Stilling Basins

18.1 INTRODUCTION

Stilling basins and energy dissipators are usually provided in conjunction with develop-ment of spillways, outlet works, and canal structures. It is often necessary to performhydraulic model studies of individual structures to be certain that these energy dissipatingdevices will operate as anticipated. A relatively large volume of data is available frommany laboratory and field studies performed in the past (Blaisdell, 1948; Bowers andToso, 1988; Bowers and Tsai, 1969; Chadwick and Morfett, 1986; Chaudhry, 1993; Chow1959; French, 1985; George, 1978; Hendreson, 1966; International Commission on LargeDams (ICOLD), 1987; Novak et al., 1990; Peterka, 1964; Robert son et al., 1988; Senturk,1994; Toso and Boweis, 1988; U.S. Bureau of Reclamation (USBR), 1974, 1987; Vischerand Hager, 1995, 1998). Based on the results of many intensive studies, in 1958, A. J.Peterka (1964) of the U.S. Bureau of Reclamation (USBR) published a summary reportof USBR’S studies entitled Hydraulic Design of Stilling Basins and Energy Dissipators,Engineering Monograph No. 25. Since then, this publication has been referenced widelywithin the hydraulic engineering community and still is one of the best references on thissubject available today. Energy dissipators are used to dissipate excess kinetic energy pos-sessed by flowing water. An effective energy dissipator must be able to retard the flow offast moving water without damage to the structure or to the channel below the structure.Vischer (1995) classified various types of energy dissipators by their features as: (1) bysudden expansions, (2) by abrupt deflections, (3) by counterflows, (4) by rough walls, (5)by vortex devices, and (6) by spray inducing devices. The stilling basins and energy dis-sipators discussed in this chapter are related to energy dissipation by expansion anddeflection.

There are two basic types of energy dissipators. They are hydraulic jump-type dissi-pators and impact-type dissipators. The hydraulic jump type energy dissipators dissipateexcess energy through formation of highly turbulent rollers within the jump. The impact-type dissipators direct the water into an obstruction that diverts the flow in all directionsand generates high levels of turbulence and in this manner dissipates the energy in theflow. In other cases, the flow is directed to plunge into a pool of water where the energy

CHAPTER 18HYDRAULIC DESIGN OFSTILLING BASINS ANDENERGY DISSIPATORS

C. Y. Wei and James E. LindellHarza Engineering Company

Chicago, Illinois.

18.1

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Source: HYDRAULIC DESIGN HANDBOOK

18.2 Chapter Eighteen

(a)

(b)

Exhibit 18.1: Wanapum project, Washington(a) General view of the spillway in operation.(b) Layout of the spillway and stilling basin.



HYDRAULIC DESIGN OF STILLING BASINS AND ENERGY DISSIPATORS

is diffused and dissipated. The impact-type energy dissipators include check drops andvertical drops, baffled outlets, baffled aprons, and vertical stilling wells. Generally, the useof an impact-type energy dissipator results in smaller and more economical structures.

18.2 STILLING BASINS

Using six test flumes, USBR conducted model studies for five stilling basin designs. Theresults are summarized and presented in the Engineering Monograph No. 25 mentionedabove (Peterka, 1964). In Basin I tests, all test flumes were used and the test data obtainedprovides basic hydraulic information concerning hydraulic jumps on a horizontal apron.The Type II basin was developed for high dam and earth dam spillways and large canalstructures where the approach velocity is high and the corresponding Froude numberexceeds 4.5. Type III stilling basin is suitable for general canal structures, small outletworks, and small spillways where the approach velocity is moderate or low and does notexceed 50–60 ft/s (15–18 m/s) and the unit discharge is less than 200 ft3/s/ft (18 m3/s). Forsmaller canal structures, outlet works, and diversion dams where the approach Froudenumber is relatively low (between 2.5 and 4.5) and the heads of the structures do notexceed 50 ft (15 m), Type IV stilling basin may be used. However, the jumps in the basinmay be unstable and alternative design such as the modified Type IV basin may be con-sidered. To achieve greater structure economy for high dam spillways, Type V stillingbasin with sloping apron may be considered. Photos of several stilling basin in operationare given in Exhibits 17.2, 17.4, 18.1, and 18.2.

