Lecture_Hydrometery measurement and analysis.pptx

Hydrological measurement and analysis

1. Course Content Lecture one: Hydro-Metrological Network Design Lecture two: Measurement of river Stage, depth, velocity Lecture three: Hydrometric Measurement Lecture four: Discharge-stage relationship (Rating curve) Evaluation Quizzes = 10% Test = 10% Field practice = 40% Final examination = 30% Attendance = 10% Pre-request Introduction to Hydrology, Probability and statistics

2. WOLAITA SODO UNIVERSITY DEPARTMENT OF HYDRAULIC AND WATER RESOURCES ENGINEERING Hydrological Measurement and analysis( HWRE-3122 ) Lecture One Hydro-Metrological Network Design 3 rd year HWRE (2024 G.C.) By: Manamno B. (MSc [email protected]

3. Introduction of hydrometeorological network design A hydro-meteorological network is an organized system for collection of information of specific kinds such as precipitation, run off, water quality, sedimentation and other climate parameters. The accuracy in the estimation of both quality and quantity of water resources and thus for making the decisions for integrated water resources development and management depends on how much information are available for the region concerned. Having enough relevant and accurate hydrologic information reduces the chances of under- design or overdesign and thus minimizes the economic losses, which leads to the overall increase in the benefit/ cost ratio. While designing hydro-meteorological networks, the decisions to be taken are: i . The variables to be measured and the frequencies and duration of observations; ii. The location of gauging stations; iii. The instruments to be installed and methods of observation; and iv. data observation and transmission system.

4. Objective of network design The objectives for an observation network be identified and decided before the designing is taken up. Some of the important objectives are listed below:  Water resources assessment at basin or sub-basin scale Water resources assessment for administrative geographical unit Water resources project planning including:  Irrigation,  Domestic (domestic use, livestock watering),  Hydroelectric power and other power generation,  Environmental requirements,  Industrial requirements,  Navigation,  Tourism,  recreation  Flood management  Assessing impacts of c limate c hange on w ater r esources

5. The Basic Network In meteorological network design, the basic network typically consists of key components and stations that are essential for monitoring and collecting meteorological data. These components help in understanding and analyzing weather patterns, climate trends, and atmospheric conditions The basic network should provide a level of hydrological information at any location within its region of applicability that would preclude any gross mistakes in water - resources decision making. Component of the basic network design i . A mechanism must be available to transfer the hydrological information from the sites at which the data are collected to any other site in the area; ii. A means for estimating the amount of hydrological information (o r, conversely, uncertainty) at any site must also exist; and iii. The suite of decisions must include the option of collecting more data

6. Structure of a Basic Network: Spatial Distribution: A basic network is strategically distributed across the monitoring area to ensure adequate spatial coverage. Stations are located in key geographical locations to capture variations in weather and hydrological conditions. Interconnectedness: The components of a basic network are interconnected to facilitate data sharing and integration. Data collected from different stations are often linked to provide a comprehensive view of the hydro-meteorological conditions in the region. Data Transmission: Modern basic networks often incorporate data transmission systems to relay real-time data to central databases or monitoring centers. This enables quick access to data for analysis, decision-making, and early warning systems. Monitoring Objectives: The structure of a basic network is designed to align with the specific monitoring objectives of the network.

7. Network Design Process Design of networks is not a one-time affair. Factors affecting network design go on evolving with time and thus the networks also require periodic review and adjustments. Design of networks to measure stream gauge and discharge involves the following steps: 1. Network de sign activity begins with collection of basin maps and background information about the area/region. Usually 1:250,000 scale topographical maps of the river basin showing basin boundaries and river network will form the base map for the network design. Ideally, the following maps should also be collected: i . Existing precipitation and gauge - dis charge gauging stations operated by various depar tments. ii. Location of existing and proposed water projects and command areas of irrigation proje cts. iii. Land use map, also showing forests, main industries and population centers. iv. Communications map showing roads, rails, power transmission lines, canals, etc. Map showing soil classification, geological formation and mining areas Contour map or Digital Elevation Model (DEM) of the basin.

8. Cont... 2. Identify the objectives of the network by define the data users and the purpose for which the data is needed. What is the required data frequency? Critically evaluate the existing network and find out how well it meets the required obje ctives? Review existing database to identify gaps, ascertain variability in catchment behavior. Identify weather the existing network is over-design (if any) or under designed. New stations may be proposed and existing stations may be deleted/shifted (if required so). Priorities stations by following appropriate classification system. Decide on approximate location of sites and carryout site surveys. Review revised network in relation to overall objectives and available budget; adjust it as neces sary. 9. Estimate average capital and recurrent costs of installing and maintaining different categories of stations and overall cost of operating and maintaining the network 10. Prepare a realistic and achievable implementation plan.

