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Hydropower Engineering caite.info (Mb application/pdf) Designed for all members of the hydropower community, this timely handbook addresses a . HYDROPOWER ENGINEERING. For. Diploma Level Courses. For Department of Technical Education. Govt. of Uttarakhand. ALTERNATE HYDRO ENERGY. of hydropower increased during the second half of the 19th century, when the . hydraulic fundamentals in hydropower engineering address the conversion of.
This then resulted in fatigue-like destruction and failure of the lnetal. Planimetering of the areas between isohyetal lines provides the data given in Table 5. T h e slats o r foils are attached a t each end t o a moving sprocket chain that moves around the sprockets. A1 nCIDl sin al water as it exits from the runner equal to the discharge divided by the area o f the draft tube at its entrance. Very few Deriaz turbines have been built. This is often referred t o as a sequential-flow study. Since relative velocity.
An extensive impoundment at the power plant or at reservoirs upstream of tlie power plant permits changing the flow of the river by storing water during high-flow periods to augment the water available during the low-flow periods. The challenge to the engineer is and will be to plan and design econondcally feasible develnpmcnts to meet the needs of the future and at the same time protect and preserve the quality of our environment.
This technique is really an energy-storing system. Tidal power developments. These developments use the water flowing back and forth as a result of tidal action and the fact that there is a significant difference in elevation of the water surface in the estuary from one stage of tide to another. Storage or pondage of the water supply i necessary.
Hydropower plants can be started and stopped more rapidly and economicall than fossil fuel and nuclear plants. The water is then run back down through turbines to produce more valuable. Pumpedlstorage developments. Water is pumped from a lower reservoir to a higher reservoir using inexpensive dump power during periods of low energy demand.
The word storage is used for long-time impounding of. The large hydropower plants of the Pacifi Northwest rivers were originally base-load plants but are being used more and mor for peaking power as large fossil fuel and nuclear power plants become operative i the region to supply the base load. The water is diverted from the natural channel into s canal or a 1or.
Hydropower production is just one of many purposes for which the water resources are used. The water is used only for the purpose ol I i. In some estuaries. Single-purpose developments. Peak demands for electric power occur daily weekly. Storage regulation developments. Water is pumped from a lower reservoir to a higher onc using inexpensive "dump" energy produced during periods of low demand by power plants which cannot economically be shut down. Peak-load developments. Another way of classifying hydropower development is with respect t o thc manner in which the hydropower plant is used t o meet the demand for electrica power.
Diversion and canal developments. Although the relative percentage of electrical energy produced by hydropower has not increased during the last forty years. Barring some now un!
A dam with a short penstock supply pipe directs tlie water to the turbines. The water is then run down through the turbines t o produce power to meet peak demands. The following classification system is used in this text: Run-of-river developments. Other uses might include. I I Multipurpose developments. Hydro-electric Power Stations. Vational Hydroelectric Power Resources Study. New York: Idaho Water Resources Research Institute.
Fluid Mechanics of Turbornachinery. A Science Museum Booklet. Blackie L Son Ltd. McGraw-Hill Book Company. Water Turbines. Her hlajesty's Stationery Office. The Ronald Press Company.
IVater Power Engineering. New Delhi: Amerind Publishing Co. Government Printing Office. July March Army Corps of Engineers. McGraw-Hill Book Corn any. Ifj8dro-electricEngineering Practice. Praeger Publishers.. Develop a table or graph showing the relative importance of hydropower 1.
Pergamon Press Ltd. JIydroelech-ic Handbook. John Viley S Sons. Present physical characteristics that demonstrate the type of development. Theory of Turbonlachines.. University of Idaho. Introduction Chap. Characterize two different types of hydropower developments in your area.
Israel Program for Scientific Translation Ltd. New York. Develop a list of sources for finding information o n hydropower production. Gladwell and C. Engineering Monograph No. Manufacturers of hydraulic turbines are usually required t o specify what the rated capacity o f their units is in either horsepower or kilowatts. The energy from water can be either potential energy by virtue of position. Rated head is the lowest head a t which the full-gate discharge of thz turbine will produce the rated capacity of the generator.