18.2.1 General Hydraulic Jump Basin (Basin I)

The basic elements and characteristics of a hydraulic jump on horizontal aprons (Fig.18.1) is provided to aid designers in selecting more practical basins such as Basins II, III,IV, V, and VI. Jump occurs on a flat floor with no chute blocks, baffled piers or end sill inthe basin. Usually, it is not a practical basin because of its excessive length. For ahigh–velocity flow down a spillway chute with known terminal velocity (Fig. 18.1) anddepth entering the basin, the required tail water depth, the length of jump, and loss of ener-gy can be determined based on the curves provided in Fig. 18.2a–e.

18.2.2 Stilling Basins for High Dam and Earth Dam Spillways and Large Canal Structures (Basin II)

This stilling basin was developed for use on high spillways, large canal structures, andso forth for approach Froude numbers above 4.5. With chute blocks and dentated end sill,the jump and basin length can be reduced by about 33 percent. The basic design featuresof Basin II stilling basin are given in Fig. 18.3a. For preliminary designs, the curves forestimating required tailwater depth, and length of jump are given in Figures 18.3b and c.The water surface and pressure profiles can be determined based on Fig. 18.3d and e.The water surface profile in this basin can be closely approximated by a straight linemaking an angle a �(jump angle) with the horizontal. This line can also be considered asa pressure profile. The USBR guidelines for designing this type of stilling basins aregiven as follows:

Hydraulic Design of Stilling Basins and Energy Dissipators 18.3





(a)





(b)

(c)

Exhibit 18.2 Mayfield hydroelectric project, Washinton(a) Layout of the spillway including flip bucke.(b) General view of the spillway and the stilling pool(c) General view of the spillway and stilling pool.





FIGURE 18.1 Curves for velocity entering stilling basins from 0.8:1 to 0.6:1 steep slopes.(FromPeterka, 1964)





FIGURE 18.2 Basic hydraulic jump basins on horizontal aprons. (Basin I) (From Peterka, 1964)





FIGURE 18.3 Stilling basins for high dam and earth dam spillways and large canal structures. (BasinII)(From Peterka, 1964)




1. Determine velocity V1VV of flow entering the jump. Figure 18.1 may be used. Thischart represents a composite of experience, computation, and a limited amount ofexperimental information obtained from prototype tests on Shasta and Grand CouleeDams. The chart provides a fair degree of accuracy for chute having slopes of 0.8:1or steeper, where computation is a difficult and arduous procedure. The asymptot-ic nature of the terminal velocity curves is also depicted in Fig. 18.1. For a constanthead of 2.5 ft (0.8m) on the spillway crest, the terminal velocity does not increasesignificantly (from 51 ft/s or 15.5 m/s to 53 ft/s or 16.2 m/s) as the vertical distance(fall) from the reservoir level to stilling basin floor increases from 200 to 600 ft(61–183 m).

2. Set apron elevation to utilize full conjugate tail water depth. Add a factor of safetyif needed. A minimum margin of safety of 5 percent of tailwater depth (D2) is rec-ommended.

3. Exercise caution with effectiveness of the basin at lower values of the Froude number(V1VV / (gD1)

1/2) of 4 or lower. D1 is the depth of the flow entering the basin.

4. Determine the length of basin using the curve shown in Fig. 18.3c.

5. Use the depth of flow entering the basin, D1 as the height of chute blocks. Thewidth and spacing should be equal to approximately D1 but can be varied to avoidfractional blocks. A space equal to D1/2 is preferable along each side of wall toreduce spray and maintain desirable pressures.

6. As shown in Fig. 18.3a, set the height of the dentated sill equal to 0.2D2 and themaximum spacing approximately 0.15D2. For narrow basins, the width and spac-ing may be reduced but they should remain equal.

7. It is not necessary to stagger the chute blocks with respect to the sill dentates.

8. It is recommended that the sharp intersection between chute and basin apron bereplace with a curve of reasonable radius of at least 4D1 when the chute slope is 1:1or greater. Chute blocks can be incorporated on the curve surface as readily as onthe plane surfaces. The chute slope (0.6:1–2:1) does not have significant effect onthe stilling basin action unless it is nearly horizontal.