9. WMO Criteria for Minimum Network Density The World Meteorological Organisation (1976) has recommended the minimum network densities for general hydro-meteorological practices. i . For plain regions of temperate Mediterranean and tropical zones one station for 600-900 sq. km. ii. For mountainous region of temperate Mediterranean and tropical zones one station for 100-250 sq. km. iii. For arid and polar region one station for 1,500-10,000 sq. km.

10. Meteorological stations distribution in Ethiopia

11. Rain gauge Network Design Methods 1. IS: 4986-1968 guidelines The Bureau of Indian Standard (BIS) suggests that one rain gauge up to 500 sq. km might be sufficient in non -orographic regions. In regions of moderate elevation (up to 1000 m above msl), the network density might be one rain gauge for 260 - 390 sq. km. In predominantly hilly areas and areas of heavy rainfall, the density re commended is one for 130 sq. km. Recommended minimum densities of station(area in km2 per station)

12. 2. C v method The problem of ascertaining the optimum number of rain gauges in various basins is of statistical nature and depends on spatial variation of rainfall. Thus, the coefficient of spatial variation of rainfall from the existing stations is utilized for determining the optimum number of rain gauges. If there are already some rain gauges in the catchment, the optimal number of stations that should exist to have an assigned percentage of error in the estimation of mean rainfall is obtained by statistical analysis as:

13. Cont...

14. Cont... 3. Key station network method 4. Spatial correlation method 5. Entropy Method

15. Stream gauging Station General site selection guidelines The approach channel should be of uniform cross-section and free from irregularities and the flow shall have a regular velocity distribution. There should be straight, uniform, well defined approach channel upstream of the measuring section to ensure parallel and non-turbulent flow. For rivers less than 100 m wide, a straight approach of 4 times channel width should be preferred. For rivers more than 100 m wide, a straight approach channel of minimum 400 m is desirable. 2. Sites where high sediment deposition or scouring occurs or those which are subject to weed growth should be avoided, if possible. 3. Locations which are subject to high turbulence or wind effects should be avoided. 4. In needs to be ensured that there is no parallel by-pass channel, natural or man-made, on the surface or sub-surface, around the station. 5. The channel bed should be solid, relatively smooth and free from obstructions and debris. 6. The control shall be sensitive, such that a significant change in discharge, even for the lowest discharges, should result in a significant change in stage.

16. Cont... 7. The station should be located where the flood plain is at its narrowest and the out-of- bank flood flow is the minimum. 8. The banks of the river should be high and steep and free from larger vegetation. 9. River banks at the site should be well-defined, stable, and free from vegetation and other obstructions. 10. Downstream conditions should preferably be stable. 11. Factors such as unhindered access to the site in all seasons, availability of office accommodation, living space for the observers, electricity and other services should also be taken into account. 12. Enough land should be available near the site to install various instruments. 13. Sites with a tendency for formation of vortices, reverse flow or dead water shall be avoided. 14. The measuring section should be away from obstructions (artificial and natural) and control structures, e.g., dams, weirs

17. Criteria for Water Level Gauging Sites Water level or river stage is the primary variable that is measured at stream gauging sites and most frequent measurements pertain to river stage. Stage (height of water surface) is observed at all stream-gauging stations to determine discharge. There are places where additional observations of water level only are needed as part of a minimum network: a) At all major cities along rivers, river stages are used for flood forecasting, water supply, and transportation purposes; and b) On major rivers, at points between stream-gauging stations, records of river stage may be used for flood routing and forecasting purposes. For stage monitoring, the following additional site selection guidelines apply. Steep banks or sides are preferred The stage measurement device should be installed as close to the edge of the stream as possible. To minimize the effects of turbulence and high velocities, water level measuring devices can be installed in a suitable stilling bay at the bank. It is desirable to have access to the site and gauge posts at all times. The site should not a tendency to collect floating debris which may hinder working of water level measurement device.

18. Lake and reservoir stages Stage, temperature, surge, salinity, ice formation, etc., should be observed at lake and reservoir stations. Stations should be established on lakes and reservoirs with surface areas greater than 100 km 2 .