Power is the rate of transferring energy or work per unit of time. Net head is the effective head o n the turbine and is equal t o the gross head minus the hydraulic losses before entrance t o the turbine and outlet losses.
Work is transferred energy and is the product of force times the distance moved.
The rotating part of the turbine or water wheel is often referred t o as the runner. Demand refers' t o the amount of power needed o r desired. It is calculated as force times distance divided by time. An important job of the engineer is t o plan for and match power capacity a t hydro plants with energy loads and demands.
In this context. This head will produce maximum discharge through the turbine. The term is sometimes used interchangeably with the term effective head. Department of the Interior defines critical head as the net head or effective head at which full-gate output of the turbine produces the permissible overload o n the generator a t unit power factor.
One type is an im-. Rotary action of the turbine in turn drives an electrical generator that produces electrical energy or could drive other rotating machinery. The terms are often used synonymously. The turbine has vanes. Hydraulic head is the elevation difference the water falls in passing through the plant.
The work done by water in producing electrical energy is usually measured in kilowatt-hours kwh. Gross head of a hydropower facility is the difference between headwater elevation and tailwater elevation. Energy is the capacity t o d o work. Headwater is the water in the forebay or impoundment supplying the turbine.
At maximum rated head and full gate. It is normally referred t o as the rated net head in the guarantee of the manufacturer. Two words frequently used in hydroelectric terminology are demand and load. Rated discharge refers t o a gate opening or plant discharge which a t rated head produces the rated power output of the turbine. Sheldon and Russell present a composite reference of the various head definitions and terms. Power capacity is often used in referring t o the rated capability of the hydro plant t o produce energy.
FLIIIgate discharge is the flow condition which prevails when turbine gates o r valves are fully open. It should be noted that load and demand are related t o the uses that are being made of the electrical energy. Implied is the need t o have hydropower energy integrated with other modes of energy production. Doland defines design head as the effective head for which the turbine is designed for best speed and efficiency.
Later mathematical expressions and graphical prescntations will verify this statement. Such words as work. They can be grouped into two types. Hydraulic turbines are machines that develop torque from the dynamic and pressure action of water. A deflector arrangement in ore sophisticatzd designs is used to direct the water away from the turbine. The notch serves to keep the jet from striking the bucket until the jet is scntially rangent with the circular path of the bucket. Reaction turbines can be further divided into several ypes.
The jet of. Figure 2. Lester Pelton. The position of the needle: Impulse Turbines Governor The impulse turbine is frequently called a Pelton wileel after one of its early evelopers.
Impulse runners have rnultiple jets and the mounting can be with [her a horizontal or a vertical shaft. The second type is a reaction whine. The water striking the buckets of the runner is regulated through the use of bulb-shaped needle in a nozzle. The phenomenon of water hammer will be discussed later. The buckets are constrained by a rim on the discharge side of the runner.
Adjustable inlet valves or gates control flow t o separate portions of the runner so that a cross-flow turbine can operate over a wide range of flows. The advantage claimed for this type of unit is that a larger jet can be applied. The impulse or Pelton turbines have advantages for high-head installations. Another type of impulse unit is the cross-flow turbine Stapenhorst. Double-overhung installations are made with a generator in the center and the runners positioned on the two overhanging ends of a single shaft.
This type of unit has been manufactured in Europe for many years. The name "cross-flow" comes from the fa. A good discussion of this type of unit is presented by Wilson Turgo impulse turbine Difference between Pelton turbine and Turgo impulse turbine.
They arc also used a1 lower heads for small-capacity units. Some impulse runners are made with individually bolted buckets and others are solid cast. The ratio of the wheel diameter to the spouting velocity of the water determines the applicability of an impulse turbine. The cross-flow principle was developed by Michell. Professor Banki. Its advantages are that standard unit sizes are available and an even higher rotationd speed is obtained than from other impulse turbines.
Stapenhorst The turbine is designed so that the jet of water strikes the buckets at an angle t o the face of the runner and the water passes over the buckets in an axial direction before being discharged at the opposite side. The runner blades are set at an angle around the rim o f a conical hub. B Figure 2. Francis turbines have a crown ant1 band enclosing the upper and lower portions of the buckets.
