - - - - 16 This can be explained as follows:This can be explained as follows: If the stream is assumed to be a large If the stream is assumed to be a large

rectangular channel (wide channel), thenrectangular channel (wide channel), thenR = A/P = Bxy/(B+2y) (where P = Wetted R = A/P = Bxy/(B+2y) (where P = Wetted

perimeter)perimeter)

Continued….

Extension of Rating CurveExtension of Rating Curve For a wide channel ‘2y’ can be neglected.For a wide channel ‘2y’ can be neglected.

R = A/P = Bxy/(B+2y) ≈ y = DR = A/P = Bxy/(B+2y) ≈ y = DQ = K A√DQ = K A√Dor Q α A√D or Q α A√D

Knowing the values of Q and A we can plot a Knowing the values of Q and A we can plot a graph and get a straight line, which may be graph and get a straight line, which may be extended. extended.

Values of A for stages above the existing rating Values of A for stages above the existing rating can be obtained by field measurements and can be obtained by field measurements and used with the extended curve for estimates of used with the extended curve for estimates of Q.Q.

Continued….

Extension of Rating CurveExtension of Rating Curve Slope Area MethodSlope Area Method

This method of estimating high flows is by This method of estimating high flows is by application of hydraulic principles. Sufficient application of hydraulic principles. Sufficient high water marks must be located along a high water marks must be located along a reach of channel to determine water surface reach of channel to determine water surface slope at the time of peak.slope at the time of peak.

Cross sections of the channel may be Cross sections of the channel may be determined by leveling or sounding, and the determined by leveling or sounding, and the area and hydraulic radius calculated. area and hydraulic radius calculated.

The Chezy-Manning formula is ordinarily used The Chezy-Manning formula is ordinarily used to calculate discharge. to calculate discharge.

Continued….


Manning’s Formula is different for both Manning’s Formula is different for both M.K.S. & F.P.S.M.K.S. & F.P.S.Q = A(1/n) R2/3√SfQ = A(1/n) R2/3√Sf (M.K.S) - - - - - - 17(M.K.S) - - - - - - 17Q = A(1.49/n) R2/3√Sf Q = A(1.49/n) R2/3√Sf (F.P.S) - - - - - - - (F.P.S) - - - - - - - 1818A = Area of cross section,A = Area of cross section, Sf = Frictional Sf = Frictional slopeslopen = Manning’s Constant ,n = Manning’s Constant , R= Hydraulic R= Hydraulic RadiusRadius

Continued….

Extension of Rating CurveExtension of Rating Curve The main source of error in applying The main source of error in applying

this equation is in estimating the this equation is in estimating the roughness coefficient “n”. roughness coefficient “n”.

Since Q depends upon 1/n and the Since Q depends upon 1/n and the average value of “n” for natural stream average value of “n” for natural stream is about 0.035, an error of 0.001 in “n” is about 0.035, an error of 0.001 in “n” represents about 3% in discharge.represents about 3% in discharge.

Under the most favorable conditions an Under the most favorable conditions an error of 10% may be expected in a slope error of 10% may be expected in a slope area estimate of flow.area estimate of flow.

Continued….

Extension of Rating CurveExtension of Rating Curve Example 5Example 5

Find discharge in a rectangular channel having Manning’s Find discharge in a rectangular channel having Manning’s n=0.04, Sf=0.0005, width of 5 m and depth of flow of 1.5 m. n=0.04, Sf=0.0005, width of 5 m and depth of flow of 1.5 m.

SolutionSolutionFrom Equation 5.17From Equation 5.17Q=Q= A (1/n) R2/3√SfA (1/n) R2/3√SfWe have the values of We have the values of n = 0.04 & n = 0.04 & Sf =0.0005 Sf =0.0005 B = 5 m and B = 5 m and Y = 1.5 m.Y = 1.5 m.So we have to calculate R(hydraulic radius) R=A/PSo we have to calculate R(hydraulic radius) R=A/Pwhere P = wetted perimeterwhere P = wetted perimeterNowNow P = 5+2x 1.5 = 5 + 3 = 8 mP = 5+2x 1.5 = 5 + 3 = 8 marea area A = 5x1.5 = 7.50 m2 A = 5x1.5 = 7.50 m2 R= A/P = 7.5/8 = 0.94 m R= A/P = 7.5/8 = 0.94 m Discharge Q = 7.5x(1/0.04)x(0.94)0.667x(0.0005)0.5Discharge Q = 7.5x(1/0.04)x(0.94)0.667x(0.0005)0.5Q = 4.02 m³/sQ = 4.02 m³/s

Continued….