19. Criteria for Streamflow Measurement Sites Current meter is a commonly used instrument and velocity area method is the preferred approach to measure river discharge. A stage and discharge measurement station should have appropriate conditions to install a stage measurement device and to measure discharge. The required features of a good discharge gauging site are as follows: 1. The measurement section should be clearly visible across its width and unobstructed by trees, aquatic growth or other obstacles. 2. There should be sufficient depth of flow across the whole cross-section: 3. Sites with mobile beds and bank shall be avoided. In some rivers, this is not possible and the site may be chosen so that the bed and bank changes are minimized. 4. Ideally, flow should be confined to a single channel. When this is not possible, each channel should be gauged separately to obtain the total flow. 5. The site shall be sufficiently far away from the disturbance caused by rapids and falls. 6. If the site is upstream of confluence of two rivers, it should be located sufficiently far upstream so that it is beyond backwater and any disturbance due to joining of two rivers. 7. Velocities should be well in excess of the minimum required speed of the current meter over the full flow range.

20. Lecture Two Measurement of river Stage, depth, velocity

21. How can you measure an instant discharge value as an engineer?

22. Introduction Runoff is that part of precipitation which reaches the stream. The water that constitutes the flow in the surface stream is called stream flow . If the stream flow is unaffected by the artificial diversions, storage, or other works of man in or on the stream channels, then it is called as runoff. In other words runoff means the virgin stream flow . Stream flow forms the most important data for engineers and hydrologists since they are concerned mainly with estimating rates and volumes of the stream flow to be used in the design of water resources projects. It is rather difficult to measure the discharge of flow in the natural streams directly as it is done in the case of flow in pipes or laboratory flumes using the flow meters such as venturi meter, venturi flume etc.

23. Cont... But it is very easy to make a direct and continuous measurement of stage in the river above some arbitrary datum. Obviously the higher the stage in the river, the higher is the discharge. The general practice in the stream flow measurement is therefore, to record the river stage and to convert the data on the stage into the discharge data. This is accomplished through the stage-discharge relationship which is first established by actual measurements of discharge in the river at different stages. Once a stable stage-discharge relationship is established at a gauging site, the discharge measurement is discontinued and only the stage is recorded continuously. Discharge is the quantity of liquid passing through the given area per unit time

24. Cont... The stage data is often presented in the form of a plot of stage against chronological time (Fig. below) - known as stage hydrograph. In addition to its use in the determination of stream discharge, stage data itself is of importance in flood warning and flood - protection works. Reliable long-term stage data corresponding to peak floods can be analyzed statistically to estimate the design peak river stages for use in the design of hydraulic structures, such as bridges, weirs etc. In view of these multifarious uses, the river stage forms an important hydrologic parameter chosen for regular observation and recording.

25. Cont...

26. Type of Stage measurement Stage measuring instruments may be conveniently separated in to two types, direct reading and indirect reading Direct reading gauges The significant feature of direct-reading gauges is that the stage measurement is made directly in units of length without any intervening influences Staff gauge These are a wooden or metal rod scaled in centimeters . More than one gage is used if the stage varies in a wide range.

27. Cont... The stage can be very easily measured by installing a vertical staff gauge which is a graduated scale such that a portion of it is always in the water at all times. It can be conveniently attached to a bridge pier or any other existing structure. It is read manually by noting the level of water surface in contact with it. When the flow in the stream is subjected to large variations resulting in correspondingly large fluctuations in the stage, it may be beyond the range of a single vertical staff gauge to record the entire rise or fall in the water surface. In such situations it may be convenient to use vertical staff gauge as shown in Fig.

28. Cont... 2. Wire weight gauges: In this method a weight attached to a rope is lowered from a fixed reference point on a bridge or other overhead structure till it touches the water surface. By subtracting the length of the rope lowered from the reduced level of the fixed reference point the stage is obtained. It is simple and inexpensive they must be read frequently to get a continuous curve of the stream flow, especially when the stage is changing rapidly. A dvantages: i t is not harmed by the flow and it can be reached at high flow rates because it is outside of the water. Disadvantages: it is likely that the peak stage may be missed when it occurs between the observations

29. Cont... 3. Float-tape gauge: It is used mainly as an inside stilling well reference gauge for a water level recorded and consists of a float attached to a counter weight by means of a graduated stainless steel tape and an index pointer. The float pulley consists of a wheel about 150mm in diameter is grooved on the circumference to accommodate the tape and is mounted on a support. The tape is fastened to the upper side of the float and runs over the pulley. It is kept fight by a counter weight at the free end. The stage fluctuations, sensed by the float, position the tape with respect to the pointer. A float gauge must be positioned directly above the water surface and should be housed in a stilling well to protect the float from water surface oscillations and the tape from the effects of wind.