Following the above rules should result in a safe, conservative stilling basin forspillways up to 200 ft (60 ms) high and for flows up to about 500 (ft3/s/ft) [46.5(m3/s/m)] basin width, provided that jet entering the basin is reasonably uniformboth as to velocity and depth. For greater falls, larger unit discharges, or possibleasymmetry, a model study of the specific design is recommended.

18.2.3 Short Stilling Basins for Canal Structures, Small Outlet Works,and Small Spillways [Basin III and the St. Anthony (SAF) Basin]

For structures carrying relatively small discharges at moderate velocities, a shorter basinhaving a simpler end sill may be used if baffled piers are placed downstream from thechute blocks (Fig. 18.4). In this section, stilling basins for smaller structures in whichvelocity at the entrance to the basin are moderate or low ( up to 50–60 ft/s or 15–18 m/s)and discharges of up to 200 ft3/s/ft of width or 18 m3/s/m of width are discussed. The still-ing basin action is very stable for this design. It has a large factor of safety against sweep-out of the jump and operates equally well for all values of the Froude number above 4.0.






FIGURE 18.4 Short stilling basins for canal structures, small outlet works and small spillways.(BasinIII) (From Peterka, 1964)





This basin should not be used for velocities above 50 ft/s or 15 m/s to avoid potential cav-itation damages aginst baffle piers. Instead, Basin II type stilling basin should be consid-ered or hydraulic model studies should be performed. The following USBR guidelinespertain to the design of the Basin III type stilling basin:

1. The stilling basin operates best at full conjugate tail water depth, D2. A reasonablefactor of safety is inherent in the conjugate depth for all values of the Froude num-ber and it is recommended that this margin of safety not be reduced.

2. Determine the length of basin using the design curve given in Fig. 18.4c. It is lessthan one-half the length of the natural jump. It should be noted that an excess of tailwater depth does not substitute for basin length or vice versa.

3. Exercise caution with effectiveness of the basin at lower values of the approachFroude number [V1VV / (gD1)

1/2] of 4.5 or lower.

4. Height, width, and spacing of chute blocks should equal the average depth of flowentering the basin, or D1. Width of blocks may be decreased, provide spacing isreduced a like amount. Should D1 proved to be less than 8 in or 20 cm, the blocksshould be made 8 in or 20 cm high.

5. The height of the baffle piers (Fig. 18.4a) varies with the Froude number and isgiven in Fig. 18.4d. In narrow structures, block width and spacing may be reduced,provided both are reduced a like amount. A half space is recommended adjacent tothe walls.

6. The upstream face of the baffle piers should be set at a distance of 0.8D2 from thedownstream face of the chute blocks. This dimension is important.

7. The height of the solid end sill is given in Fig. 18.4d. The slope is 2:1 upward inthe direction of flow.

8. It is undesirable to round or streamline the edges of the chute blocks, end sill, orbaffle piers. It reduces the effectiveness of the energy dissipation. However, smallchamfers on the block edges to prevent chipping of the edges and to reduce cavita-tion erosion may be used.

9. It is recommended that a radius of reasonable length greater than 4D1 be used at theintersection of the chute and basin apron for slopes of 45º or greater.

10. As a general rule, the slope of the chute has little effect on the stilling basin actionunless long flat slopes are involved.

11. Experience indicates that the Type III basin works well for flow less than 200ft3/s/ft or 18 m3/s/m based on basin width and approach velocity at the entrance ofup to 50–60 ft/s or 15–18 m/s.