Example 6 Example 6 Given in Table 4 Given in Table 4

below is data for a below is data for a station rating curve. station rating curve. Find the flow at 4.42 Find the flow at 4.42 m stage, both by m stage, both by logarithmic and A√D logarithmic and A√D methods.methods.

Stage ‘g’ Stage ‘g’ (m)(m)

A = Cross-Sectional A = Cross-Sectional Area (m²)Area (m²)

D = Mean D = Mean Depth (m)Depth (m)

Discharge Discharge 'Q' (m³/s)'Q' (m³/s)

0.520.52 24.4324.43 0.460.46 2929

0.760.76 62.6262.62 0.550.55 7676

1.061.06 111.5111.5 0.640.64 139139

1.231.23 145.86145.86 0.850.85 187187

1.31.3 166.3166.3 0.980.98 218218

1.551.55 199.74199.74 1.191.19 268268

1.711.71 221.11221.11 1.41.4 303303

1.821.82 270.35270.35 1.491.49 371371

2.042.04 304.72304.72 1.581.58 428428

2.082.08 317.73317.73 1.651.65 456456

2.382.38 367.9367.9 1.741.74 538538

2.672.67 447.79447.79 1.831.83 682682

2.812.81 464.52464.52 1.861.86 708708

3.023.02 487.74487.74 1.981.98 773773

4.424.42 761.81761.81 2.742.74Table 4: Stage vs Discharge Data

Extension of Rating CurveExtension of Rating CurveSolution:Solution: Logarithmic Method:Logarithmic Method:

The method involves choosing trial The method involves choosing trial values of ‘a’, finding logarithm of (g-a) values of ‘a’, finding logarithm of (g-a) and Q. Then plotting Log Q against Log and Q. Then plotting Log Q against Log (g-a) as shown in Fig. 7. The best fit line (g-a) as shown in Fig. 7. The best fit line is drawn through points for most is drawn through points for most suitable ‘a’ value. This line is extended suitable ‘a’ value. This line is extended to read required discharge.to read required discharge.

Continued….

Extension of Rating CurveExtension of Rating Curve The calculations are shown in Table 5 The calculations are shown in Table 5

and graph is shown in Figure 6. and graph is shown in Figure 6. The value of ‘a’ for which we obtain a The value of ‘a’ for which we obtain a

straight line is 0.4 m. straight line is 0.4 m. The discharge required is The discharge required is

corresponding to log (4.42-0.4) = 0.60. corresponding to log (4.42-0.4) = 0.60. The value of log Q against stage of 4.42 The value of log Q against stage of 4.42

m is therefore 3.1 which corresponds to m is therefore 3.1 which corresponds to a discharge of = 1260 m³/s.a discharge of = 1260 m³/s.

Continued….


The value of discharge found by The value of discharge found by logarithmic method is approximated one logarithmic method is approximated one because it depends upon plotting accuracy because it depends upon plotting accuracy and judgment of drawing best fit line. and judgment of drawing best fit line.

Suppose for example if value of log Q Suppose for example if value of log Q would have been read as 3.15, the would have been read as 3.15, the discharge value would have been 1412 discharge value would have been 1412 m³/s which is 12 % more than previous m³/s which is 12 % more than previous computed value of 1260 m³/s. computed value of 1260 m³/s.

Continued….

Extension of Rating CurveExtension of Rating CurveExtension of Rating Curve by Logarithmic Method

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

log (g-a)

log

Q

a =0.3 a = 0.4 a = 0.5

Fig 7: Rating Curve Continued….