30. Cont... 4. Hook and point gauge: used in the laboratory or in research stations and for measurement of evaporation tank. 5. Electric Tape Gage Have high measuring accuracy, but also have the disadvantage of a limited measuring range, the length of the movable scale being usually 1m. This disadvantage can be overcome, however, by installing datum plates at different levels throughout the range in stage to be measured. It is used primarily as an inside reference gage (base gage) over a stilling well. It consists of an aluminum frame holding a voltmeter, a reel to hold steel tape, and a base to bolt the assembly to a tabletop. A battery of less than 6 volts is required, but not furnished. The weight is lowered until it contacts the water surface; this contact completes the electric circuit and produces a signal on the voltmeter. With the weight held in the position of first contact, the tape reading is observed at the index provided on the reel mounting.

31. Cont... Indirect- reading gauges/Recording gauges It include those devices, which convert a pressure or acoustic signal to an output, which is proportional to the water level. Pressure Transducers: It is based on the principle that, the hydrostatic pressure at a point in a water column is proportional to the height of the water column above that point. The transducer converts changes in water pressure into changing electrical signals, which are logged remotely from the point of measurement. There are several types of pressure transducer distinguished in the way that they convert the mechanical pressure signal into an electrical output. Typically, an electrical pressure transducer may be considered as having two main components, the force summing device , which responds to water pressure, and the sensor, which converts the output into an electrical signal, which can be conveniently connected to a chart recorder or solid-state logger. If the pressure sensor can be located at or below the point, the pressure can be transmitted directly. However, if the sensor is located above the point, the direct method is usually not satisfactory because gasses entrained in the water accumulate in the line and can create air locks. Additionally, if the water is highly corrosive or contains sediment, it is undesirable to bring it into contact with the sensor.

32. Cont... 2. Gas purge (bubbler) gauges: In the bubbler technique, a small discharge of non-corrosive gas-nitrogen or compressed air for example- is allowed to bleed into a tube, the free end of which has been lowered into the water and fixed at a known elevation below the water column to be measured. The sensor, which is located at the opposite end, detects the pressure of the gas required to displace the liquid in the tube, this pressure being directly proportional to the head of liquid above the orifice of the gauge. This technique may be used when the elevation of water column is below the elevation of the pressure sensor And since the sensor does not come in contact with the water, it is suitable for use in highly corrosive waters.

33. Measurement of velocity 1. Current meter: The velocity at a point in a cross section is measured by a current meter, which consists of a propeller rotated by the flow around a horizontal axle, a tail piece and a weight is required to prevent the current meter to be moved by the flow. The rotation of the propeller is related to the flow velocity. The number of rotations in a minute, n, is related linearly to the flow velocity V: n : number of rotations per sec The coefficients a and b are given by the manufacturer for various ranges of n. To measure very low velocities is not possible with that type of velocity meter. V : velocity If h<0.5m the velocity is measured at 0.6 of the flow depth below the water surface. If h>0.5m the velocities measured at points 0.2 and 0.8 of the depth below the water surface e. Later, they are averaged

34. Cont... Type of current meter A. Propeller type current meter: It has a propeller with a horizontal axis, and is preferred for turbulent and high velocity flows. rope is pulled across the river

35. Cont... B . Cup-type current meter: It has has a vertical revolution axis and a horizontal wheel with six conical cups. It can rotate in even very small velocities . Vertical velocity components can rotate the cups causing higher velocity measurement than it is

36. Cont.... 2. Floats: A floating object on the surface of a stream when timed can yield the surface velocity by the relation This method of measuring velocities while primitive still finds applications in special circumstances, such as: A small stream in flood Small stream with a rapidly changing water surface and P Preliminary or exploratory surveys. Where S = distance traveled in time t

37. Lecture 3 Hydrometric Measurement

38. Introduction Surface water hydrology deals with the movement of water a long earth’s surface as a result of precipitation and snow melt Knowledge of quantity and quality of stream flow is a request of municipal, industrial, agricultural and other water supply projects. The water flowing in stream is measured as discharge of water with a unit of volume (m 3 /sec, cubic of feet per second – cfs )

39. Stream flow measurement 1) Direct measurement of stream Area-velocity methods Dilution techniques Electromagnetic methods Ultrasonic method 2) Indirect measurement of stream Hydraulic structure such as weir, flumes and gated structure Slope area method

40. Cont.... Area-Velocity method The discharge equations for flow in open channels and pipes are based on the velocity area principle Q=V*A where Q is discharge, A is wetted area and V is velocity. The procedure, therefore, is one of estimating velocity and area either directly or indirectly. The velocity area method for the determination of discharge in open channels consists of measurements of stream velocity, depth of flow and distance across the channel b/n observation verticals. The velocity is measured at one or more points in each vertical. The discharge is derived from the sum of the product of mean velocity, depth and width b/n verticals.