The St. Anthony Falls (SAF) Hydraulic Laboratory of the University of Minnesota hadalso developed a similar basin for small spillways, outlet works, and small canal structuresfor approach Froude numbers ranging from 1.7 to 17 (Blaisdell, 1948; Chow, 1959). Thisbasin was developed to achieve about 70 to 90 percent reduction of the jump lengths.This basin is commonly known as the SAF stilling basin (Fig. 18.5). Since the basin isrelatively short so that a significant amount of residual energy can still exist downstreamfrom the end sill, the channel reach downstream from the stilling basin should be allowedto erode until a stable scour depth is reached. Otherwise riprap protection should be pro-vided to minimize scour (Sec. 18.7). The guidelines for designing this basin are summa-rized as follows (Blaisdell, 1948; Chow, 1959):





FIGURE 18.5 The SAF stilling basin. (From Blaisdell, 1948)





1. The length L of the stilling basin is determined by the following equation.

L � �4F.

1

50.

y76

2�

where y2 is the theoretical sequent depth of the jump corresponding to the approachflow depth y1 and F1 is the approach Froude number.

2. The height of the chute blocks and floor blocks is y1, and the width and spacing areapproximately 0.75y1.

3. The distance from the upstream end of the stilling basin to the floor blocks is L/3.LL

4. No floor blocks should be placed closer to the side-wall than 3y1/8.

5. The floor blocks should be placed downstream from openings between the chuteblocks.

6. The total width of the floor blocks should occupies about 40 to 55 percent of thestilling basin width.

7. The widths and spacings of the floor blocks for diverging stilling basins shouldbe increased in proportion to the increase in stilling basin width at the floor blocklocation.

8. The height of end sill is given by c � 0.07y2.

9. The depth of tailwater above the stilling basin floor is given by

y'2 �

1.10 � �1

F21

0

2

�

y2 for F1 � 1.7 to 5.5

y'2 � 0.85y2 for F1 � 5.5 to 11.0

y'2 �

1.00 � �8

F01

0

2

�

y

2 for F1 � 11 to 17

10. The top of the side-wall above the maximum tailwater level to be expected duringthe life of the structure is given by z � y2/3.

11. Wing-walls should be equal in height to the stilling basin side-walls. The top of thewing-wall should have a slope of 1H:1V.VV

12. The wing-wall should be placed at an angle of 45º to the outlet center line.

13. The stilling basin side-walls may be parallel for a rectangular stilling basin or theymay diverge as an extension of the transition side-walls for a trapezoidal stillingbasin as shown in Fig. 18.5.

14. A cutoff wall of nominal depth should be used at the end of the stilling basin.

15. The effect of entrained air should be neglected in the design of the stilling basin.

18.2.4 Low Froude Number Stilling Basins(Basin IV and Modified Basin IV)

This stilling basin was developed for canal structures, outlet works, and diversion damswhere the approach Froude number of the basin is relatively low (between 2.5 and 4.5)





and the heads of the structures are about 50 ft (or 15 m). In this case, the jump is not fullydeveloped and unstable and the methods of design discussed previously do not apply.Alternative design and/or wave suppressors or Basin VI type stilling basin with a hang-ing baffle for energy dissipation may be considered. Guidelines for developinga low Froude number stilling basin (Basin IV) as depicted in Fig. 18.6 are given asfollows (Peterka, 1964):

1. A model study of the stilling basin is imperative.

2. Reduction of excessive waves created in the unstable jump is the main problemconcerning the design of the stilling basin.

3. A tailwater depth of 10 percent greater than the conjugate depth is strongly recom-mended.

4. Place as few appurtenances as possible in the path of the flow, as volume occupiedby appurtenances helps to create a backwater problem, thus requiring highertraining walls.

5. Use Fig. 18.6 to develop the design of the stilling basin. The number of deflectorblocks shown in the figure is a minimum requirement.

6. The length of basin can be obtained from Fig. 18.2c. No baffle piers are needed inthe basin.

7. The recommended maximum width of the deflector blocks is equal to D1 but0.75D1 is preferable from a hydraulic standpoint. The ratio of block width to spac-ing should be maintained as 1:2.5.

8. The extreme tops of the deflector blocks are 2D1 above the floor of the stillingbasin.

9. To accommodate the various slopes of chutes and ogee shapes encountered, thehorizontal top length of the deflector blocks should be at least 2D1. The upper sur-face of each block is sloped at 5º in a downstream direction for better operationespecially at lower discharges.