Stage 'g' (m)Stage 'g' (m) Discharge 'Q' (m³/s)Discharge 'Q' (m³/s) LogLog1010QQLogLog1010(g-a)(g-a)

a = 0.3a = 0.3 a = 0.4a = 0.4 a = 0.5a = 0.5

0.520.52 2929 1.461.46 -0.649-0.649 -0.906-0.906 -1.615-1.615

0.760.76 7676 1.881.88 -0.335-0.335 -0.441-0.441 -0.582-0.582

1.061.06 139139 2.142.14 -0.121-0.121 -0.182-0.182 -0.254-0.254

1.231.23 187187 2.272.27 -0.034-0.034 -0.083-0.083 -0.139-0.139

1.301.30 218218 2.342.34 -0.001-0.001 -0.047-0.047 -0.098-0.098

1.551.55 268268 2.432.43 0.0960.096 0.0600.060 0.0210.021

1.711.71 303303 2.482.48 0.1490.149 0.1170.117 0.0830.083

1.821.82 371371 2.572.57 0.1830.183 0.1530.153 0.1210.121

2.042.04 428428 2.632.63 0.2410.241 0.2150.215 0.1880.188

2.082.08 456456 2.662.66 0.2510.251 0.2260.226 0.1990.199

2.382.38 538538 2.732.73 0.3180.318 0.2960.296 0.2740.274

2.672.67 682682 2.832.83 0.3740.374 0.3550.355 0.3360.336

2.812.81 708708 2.852.85 0.3990.399 0.3820.382 0.3630.363

3.023.02 773773 2.892.89 0.4340.434 0.4180.418 0.4010.401

4.424.42 0.6150.615 0.6040.604 0.5930.593

Tabl

e 5:

E

xten

sion

of R

atin

g C

urve

A√D MethodA√D Method The cross sectional area A and Mean Depth The cross sectional area A and Mean Depth

D are given. Value of A√D is calculated for D are given. Value of A√D is calculated for each stage value as shown in table 6. A√D each stage value as shown in table 6. A√D is plotted against Q as shown in Fig 8. is plotted against Q as shown in Fig 8.

The value of Q corresponding to stage in The value of Q corresponding to stage in question is required discharge. question is required discharge.

For example, for a stage of 4.42 m, value of For example, for a stage of 4.42 m, value of A√D is 1261. This corresponds to 1375 A√D is 1261. This corresponds to 1375 m³/s. m³/s.

Here again an estimated discharge is Here again an estimated discharge is found. found.

Continued….

A√D MethodA√D Method

Table 6: Extension of Rating CurveTable 6: Extension of Rating Curve

Stage 'g' (m)Stage 'g' (m) A = Cross-Sectional Area (m²)A = Cross-Sectional Area (m²) D = Mead Depth (m)D = Mead Depth (m) Discharge 'Q' (m³/s)Discharge 'Q' (m³/s) A√DA√D

0.520.52 24.4324.43 0.460.46 2929 16.5716.57

0.760.76 62.6262.62 0.550.55 7676 46.4446.44

1.061.06 111.5111.5 0.640.64 139139 89.2089.20

1.231.23 145.86145.86 0.850.85 187187 134.48134.48

1.31.3 166.3166.3 0.980.98 218218 164.63164.63

1.551.55 199.74199.74 1.191.19 268268 217.89217.89

1.711.71 221.11221.11 1.41.4 303303 261.62261.62

1.821.82 270.35270.35 1.491.49 371371 330.00330.00

2.042.04 304.72304.72 1.581.58 428428 383.03383.03

2.082.08 317.73317.73 1.651.65 456456 408.13408.13

2.382.38 367.9367.9 1.741.74 538538 485.29485.29

2.672.67 447.79447.79 1.831.83 682682 605.76605.76

2.812.81 464.52464.52 1.861.86 708708 633.52633.52

3.023.02 487.74487.74 1.981.98 773773 686.31686.31

4.424.42 761.81761.81 2.742.74 1261.021261.02

A√D MethodA√D Method

Extension Of Rating Curve by Chezy's Method

0

500

1000

1500

2000

0 200 400 600 800 1000 1200 1400

Value of AxSQRT(D)

Dis

char

ge (Q

m³/s

)

Fig 8: Rating Curve

Stream Flow UnitsStream Flow Units Rate of Run Off:Rate of Run Off:

It may be measured in cubic foot per It may be measured in cubic foot per second or cubic meter per second. One second or cubic meter per second. One cubic foot per second is a volume of one cubic foot per second is a volume of one ft³ when collected in one second.ft³ when collected in one second.