41. Cont.... The spacing and number of verticals is critical for an accurate measurement of discharge and for this reason b/n 20 and 30 verticals are normally used. This practice applied to rivers of all widths except where the channel is so narrow that 20 –30 verticals would be impractical. But generally the spacing as in table below is recommended

42. Cont.... Computation of mean velocity The mean velocity in each vertical is determined by current meter observations by any of the following methods. Velocity distribution method: In this method velocity observations are on each vertical at a sufficient number of points distributed b/n the water surface and bed to define effectively the vertical velocity curve, the mean velocity being obtained by dividing the area b/n the curve and the plotting axes by the depth. In a rough turbulent flow the velocity distribution is given by; Where V = Velocity at a point y about the bed, V* = Shear velocity, Ks = Equivalent sand - grain roughness

43. Cont.... II. The 0.6 Depth Method: In shallow streams of depth up to about 3.0 m, the velocity measured at 0.6 times the depth of flow below the water surface is taken as the average velocity in the vertical. III. The 0.2 and 0.8 depth method: Velocity is observed for moderately deep streams at two points at 0.2 and 0.8 of the depth from the surface and the average of the two readings is taken as the mean for the vertical. IV: Six-point method: Velocity observations are made by taking current meter readings on each vertical at 0.2, 0.4, 0.6 and 0.8 of the depth below the surface and as near as possible to the surface and bed. The mean velocity may be found by the equation

44. Cont.... V. Five-point method: Velocity observations are made by taking current meter readings on each vertical at 0.2, 0.6 and 0.8 of the depth below the surface and as near as possible to the surface and bed. The mean velocity may be found by plotting in graphical form and using a planimeter, or from the equation; VI. Three-point method: Velocity observations are made by taking current meter readings on each vertical at 0.2, 0.6 and 0.8 of the depth below the surface.

45. Cont.... Computation of discharge (Area-Velocity method) Arithmetic mean method Graphical method Arithmetic mean method (Mean-section and Mid-section method) Mean-section method: The cross-section is regarded as being made up of a number of panels or subsections, each bordered by two adjacent verticals. If 1 and 2 are the mean velocities at the first and second vertical respectively, and if d 1 and d 2 are the depths measured at the verticals I and II respectively, and ‘b’ is the width between the said verticals, then the discharge of the panel is to be calculated as Where Q p is the total partial discharge through the considered panel. This is to be repeated for each panel and the total discharge is the summation of the discharges per panel

46. Cont.... For the panels at the site (close to the bank) the same equation can be used as above, whereas the velocity at the bank is taken as zero. One should realize, however, that the mean velocity in horizontal direction towards the banks in many cases has a parabolic form and therefore it may give a better estimate to calculate Q p for the panels near the banks as Where b is the width from the bank to the vertical I and is the mean velocity in vertical I  

47. Cont.... B. Mid-section method: Assuming a straight line variation of , the discharge in each section should be computed by multiplying by the corresponding width measured along the water surface line. This width should be taken to be the sum of half the width of the adjacent vertical to the vertical for which has been calculated, plus half the width of this vertical to the corresponding adjacent vertical on the other side. The discharge around vertical II is calculated using;   in which b 2 the horizontal distance between vertical I and II; b 3 the horizontal distance between vertical II and III The value of in the two half-widths next to the banks should be taken as zero. The total discharge is a summation of all the calculated Q p ’s.  

48. Cont.... 2. Moving-Boat method Discharge measurement of large alluvial rivers, such as the Barro River, by the standard current meter method is very time - consuming even when the flow is low or moderate. When the river is in spate, it is almost impossible to use the standard current meter technique due to the difficulty of keeping the boat stationary on the fast - moving surface of the stream for observation purposes. It is in such circumstance that the newly developed moving boat techniques prove very helpful

49. Cont.... In this method a special propeller type current meter, which is free to move about a vertical axis, is towed in a boat at a velocity V b at right angles to the stream flow. If the flow velocity is V f the meter will align itself in the direction of the resultant velocity V R making an angle with the direction of the boat. Further, the meter will register the velocity V R . If V b is normal to V f If the time of transit between two verticals is t, then the width between the two verticals is  

50. Cont.... The flow in the sub area between two verticals i and i + 1, where the depths are y i and y i + 1 respectively, by assuming the current meter to measure the average velocity in the vertical, is