An early type of radial-flow machine was the Fourneyron turbine. There is n o band around the blades. Three conditions of flow determine the designs o f reaction whecls. They have the advantage of mailltaining good efficiency over a wide range o f flow.
Terminology and Types o f Turbines Chap. I Wicket gate I I 1. AllisChalmers Corporation. In the operation of reaction turbines. Many early reaction wheels were radialiy inward-flow runners.
Guide bearing I- b. The units have been developed for use as reversible pump turbines. The most common mixed-flow turbine was developed by James B Francis and bears his name. Reaction turbine Figure 2. If the flow is perpendicular t o the axis of rotation.
An excellent reference to the design of Deriaz turbines is Mathews Other references are Kovalev 1 and Kvyatkovski Very few Deriaz turbines have been built. Axial-Flow Reaction Turbines. Allis-Chalmers Corporation. Propeller turbines. The direction of flow for most propeller turbines is axial, parallel to the axis of rotation: Early developments utilized propeller units with vertical shafts.
More recent developments utilize a horizontal shaft, as discussed and illustrated later. Propeller turbines can have thc blades of the runner rigidly attached to the hub; these are called fured-blade runners.
The blades of the runners can also be made adjustable so that: TUBE turbine in a egis[ered tradenlark of the Allis-Chalmers Corporation for a type ofu,lit in which 'Ie Senerator is llloullted outside the water parrage with direct or gear drive connec-.
These units are now being produced in standardized sizes. Brilb hydropower units include propeller turbines that drive a generator encapsulated and sealed t o operate within the water passage.
The generator design is such that all mechanisms are conipressed into a diameter that is approximately equal t o the propeller diameter. It does require special cooling and air circulation within the generator bulb. This type of unit is being manufactured b y several companies. Rim-generator turbines have been developed from an American patent filed by L. Units were built and promoted first b y European firms during World War The generator rotor is attached t o the periphery of the propeller runner and the stator is mounted within the civil works surrounding the water passage.
This arrangement shortens the powerhouse. Only a single crane is required for maintenance, thus reducing space requirements and civil works complexities. The relatively larger diameter rotor provides. Energy translator. A recent invention o f D.
Schneider reported by Kocivar is a hydraulic machine known as the Schneider Hydrodynamic Power Generator. It is also referred t o as the Scllneider Lift Translator. As shown in. T w o installations are presently being developed on very low head sites o n canal systems in California. T h e slats o r foils are attached a t each end t o a moving sprocket chain that moves around the sprockets.
A generator is connected to the shaft o f o n e of the sprockets. Doland, J. T h e Ronald Press Conlpany, Kocivar, B. Kovalev, N. Segal, trans. Kvyatkovski, V. Mathews, R. Brown, cd. Elackie 8: Son Ltd. Idaho Falls, Idaho: Department of Energy, Energy and Technology Division, Schneider, D. Idahc Falls, Idaho: Department of Energy, Sheldon, L.
November Stapenhorst, F. Warnick, eds. Moscow, Idaho: Denver, Colo.: Department of the Interior, Bureau of Reclamation, Wilson, P. Her Majesty's Stationery Office, Develop a classification table for types of turbines, showing the characteristics of t h e various types with respect t o range o f head, water pressure condition at exit to runner, direction of water flow, and type of energy used. By observing the elements of Fig.
The h has been purposely designated as slightly below the headwater or forebay level. As one pproach for developing the necessary theory. The power extracted by the hydropower unit is the rate of doing work and can be represented mathematically as fpllows: Effective head is the difference between energy head at the entrance to the turbine and the energy head at the exit of the draft tube.
The actual output is diminished by the fact that the turbine has losses ill transforming the potential and kinetic energy into mechanical energy. The Bernoulli equation is related to the energy grade line. For equations using the metric or SI system. The foregoing equations are for theoretical conditions. To compare kilowatts and horsepower. Thus an efficiency term q.