The ft³/second are also called cusec or The ft³/second are also called cusec or cfs. In the metric system the cubic cfs. In the metric system the cubic meter per second are also called cumec.meter per second are also called cumec.

Continued….

Stream Flow UnitsStream Flow Units Volume Run Off:Volume Run Off:

Volume of flow is expressed in Volume of flow is expressed in cubic cubic feetfeet, , cubiccubic metersmeters, , cubic inchescubic inches and and also in also in Acre footAcre foot and and second foot dayssecond foot days. .

Continued….

Second Foot Day (SFD)Second Foot Day (SFD) It is the volume of water collected in 24 It is the volume of water collected in 24

hours (one day) at the rate of 1 cubic foot hours (one day) at the rate of 1 cubic foot per second.per second.

1 Sfd = 24 x 60x60 =86400 ft³.1 Sfd = 24 x 60x60 =86400 ft³. The smaller unit is second foot hour i.e. The smaller unit is second foot hour i.e.

volume collected in one hour at the rate of volume collected in one hour at the rate of 1cfs.1cfs.

1 sfh = 60x60 =3600 ft³.1 sfh = 60x60 =3600 ft³.

Continued….

Acre FootAcre Foot If an area of one acre is converted If an area of one acre is converted

by a uniform depth of 1ft of water. by a uniform depth of 1ft of water. The total volume thus collected is 1 The total volume thus collected is 1

Acre foot.Acre foot.One Acre = 4840 (yards)²One Acre = 4840 (yards)²1 Acre - foot = (4840x9)x1 = 43560 ft³1 Acre - foot = (4840x9)x1 = 43560 ft³and 1 Sfd = 1.9835 Acre foot.and 1 Sfd = 1.9835 Acre foot.

Continued….

Hectare MeterHectare Meter If an area of one hectare is covered If an area of one hectare is covered

by a uniform depth of 1m of water. by a uniform depth of 1m of water. The total volume thus collected is 1 The total volume thus collected is 1

Hectare-meter.Hectare-meter.One Hectare-meter = 104 m³One Hectare-meter = 104 m³

Continued….

Inches of Run OffInches of Run Off If a certain catchment area is If a certain catchment area is

having a uniform depth of 1 cm of having a uniform depth of 1 cm of water, the total Run off is 1 cm for water, the total Run off is 1 cm for that very catchment area.that very catchment area.

Continued….

Example 7 Example 7 What volume is represented by 3.5 cm of What volume is represented by 3.5 cm of

run off from a basin of 650 Square run off from a basin of 650 Square Kilometers. Give answer in cubic meters Kilometers. Give answer in cubic meters and Hectare-meter.and Hectare-meter.

SolutionSolutionVolume = 3.5x10-2x650x106Volume = 3.5x10-2x650x106 = 22.75x106 m³= 22.75x106 m³

= 2275 Hectare-meters= 2275 Hectare-meters

Continued….

Example 8Example 8 Given below are the daily mean flows in Cubic Given below are the daily mean flows in Cubic

meters per second at a gauging station for a period meters per second at a gauging station for a period of 5 days. What is the mean flow rate for the period of 5 days. What is the mean flow rate for the period in cubic meters per second? What is the total flow in cubic meters per second? What is the total flow during the period in Hectare-meters. The drainage during the period in Hectare-meters. The drainage area is 1935 square kilometers what is run off area is 1935 square kilometers what is run off volume in cm.volume in cm.

DayDay Discharge 'Q' (m³/s)Discharge 'Q' (m³/s)

11 2020

22 136136

33 8888

44 5757

55 3737

Table 7 Continued….

SolutionSolution Mean Flow = Mean Flow = 338338 = 67.6 m³/s. = 67.6 m³/s.

55 Discharge in Hectare-meters = Discharge in Hectare-meters =

67.6x5x24x3600/104 67.6x5x24x3600/104 = 5x584.06 Hectare-= 5x584.06 Hectare-

meters meters = 2920.32 Hectare-= 2920.32 Hectare-

meters.meters. Drainage area = 1935 km²Drainage area = 1935 km² Volume in cm = 5x584.06x104x10²÷1935x106Volume in cm = 5x584.06x104x10²÷1935x106

= 5x0.30 cm = 1.50 cm= 5x0.30 cm = 1.50 cm

Components of Run Off:Components of Run Off:

The components of run off are following:The components of run off are following: Overland or Surface Flow:Overland or Surface Flow:

When rain falling on ground attains When rain falling on ground attains sufficient depth, water begins flowing down sufficient depth, water begins flowing down slope and establish surface channel. A slope and establish surface channel. A route to the channel is formed. Then the route to the channel is formed. Then the water is designated as over land flow and water is designated as over land flow and upon entering channel it becomes surface upon entering channel it becomes surface run off.run off.