51. Cont.... 3. Dilution technique of stream flow measurement It is generally used for purposes of calibration or for spot gauging mainly because of the costs of performing a gauging and a chemical analysis of the tracer samples. Nevertheless the method can often provide very accurate results given a suitable reach of river. The outstanding advantage of the dilution technique is that it is an absolute method because discharge is computed from volume and time only. Tracer concentrations need be determined only in dimensionless relative readings. This method is likely to be successful at the first attempt in well-defined channels such as sewers, pipe flowing full of water, rock-strewn shallow streams or when rivers are in extreme conditions of flood or drought The dilution method may provide the only effective means of estimation flow. The disadvantages of the method are the difficulties in containing complete mixing of the tracer without loss of tracer and the problem of obtaining permission in some countries to inject tracers in to rivers.

52. Cont.... The basic principle of the dilution method is the addition of suitably selected tracer to the flow. Downstream of the injection point, when dispersion throughout the flow is effected, the discharge may be calculated from the determination of the dilution of the tracer. If this tracer was present in the flow before the injection, the increase in concentration of tracer due to the injection is known as the concentration of added tracer There are two basic injection techniques:- : the sudden - injection (gulp or integration) method and the constant rate injection method

53. Cont.... Constant rate injection method Solution of concentration C 1 of a suitably chosen tracer is injected at constant rate, q , in to a cross-section located at the beginning of the assuring reach of the channel in which the discharge, Q , remains constant for the duration of the gauging. At a second cross-section downstream from this reach, at a sufficient distance for the injected solution to be uniformly diluted, the concentration is measured for a sufficient period of time and at a sufficient number of points to enable a check to be made that good mixing has been obtained and that the concentration of at section two, C 2 has attained a constant value. Under these conditions, if all of the tracer injected passes through the sampling cross-section, the mass rate of tracer at the injection point is equal to that passing thought the sampling cross-section

54. Cont.... The mass rate at which the tracer enters the test reach is; Similarly the rate at which the tracer leaves the test reach is; Equating these two rates From which Where q and Q are in liter s –1 or m 3 s –1 , and C 1 and C 2 are in mg liter –1 or kg m -3 The discharge can therefore be determined by comparing the concentration of the injected solution with that measured at the sampling cross-section C 1 /C 2 is termed the dilution ratio, N.

55. Cont.... Indirect Measurement 1. Slope area method The area slope method can be improved to give good results by incorporating the principle of conservation of energy between the two points of the selected reach. Considering reference datum as the channel bed at points (1) and (2) as shown in Fig. below, Bernoulli’s equation can be applied to calculate the head loss as:

56. Cont.... Energy slope over length between the two sections (3) where Y1 and Y2 are the depths of water in the channel at section (1) and (2), respectively, with velocities V1 and K is the channel conveyance which can be obtained from Manning’s equation as

57. Cont.... R is the hydraulic radius = A/P, A the area of cross section of the channel in (m2 ), P the wetted perimeter (m). From the equation (4), the slope of energy line Sf of equation (3) can be obtained. If two sections have different conveyance factors K1 and K2 with roughness n1 and n2 respectively, then the equivalent K between those sections can be calculated as

58. Cont.... The procedure for using area-slope method is: Select the stream reach between two sections (1) and (2) shown in Fig. above. From the cross section at (1) and (2), find the depths of water during the flood at the two sections from the flood marks left by floating debris. Compute cross sectional areas A1 and A2 and wetted perimeters P1 and P2 corresponding to the flood depths of step (2) of the particular flood. Calculate the hydraulic radii R1 and R2 and the conveyances K1 and K2 after selecting suitable roughness coefficient n1 and n2 for the section (1) and (2) respectively Obtain the average or equivalent conveyance K between Section (1) and (2)

59. Cont.... 6. Calculate the discharge Q from equation (4) by assuming a suitable value of Sf. 7. Calculate the velocity V1 and V2 at the two sections (1) and (2) from the relation 8. From equation (1) and (2), calculate H1 and H2 and the energy slope from equation (3). 9. The assumed value of Sf in step (6) should be the same the calculated value of If the two values differ then take the energy slope of step (8) and repeat the steps (6) to (8) till the energy slope at the end of the iteration are the same. 10. The discharge calculated at the end of step (9) is the estimated flood discharge.