FIGURE 18.6 Low Froude number (2.5–4.5) stilling basin design (BasinIV).(From Peterka, 1964)





10. The addition of a small triangular sill placed at the end of the apron for scour con-trol is desirable. An end sill of the type developed for short stilling basins (BasinIII) can be used. The slope of the upstream face of the sill is 2:1 and the height ofthe sill can be determined based on Fig. 18.4d.

11. Basin IV stilling basin is applicable to rectangular cross sections only to minimizepotential wave–related problems.

Type IV stilling basin performs effectively in dissipating the energy at low Froudenumber flows for small canals and for structures with small unit discharges. It is alsoeffective in minimizing wave problems. Based on additional model tests, the U.S. Bureauof Reclamation (USBR) has developed a modified stilling basin for low Froude numberapproach flows (George, 1978). This stilling basin is suitable for approach flows withFroude numbers ranging from 2.5 to 5.0. The basin is relatively short and is provided withchute blocks, baffle piers, and a dentated end sill as shown in Fig. 18.7a. The guidelinesfor designing Modified Type IV stilling basin are given as follows (George, 1978):

FIGURE 18.7(a) Low Froude number stilling basin (Modified Basin IV).(From George, 1978)





1. A hydraulic model study is recommended to confirm the design. Erosion testsshould be included. Such tests should be made over a full range of discharges todetermine erosion potential downstream from the basin and to determine the poten-tial for the abrasive bed materials to move upstream into the basin.

2. Determine the theoretical D2 based on the known unit discharge and the approachflow depth D1.

FIGURE 18.7(b) Design curves for modified Basin IV stilling basin.(FromGeorges, 1978)




3. Determine tailwater depth as TW � 1.05 D2.

4. Set the length of the basin L � 3D2 (approximately).

5. Use Fig. 18.7a to develop the basic dimensions of the basin.

6. Determine the distance X from the chute blocks to the baffle piers. X varies from 1.3to 0.7 times D2 as the approach Froude number varies from 2.5 to 5.6 as shown inFig. 18.7b.

7. Determine the distance L1 from the toe of the chute to the upstream face of the endsill from Fig. 18.7b.

8. If (L1 � the length of the end sill) is longer than L then the stilling basin should beextended to include the end sill.

9. Set the widths of the baffle piers equal to 0.7D1 and heights equal to 1.0D1.

10. Determine the number of chute blocks and baffle piers by the following equations.

The total number of chute blocks and spaces N = (width – 2kW)/WW W

where

k � fractional width of block equal to side clearance, 0.375 � k � 0.50

width � total width of stilling basin

W � 0.70D1

The N value obtained should be rounded to the nearest odd number and then adjustvalues of W and k should be adjusted.

11. Use 0.2D1 as the top length of the baffle piers.

12. Determine end sill dimensions.

height � 0.2D2

width, W � 0.15D2

top length of end sills � 0.2 � height

The number of blocks and spaces N � (basin width)/W

(N should be rounded to the nearest odd number and then the value of Wshould be adjusted)

18.2.5 Stilling Basin with Sloping Apron

To achieve greater structural economy, a stilling basin with a sloping apron can be con-sidered. This type of stilling basin is usually used on high dam spillways. It needs greatertail water depth than horizontal apron. The energy dissipation is as effective as occurs inthe true hydraulic jump on a horizontal apron. The primary concern in sloping aprondesign is the tail water depth which is required to move the front of the jump up the slopeto the location where the jump is expected to start. It may not be economically feasible todesign the basin to confine the entire jump, especially when sloping aprons are used in






conjunction with medium or high overfall spillways where the rock foundation is in fair-ly good condition. When shorter aprons are used, the riverbed downstream must act as partof the stilling basin. On the other hand, when the quality of foundation material is ques-tionable, it is desirable to make the apron sufficiently long to confine the entire jump. Thetotal apron length may range from about 40 to 80 percent of the length of jump.The hydraulic jump may occur in several ways on a sloping apron, as depicted inFig. 18.8. The jump may have its toe form on the slope and the jump itself ends over thehorizontal apron (Case B), or ends at the junction of the slope and the horizontal apron(Case C), or the entire jumps forms on the slope (Case D). For practical purposes the actionin Cases C and D is the same. Guidelines for the design of sloping aprons are given below:

1. Determine an apron arrangement that will give the best economy for the maximumdischarge condition.

2. The first consideration should be to determine the apron slope that will require theminimum amount of excavation, the minimum amount of concrete, or both, for themaximum discharge and tailwater condition.