Continued….

Components of Run OffComponents of Run Off Inter Flow or Sub Surface Flow:Inter Flow or Sub Surface Flow:

Water which infiltrates the soil may Water which infiltrates the soil may move laterally through the upper layer move laterally through the upper layer of the soil until it enters a stream of the soil until it enters a stream channel. This water is known as inter channel. This water is known as inter flow or sub surface flow.flow or sub surface flow.

Continued….

Components of Run OffComponents of Run Off

Base Flow or Groundwater Flow:Base Flow or Groundwater Flow: The infiltrated water may percolate downward until The infiltrated water may percolate downward until

it reaches the water table. This water may ultimately it reaches the water table. This water may ultimately discharge into the stream as groundwater flow if the discharge into the stream as groundwater flow if the water table intersects the stream channel. This type water table intersects the stream channel. This type of flow is known as Dry Weather Flow.of flow is known as Dry Weather Flow.

However, the total flow is divided into two parts However, the total flow is divided into two parts depending upon the time of arrival in the stream depending upon the time of arrival in the stream rather than the path of flow. they are (i) Direct rather than the path of flow. they are (i) Direct runoff (DRO) (ii) Base Flow.runoff (DRO) (ii) Base Flow.

The direct run off is the sum of surface run off and The direct run off is the sum of surface run off and the initial part of the inter flow and the base flow is the initial part of the inter flow and the base flow is the sum of the ground water and the latter portions the sum of the ground water and the latter portions of the inter flow.of the inter flow.

QuestionsQuestions Define ‘River Stage’. Describe the ‘Staff Gauges’ Define ‘River Stage’. Describe the ‘Staff Gauges’

used for measuring river stage?used for measuring river stage? Describe with the help of a neat sketch the ‘Price Describe with the help of a neat sketch the ‘Price

Current Meter’. What is the difference between Current Meter’. What is the difference between Price Current Meter and Propeller Type Current Price Current Meter and Propeller Type Current Meter?Meter?

Why is the stage-discharge relationship Why is the stage-discharge relationship important in hydrologic analysis? What are the important in hydrologic analysis? What are the different methods of extending the stage-different methods of extending the stage-discharge relationship?discharge relationship?

What do you understand by the term ‘control What do you understand by the term ‘control point’ with reference to a stream gauging point’ with reference to a stream gauging station?station?

Continued….

QuestionsQuestions What is meant by a ‘Rating Curve’. Describe What is meant by a ‘Rating Curve’. Describe

the ‘Logarithmic Method’ of extension of rating the ‘Logarithmic Method’ of extension of rating curves?curves?

Describe the working principle and use of Describe the working principle and use of ‘Water Stage Recorder’?‘Water Stage Recorder’?

Explain measurement of depth of flow in a Explain measurement of depth of flow in a river?river?

Describe chemical gauging method of Describe chemical gauging method of discharge measurement?discharge measurement?

Describe discharge measurement byDescribe discharge measurement by FloatsFloats Current MeterCurrent Meter

ExerciseExercise Problem 1Problem 1

Following is the data for a Following is the data for a rating curve given in Table rating curve given in Table 8. Extend this rating curve 8. Extend this rating curve to find out the discharge to find out the discharge against a stage of 4.42 m byagainst a stage of 4.42 m by

Logarithmic MethodLogarithmic Method Chezy’s Method Chezy’s Method

Stage (m)Stage (m) Discharge Discharge (m³/s)(m³/s)

0.520.52 28.8828.880.760.76 76.4676.461.061.06 138.75138.751.231.23 186.89186.891.301.30 218.04218.041.551.55 267.60267.601.711.71 302.99302.991.821.82 370.95370.952.042.04 427.59427.592.082.08 455.90455.902.382.38 538.02538.022.672.67 682.44682.442.812.81 707.92707.923.023.02 773.05773.054.424.42 ----Table 8: Data for Rating Curve


Using the current meter data given in Table 9 below, Using the current meter data given in Table 9 below, determine the cross-sectional area, the discharge, the determine the cross-sectional area, the discharge, the mean velocity and the average depth for the entire section.mean velocity and the average depth for the entire section.