60. Cont.... 2. Discharge Measuring Structures Under this category are included those methods which make use of the relationship between the flow discharge and the depths at specified locations. Discharge measuring structures may be constructed for measuring discharges in small streams. They use indirect method of computing discharges from stages using standard equations. The different types of flow measuring structures generally considered in practice are weirs. A weirs are may be defined in general way as an obstruction in a channel that causes upstream storage and flow over or through the obstruction. This definition, therefore, includes many hydraulic structures, such as spillways and drop structures. Most, if not all, of these structures can be therefore be rated and used for the purpose of flow measurement.

61. Cont.... The commonly used weir types for flow measurements are: Sharp-crested triangular, Sharp-crested rectangular, Broad-crested weir etc. The term "sharp-crested" means that the weir is so constructed that there is only a line contact of the flow with the weir crest, whereas "broad-crested" means the flow is in contact with the crest for a finite distance parallel to the flow direction. This is the most reliable method of discharge measurement. For weirs of the type commonly employed, the discharge is simply related to the head over the crest with the result that it can be computed with the help of theoretical formulae by making a direct measurement of this head.

62. Cont.... The equation used for different weirs are: 1. Triangular notch, up to 1.5 m3 /s (sharp crested, V shaped triangular structure 2. Rectangular notch (sharp crested rectangular opening)

63. Cont.... 3. Trapezoidal notch (sharp crested) 4. Weirs Different forms of weir structure and values of

64. Cont.... Example 1 The following data were collected during a stream-gauging operation in a river. Compute the discharge using Mid-section method. Distance from left water edge(m) Depth(m) Velocity(m/s) At 0.2d At 0.8d 1.5 1.3 0.6 0.4 3 2.5 0.9 0.6 4.5 1.7 0.7 0.5 6 1 0.6 0.4 7.5 0.4 0.4 0.3 9

65. Cont.... Solution Average width for the first and last vertical/panel   Distance from left water edge(m) Average width(m) Depth(m) Velocity(m/s) Mean velocity(m/s) Segmental discharge  (m 3 /s) At 0.2d At 0.8d   - - 1.5 1.6875 1.3 0.6 0.4 0.5 1.096875 3 1.5 2.5 0.9 0.6 0.75 2.8125 4.5 1.5 1.7 0.7 0.5 0.6 1.53 6 1.5 1 0.6 0.4 0.5 0.75 7.5 1.6875 0.4 0.4 0.3 0.35 0.23625 9   - Sum 6.425625m 3 /s

66. Cont.... Example 2 Common salt solution of concentration 200 gm/l was added to a stream at a constant rate of 0.2cm 3 /sec. Concentration of this salt in the stream already present was 0.01ppm. At sufficiently downstream, the concentration of the salt in the stream water was measured as 0.05 ppm. Estimate the stream discharge.

67. Cont.... Example 3 During a high flood, a river reach of 1 km apart was having the following information Up stream: Area of cross section A1 = 180 sq m Wetted perimeter P1 = 50 m Manning’s roughness coefficient n1 = 0,03 Reduced level of water = 78.3 m Down stream: Area of cross section A2 = 183 sq m Wetted perimeter P2 = 51 m Manning’s roughness coefficient n2 = 0,025 Reduced level of water = 78 m Calculate the flood discharge. Neglect other losses.

68. Cont.... Solution Upstream (u/s) hydraulic radius R1 = A1/P1 = (180/50) = 3.6 m Downstream (d/s) hydraulic radius R2 = A1/P1 = (183/51) = 3.59 m

69. Cont.... Fall in energy head 78.30 – 78.0 = 0.30 m between the reach of 1 km

70. Cont.... Iteration It is the flood discharge during the event

71. Cont.... Exercise Compute the discharge at downstream gauge site when the water gauges at two sites 2350 m apart are 621.10 and 605.56 m. The area of cross-section at gauge 605.56 is 66.98 m2 and the wetted perimeter is 70.75 m. Manning’s n = 0.035.

72. Lecture Four Stage-Discharge Relationship

73. Introduction In any program for flow measurements, the stream discharges cannot be measured every day, or even as often as desired because of economic considerations. Furthermore, during the flood event it is also not possible to measure the discharge because of high velocities. Hence discharges occurring between periods of measurement are determined from already developed stage-discharge relationships (Rating curve), where the stage is the water surface elevation above a selected arbitrary datum plane. The stage-discharge relationship (rating curve) is developed by measuring the stage simultaneously with each measurement of discharge and plotting the same against the measured discharge. Thus, if the stage is known, the discharge can be obtained from the developed stage-discharge relationship.