A second approach t o basic hydraulic theory of hydropower engineering is the mathematical development in terms of energy grade lines and hydraulic grade lines. Because the Bernoulli equation defines terms in units of pound feet per pound of water flowing through the system. In a practical sense. Thus a change in any one of le component energies at any point aiong the path of the moving fluid must be ompensated for by an equal change of the water energy components at that point.
Now recognizing that energy per unit of time is power. Referring to Fig. The torque exerted by the jet of water is the product of the force F and. The ideal deflection angle for 8 for an impulse runner bucket is ' but for practical purposes the bucket angle is generally about ' so that the jet of water does n o t interfere with the buckets see Fig.
Wvr The theoretical power imparted is given b y the formula php Fu Wvu. KINETIC THEORY Further theory related t o the speed of the runner and the dynamic action of the water on the buckets and vanes is important for understanding the energy-converting action and is necessary in developing certain turbine constants that are used in the design and selection of runners. Since relative velocity. Brown and Wkippen indicate that a good rule of thumb for impulse turbines is to make the diameter of the runner in feet equal to the diameter of the jet in inches.
Hydraulics of Hydropower Chap. Runner diameter. The ratio is Limited by the pllysical restraints of attaching the buckets to the disk. Reaction Runner Flow Best linear velocity. The best linear speed of the turbine can be determined sing Eq. A1 nCIDl sin al water as it exits from the runner equal to the discharge divided by the area o f the draft tube at its entrance. The blade angle of the turbine is normally designed such that the angle between the tangent to the entrance edge and the tangent to the circumference is equal to P I.
Brown and Whippen The kinetic theory of axial-flow turbines is not treated in this text. Daily The relative velocity v. To determine the absolute velocity. The relationship between the various velocity terms is given by Eqs.
A good reference to this is the work of J. The required height. For best performance of the runner.
More detail on particular characteristics of impulse turbines and reaction turbines is given in the next chapter. In a practical sense it is not possible t o obtain conlpletely axial flow at all gate openings.
The mathematical relationship is better understood by referring to Fig. The angle is usu. In that diagram it is assumed that the flow is two-dimensional radial inward flow. If the acute angle between the guide vane and a tangent t o t h e outer periphery of the runner is 30' and the runner diameter a t the entrance is 3.
It is often irsumed that the relative velocity of the water leaving the runner blade is in the. A reaction turbine with an estimated overall efficiency of 0. Parts 1 and 2. Tllc absolute velocity. In modern turbines that area would be a cry colrlples surface. The magnitude of the relative velocity ]la. For reaction turbines. The advantage claimed for these dimensionless constants is that the units ofmeasur are more easily converted and the terms are more rational to work with in mathc matical expressions.
The equations are derived from fundanlental physical concepts of motion and hydraulic theory. They provide a means of predicting performance based on the perforrnancc of lnodels or the performance of units of design sindar to those that have already been built.
These similarity laws are developed and presented in a series of formulas that define what are called the turbirie constants. The fact that the similarity laws can be used is oiten referred t o as the llomologous nature of turbines.
The power outputs. Then n l is the speed in rpm of a theoretical turbine having a unit diameter ant operating under a net head of unity. Now if the linear speed of the runner is defined in terms of rotating speed an1 diameter of the runner.
By grouping all the known constant terms. Dimensionless Constants Recently. Turbine constants under this system use dimensionless ratio and metric. By grouping the variable q l and all the constant terms as before.
Grouping the n l and p l on one side of the equation. The corresponding dinlensionless unit discharge specified by international. Specific Speed To develop a more universal constant that embodies all the equations.
Then q l is the discharge of a runner with unit diameter operating under a unit! The unit discllarge equation is developed in a similar manner. In addition to this form.
The dzveloprnent is described below: Tlus is the form of the specific speed equation that is being advocated for international standardization.
Capital letters are used when metric SI units are used. The corresponding term from the dimensionless-type constant has been altered to include in the definition the turbine discharge rather than the power output. Rearranging terms. Other variations of the turbine constants with relation to torque have been developed for ease of analyzing certain characteristics of turbines. Then n. Csanady reports the specific speed i11 a similar form as follows: Then by substituting.
Table 4. Not shown in the table is the equation presented by Csanady A specific speed may be calculated for any point of turbine operation. TABLE 4. Hill curves are developed from extensive tests of model turbines.