Distance from Distance from initial point initial point

on bankon bank

Depth of FlowDepth of Flow Observational Observational DepthDepth

VelocityVelocity

(m)(m) (m)(m) (m)(m) (m/sec)(m/sec)4.57 (LEW)4.57 (LEW) 0.00.0 -- --

4.884.88 0.550.55 0.330.33 0.510.515.495.49 0.670.67 0.130.13 0.810.810.540.54 0.610.61 6.106.10 0.640.640.130.13 0.810.81 0.210.21 0.680.687.017.01 0.370.37 0.220.22 0.340.34

7.32 (REW)7.32 (REW) 0.00.0 -- --Table 9: Data for Discharge Measurement Continued….


Given below in, Table 10, are the daily mean flows Given below in, Table 10, are the daily mean flows (m³/s) at a gauging station for a period of 5 days. What (m³/s) at a gauging station for a period of 5 days. What is the mean flow rate for the period in m³/s. is the mean flow rate for the period in m³/s.

What is the total discharge during the period in second-What is the total discharge during the period in second-m-days and Hectare-m. If the drainage area is 2048 m-days and Hectare-m. If the drainage area is 2048 km², what is the runoff volume in mm.km², what is the runoff volume in mm.

DayDay Flow (m³/s)Flow (m³/s)11 26.9026.90

22 143.00143.00

33 94.8694.86

44 72.7772.77

55 44.1744.17

Table 10: Mean Flows Continued….

ExerciseExercise

Problem 4Problem 4 Using the data obtained with the help of a Using the data obtained with the help of a

current meter having constants a=0.05 and current meter having constants a=0.05 and b=2.3 as given in Table 11 below, determine the b=2.3 as given in Table 11 below, determine the cross-sectional area, discharge, mean velocity cross-sectional area, discharge, mean velocity and average depth for the entire stream.and average depth for the entire stream.

Continued….

ExerciseExerciseDistance Distance from the from the

bankbank

Depth of Depth of StreamStream

Meter Meter DepthDepth

RevolutionRevolution Time Time (sec)(sec)

(m)(m) (m)(m) (m)(m)0.900.90 0.300.30 0.200.20 1515 40401.501.50 0.900.90 0.750.75 2525 4242

0.200.20 3030 45452.102.10 1.401.40 1.101.10 4040 4343

0.270.27 5050 48482.752.75 1.901.90 1.501.50 6060 4848

0.400.40 5050 44443.703.70 1.501.50 1.201.20 3535 4242

0.300.30 2525 40404.604.60 0.450.45 0.300.30 2020 35355.205.20 00 -- -- --Table 11: Current Meter Observations Continued….


One field party measured the following One field party measured the following data given in Table 12 using the current data given in Table 12 using the current metering approach to measure the metering approach to measure the discharge. Assuming a=0.05 and b=2.3 discharge. Assuming a=0.05 and b=2.3 for computing velocity in m/s. Calculate for computing velocity in m/s. Calculate the discharge of the stream.the discharge of the stream.

Continued….

ExerciseExerciseDistance Distance from the from the bank (m)bank (m)

Depth (m)Depth (m) Meter Meter Depth (m)Depth (m)

RevolutionRevolution Time (sec)Time (sec)

0.600.60 0.300.30 0.180.18 1010 50501.201.20 1.071.07 0.850.85 2222 5555

0.210.21 3535 52521.801.80 1.591.59 1.281.28 2828 5353

0.300.30 4040 58582.702.70 1.921.92 1.521.52 3232 5858

0.400.40 4545 60603.303.30 1.341.34 1.071.07 2828 4545

0.270.27 3333 46463.903.90 0.670.67 0.400.40 2222 50504.504.50 0.240.24 0.150.15 1212 49495.105.10 0.000.00 -- -- --Table 12: Current Meter Observations

Engineering

Stream Gauging