74. Types of Rating Curve Simple rating curve If the measured discharge is plotted against the corresponding stage, the data will normally define a curve which is approximately parabolic Such a curve is generally satisfactory for a good majority of rivers where the discharge station has been selected with due regard to the essential requirements of good gauge site and stream is not subjected to too rapid fluctuations of the stage. The rating curve remains valid so long as the conditions at the gauging site remain stable. The combined effect of all the channel and flow parameters is termed as control. When the rating curve remains unchanged with time, we call the site to be a permanent control , and when it changes with time, the site is known as shifting control .

75. Cont.... Shifting control A station is subjected to shifting control when the stage-discharge relationship changes either gradually or rapidly as a result of physical changes in the control. In case the control shifts abruptly and remain unchanged for some period of time, separate rating curve can be drawn for each specific interval of time. When the control changes gradually as a result of silting or other channel changes in streams moving through channels of soft erodible bed and banks, the rapidity with which changes occur in the control should be ascertained and a new rating curve developed to be used for the period until gauging indicate another change in the control

76. Cont.... When the change in the control is slow, no single rating curve would be applicable during the transitional period of the control. An average rating curve is drawn during the period. Rising and falling stages have great effect upon the discharge curve. During the rising stage of the river, the velocity and discharge are greater than they are for the same stage when the discharge is constant because of a change in the bed roughness and water surface slope. The reverse phenomenon occurs during the falling stage of the river.

77. Cont.... A permanent control, the rating curve does not change with time but it may be necessary to check it periodically. A site may have a single control for the full stage or different controls each serving for different range of stages. A single stage-discharge relation assumes the form (a) where G = gauging height (m) and G = the gauging height corresponding to zero discharge. It does not represent the river bed level but a value below it. Q = the discharge in m 3 /sec, c and n are constants that can be evaluated using the method of least squares, however, the value of G should be evaluated before.

78. Cont.... The above equation is assumed to be an appropriate fit between the discharge Q and the stage in the river G. The constants c, G and n are to be determined using the observed data on G and Q. The value of G is supposed to be the stage corresponding to zero discharge in the stream. Evaluation of G o : A number of alternative methods are available to determine the value of G0 like graphical, semi-graphical or analytical approaches. One approach is to take logarithms on both sides of the above equation This equation suggests that a plot of Q vs (G-G ) would plot as a straight line on a loglog paper whose slope is n and whose intercept on the discharge axis is log c

79. Cont.... Procedure In practice, G0, the gauge height corresponding to zero discharge, is not known and it is therefore to be calculated from the observed data with the following steps: Plot discharge Q versus gauge G and fit a gauge discharge curve by eye inspection such that there is equal number of points on each side of the fitted curve. Select a few points on this fitted curve and note down their coordinates Q and G Assume different values of G and plot a curve on log-log sheet, between Q versus (G- G ). The correct value of G is that which in step 3 gives a straight line as per eq. (b)

80. Cont.... 5. From this straight line of step 4 find out the value of c and n. C is the value of Q where (G- G ) is equal to one and n is the tangent of the angle the line makes with the (G- G ) axis. 6. Estimate higher values of Q for the desired gauges with the help of eq. (a).

81. Cont.... Example The stage-discharge data for a given river is as given in the Fig below. Drive the stage-discharge equation

82. Cont.... Solution Some coordinates (Q, G) points as read from the Fig. are given in column 1 and 2 of the following table

83. Cont.... The discharge Q versus (G-G0) are plotted on a Fig below on log-log scale. From the fig. it is clear that G0 621.30 gives a straight line. Hence the correct value of G0 is 621.30. To compute c and n we take two values Q as Q1 and Q2 on curve with G0 = 612.30 and find the corresponding values of (G1 -G0) and (G2 -G0). Now we solve the following equations simultaneously to find c and n. the points are (200, 2.02) and (400, 2.70). Now, log Q1 = logc + nlog(G 1 -G )logQ 2 = logc + nlog(G 2 - G )

84. Cont....

85. Cont.... Now from these equations, we have on substitution Substituting n = 2.405 in equation gives c = 34.80. The gauge-discharge relationship is

86. Cont.... The values of values of G0, n and c may also be obtained from the following short-cut method without resorting to rigorous regression analysis. In the other approach, three values of Q are selected from a G-D curve such that: From a similar ratio of the right side of stage-discharge relation we get

87. Cont.... Exercise Three points on a rating curve of a stream gauging station obtained from an eye-fit for the stage discharge data have the following coordinates (100m3 /s, 121.67m), (200m3 /s, 122.23m), and (400m3 /s, 123.04m). Determine the equation of the rating curve and compute the discharge in the stream corresponding to a stage of 124.5m.

88. Thank You END of the Class 3/2024 G.C