Superimposed o n this performance map are contour lines for equal turbine efficiency that correspond t o the simultaneous values of Qwd and Ewd and also the corresponding values of the gate-opening a. The parameters used in the hill curve o f Fig. Figure 4. The discharge coefficient. These are three-dimensional grapllical representations of the variation of various turbine constants as related t o common parameters of head. Early versions of hilJ curves use unit power.
For instance. A typical representation of a hill curve is shown in Fig. These hill curves are used in making final design selec-. Department of the Interior has also presented information relating specific speed to the design head and other parameters of design.
An excellent treatise of these experience curves is presented in a series of articles on Francis turbines desiervo and d e k v a. The U. It is useful to determine just what type of turbine is suitable for a particular. Because the specific speed is an integrated universal number it has been used as the means of relating other needed parameters to a common base characteristic. To correct for this. Kovalev lists the where the coefficients m and n are related t o the coefficients used in calculating head losses in the described system..
In preliminary design and feasibility studies. Exaniple 4. The logical relation t o be developed is the relation between specific speed. Iloody proposed that a have a value of 0. Extensive experience curves have been developed for thus purpose. Sheldon has presented data on the efficiency step-up relations showing actual 'model-prototype test data from numerous U.
More recent work of Hutton and Hutton and Salami have related the efficiency step-up t o the Reynolds number of the model and prototype for different losses within a turbine system.
Results of that study give specific values for the exponent coefficient in the Moody form of the step-up equation. Army Corps of Engineers installations. In actual practice it is found that there is not precise equality between the model and the prototype with regard to efficiency due to differences in boundary layer friction and turbulence effects..
For turbine speed. Contract No. If the turbine is directly connected to the generator. May Diameter To make estimates of turbine diameter. The applications chart in Fig. Department of t h e Interior. Speed T o make necessary calculations for determining runner speed. In conventional American system of units and constants the equation becomes.
The work of deSiervo and deLeva shows the following equation for the Francis runner: This is different from throat diameter. Bureau of. For illustration purposes. Department of the Interior gives a similar equation. The literature of deSiervo and others gives much gnater detail on other design features and provides a basis for providing infor1: This figure shows typical efficiency curves n for different types of turbines over the fill1 range of power output. Exanlple 4.
T this form even though somewhat vague and in some cases tied to a given installation. For Francis runners the U. III the conventional American system of units and constants.
Chapter 11 will treat elements of civil works powerhouse design. Example 4. For Pelton turbines. Before proceeding it is necessary to consider a generalized characteristic of turbine efficiency. This is throat diameter minus clearance. Determine the type of turbine t o be used. American Society o f Civil Engineers. Bureau of Reclamation. Refcr t o Figs. Ittstitute of Mechanical Erlgirieers. Actual Theory o f Turbomachirles. Department of the Interior. Part 2.
Make a trial selection from Fig. Design and Construction. Using the hill curve of Fig. Develop a turbine constant for the unit diameter. Department of the Interior.. Engineering hlonop-aph No.
Hydropower Engineering. From Fig. Part 1. This implies that conceptualization has been made of where water will be directed from a water source and where the water will be discharged 'from a power plant. The measurement and analyses of these parameters are primarily liydrologic problems. Remembering that hydrology is the study of the occurrence.
In some reconnaissance studies. Determine the type of turbine. Show what will happen to the runner diameter if tlie next higher synchronous speed were used. Because the headwater elevation and tailwater elevations of the impoundment can vary with stream flow. Where would the specific speed. Determine the type of turbine to be used. Turbine Constants Chap. Thus the determination of tlie potential head for a proposed hydropower plant is a surveying problem that identifies elevations of water surfaces as they are expected to exist during operation of the hydroplant.
Make any necessary assumptions as to the specific speed or head to be used. Soil Conservation Service U. These normally require duration flow data that give time variability of water discharge sufficiently accurate to make possible capacity sizing of the phdnts. Details are given later on how to treat the flow variation problem. Feasibility studies are made to formulate a specific project or projects to assess the desirability of implementing hydropower development.
The flow duration curve also. Department of Commerce. Geological Survey. Ille format will vary. Good references for conducting such data measurement and acquisition programs are those by the World Meteorological Organization and Buchanan and Somers Extrapolations and correlations with nearby gaged records may be necessary.
This study used contour maps to determine head available in the streams. A flow duration curve merely reorders the flows in order of magnitude instead of the true time ordering of flows in a flow versus time plot. The data are also available as conlputer printout and in flow duration format. These studies normally require daily or at least monthly flow. Such information is normally available from the Weather Service of the U. State Geological Survey offices. Arrny Corps of Engineers Techniques for making such extrapolations are covered in such hydrology texts and references as Linsley.
Basic data and maps for determining forebay elevation and tailwater elevation can often be obtained from such sources as the Army Map Senice. In the United States.
The extent to which measurements and more sophisticated calculation of hydro! Many times the flow data records may be incomplete. In some cases it may be necessary to make estimations of flow and runoff magnitude using precipitation data and estimates of runoff coefficients. A resource-type study Gladwell. In other countries. Defizire plan or design studies are made before proceeding with implementation of final design and initiation of construction.
A flow durariorl curve is a plot of flow versus the percent of time a particular flow can be expected t o be exceeded. More sophisticated resource evaluations were completed under the National Hydropower Survey of the U. Forest Service Bureau of Reclamation U. The records may be short-tirne records. Three types of studies are commonly made: Ln some cases. Other agencies and entities that gather flow data include: Examples of how precipitation data can be used effectively in estimation of flow duration analyses will be presented in Example 5.
Another method. From these flow duration curves are developed a family of parametric duration curves in which flow Q is plotted against the average annual runoff E.
The order numbers are then divided by the total number in the record and multiplied by to obtain the percent of time that the mean flow has been equaled or exceeded during the period of record being considered.
Another good reference on duration curves is Searcy 1 The number of flows greater than the upper limit of a class interval can be divided by the total number of flow values in the data series to obtain the exceedance percentage.
A typical flow duration curve for a gaged stream location in Idaho is shown in Fig. The values of flow for each flow duration for a given excecdance point are divided by the average annual discharge. The flow value is then plotted versus the respective computed exceedance percentage. The variations in flow may be masked out if average flows for weekly or monthly intervals are used in flow duration analysis.
A tally is made of the num- ber of flows in each. The following method for making synthetic flow duration curves at any point along a stream is based on techniques developed in a hydropower inventory of the Pacific Northwest region of the United States Gladwell. The procedure is to make plots of flow durationcurves l for al gaged streams within a rather homogeneous drainage basin. A correlation analysis is then performed to obtain the best-fitting curve for the data taken from the measured records of stream flow.
Methods are required t o develop extrapolations of measured flow duration data which will be representative of a given site on a stream. The classes range from the highest flow value in the series t o the lowest value in the time series. Department of the Interior from the U.
It is possible to obtain digital printouts of the flow duration of all streams measured by the U. Two methods o f computing ordinates for flow duration curves are the rankordered technique and the class-interval technique.
A more thorough description of both of tliese methods and a listing of computer programs for processing such data are available in a University of Idaho Ph. It is easy to recognize g.
The value of the flow for the particular upper limit of the class interval is then plotted versus the computed exceedance percent. The rank-ordered values are assigned individual order numbers.
These are then plotted against the particular exceedance interval on logarithmic probability paper as shown in Fig. A annual discharge. Thedass-interval technique is slightly different in that the time series of flow values are categorized into class intervals.
Caution should be exercised in developing flow duration curves that use average values for intervals of time longer than one day. This type of analysis is particularly useful in regions where stream flow does not vary directly with the area of the contributing drainage. References to the flow duration values at specific exceedance value are usually made as Q The resalt is a parametric flow duration curve such as the one shown in Fig. The rank-ordered technique considers a total time series of flows that represent equal increments of time for each measurement value.
Al too often the stream flow data that are available from measured gaging l stations are not from the location for which a hydropower site analysis is to be made. Exceedance percentage Figure 5.
Hydrologic Analysis for Hydropower Chap. A procedure for making that determination follows. Determination of Average Annual Discharge To use the parametric flow duration curves effectively. Average annual runoff in C.
A parametric flow duration curve has been developed for the treanls UI the river basin being studied and is shown in Fig. Example 5. The product of this coefficient and the computed normal annual precipitation input to the basin and the basin area can be used to calculate the average annual discharge using the formula where average annual discharge. Determine the average annual discharge at the marked location and develop ordinate values for a flow duration curve at the site designated.
The location is at a point where n o stream flow ecord is available. Department of Conlmerce or from a state water resource planning agency. Corps of Engineers. The individual areas between isohyetal lines are planimetered and the areas used to develop a weighted-average precipitation input to a basin on an annual basis.
A stream location on the Clearwater River in Idaho has been identified for naking a hydropower analysis. The drainage basin contributing water to the site being investigated is graphically defined o n the isohyetal map or a map on which the isohyetal lines havc been superimposed. This is the summation of the mean daily discharges for all the Jays of the year. This value can be rather subjective in determination and thus represents a place for making a considerable error.
The plani-. This saves making an extra calculation that involves the constant Lermof days. A normal-annuallrecipitation nlap showing the isohyetal lines is presented in Fig. With the average annual discharge estimate it is possible t o enter the paranetric flow duration curve and determine values of flow for different exceedance ercentages for which the parametric flow duration curve has been developed.
Figure 5. Department of Agriculture. Planimctcred Area on Map in2. Entering the parametric flow duration curve of Fig. First, determine average annual precipitation input t o basin using data from Table 5. In many parts o f the coun t r y there are storage reservoirs that have b y their operations altered the flow of thi river. It is still possiblc to use a flow duration analysis if the entire sequence 0 1 regulated flow data o f a long time period can be obtained or generated b y reservoil operation studies.
The entire record then must be subjected t o either the rank ordered technique or the class-interval technique. It niay be necessary in some cases to combine tile flow records o f a regulated flow stream with the flow o f a n ungaged natural stream t o make hydropower analy sis.
The basic approach can be explained by referring t o the physiographic layoui o f Fig. The location for which flow data arc needed is a t point B. The flow a t B is the inflow from an area of considerable extenr where there is n o stream gage record, plus inflow from the operations o f a reservoil a t station A.
A normal annual precipitation map o f the entire drainage area ir required. Also, records from a nearby streanl gage station C o n an unregulatec; stream that can be considered t o represent the sequential variation of runoff frorr drainage area M crosshatched area are required.
These long-time records must cover the same period for which regulated flow data are available a t station A. First an estimate must be made of the average annual runoff from area M. This is done b y planimetering the isohyetal map of nomial annual precipitation a: Then a coefficient of runoff for the area or1 a n annual basis must be estimated.
Multiplying the. The map used had a scale of 1: A sequence of flows coming off area M must be computed.
The time increments or periods must correspond to the records of discharge available from the reservoir operation. First a flow record at station C n u t be obtained and studied. The record a t C is assumed to have the same time distribution of flow as the runoff coming off area M refer to Fig.
An incremental fraction of flow, ai,for each increment of time in the total desired time period must be obtained for the representative gage C. Figures 5. Once the sequential flows have been computed it is a simple procedure to add, sequen'.
Planimeter N. See Eq. Distribution of flow at gage must be representative of h a t can be expzcred from ungaged tributary area. I Compute average annual runof! Care should always be taken that the correct volume and time units are used in these calculations.
A problem using this approach with real data has been included at the end of the chapter to make this more meaningful. More detail on this procedure can be found in Heitz Deterministic and Stochastic Flow Methods.
With appropriate data on precipitation, antecedent conditions, soil conditions, and terrain characteristics, it is possible to generate flow data for use in hydropower analyses. Numerous deterministic models of varying sophistication are now available to make simulations of hydrologic runoff.
Stochastic models approach the time distribution of flow as statistical and treat the occurrences as probability distributions. With good historical data it is possible to generate a time series of flow data of any length. An excellent reference on this is the work of Haan The questions to be asked regarding the use of hydrologic stream flow simulation models are: Figurc 5.