3. Position the slope so that the front of the jump will form at the upstream end of theslope for the maximum discharge and tailwater condition (Fig. 18.9). It may be nec-essary to raise or lower the apron, or change the slope entirely. Data obtained from13 existing spillways are also shown in Fig. 18.9. Each point in the figure has beenconnected with an arrow to the tan(θ) curve corresponding to the apron slope. Theadequacy of the tailwater depth of these spillways can then be evaluated.

4. Use Fig. 18.10 to determine the length of the jump for maximum or otherflows. Shorter basins may be used where a solid bed exists. For most installations,an apron length of about 60 percent of the length of jump for the maximum dis-charge condition should be sufficient. Longer basins are needed only when thedownstream riverbed is in very poor condition.

FIGURE 18.8 Stilling basins with sloping aprons. (From Peterka, 1964)





FIGURE 18.9 Comparison of existing sloping apron designs with experimental results.(From Peterka, 1964)

5. Ascertain that the tailwater and length of basin available for energy dissipationare sufficient for, say 1/4, 1/2, and 3/4 capacity. If the tailwater depth is deficient,a different slope or a new position of the sloping portion of the apron should beconsidered.

6. Horizontal and sloping aprons will perform equally well for high values of theFroude number if the proper tail water depth is provided.

7. The slope of the chute upstream from a stilling basin has no significant effect onthe hydraulic jump when the velocity distribution and depth of flow are reasonablyuniform on entering the jump.

8. A small solid triangular sill should be provided at the end of the apron to lift theflow as it leaves the apron for scour protection. The most effective height isbetween 0.05D2 and 0.10D2 and a slope of 3:1–2:1. Several existing stilling basinswith sloping aprons are shown in Fig. 18.11. All stilling basins shown weredesigned with the aid of model studies.

9. The stilling basin should be designed to operate with as nearly symmetrical flow inthe stilling basin as possible to avoid formation of large circulating eddies andtransport of riverbed material into the apron area, and the potential undermining ofthe wing walls and riprap.

10. A model study is advisable where the discharge over high spillways exceeds 500ft3/s/ft or 46.5 m3/s/m based on the apron width, where there is any form of asym-metry involved, and for the high values of the Froude number where stilling basinsbecome more costly and the performance becomes less acceptable.





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18.2.6 Other Types of Stilling Basins

Other types of stilling basins that may be considered include: (1) positive step basin, (2)negative step basin, (3) baffle–sill basin, (4) baffle-block basin, (5) expanding stillingbasin, and (6) bucket stilling basin. Detailed discussions of these basins have been pro-vided by Vischer and Hager (1995). These basins are briefly discussed as follows:

1. Positive–step basin. An upward step of a given height is provided in a prismatic chan-nel. No end sills are included. The required basin length is significantly longer thanthat of a classical jump basin.

2 Negative–step basin. A downward step is provided. No end sills are included. Itrequires a slightly longer basin length than the positive step basin. Basins with stepshave not been popular because it is easier to use sills or blocks in a horizontal apronthan to change the apron elevation at the step section.

3 Baffle–sill basin. A weir-type sill is provided to form a basin. The flow over the sillmay be submerged or free. The sill is capable of stabilizing the jump in a shorterbasin and with lower tailwater than is the classical jump basin. Sills can be econom-ical and effective devices for energy dissipation even without additional appurte-nance included.

4. Baffle–block basin. Baffle blocks are normally arranged in one or several rows that areoriented perpendicular to the direction of approach flow. Standard baffle blocks suchas the USBR blocks should be used. Baffle blocks are prone to cavitation damage andshould not be used for approach velocities above 20 m/s. For velocities between 20 and30 m/s, a chamfer on the block edges should be provided to reduce the cavitationpotential.

5. Expanding stilling basin. There are two types of expanding basins, namely graduallyexpanding basin and abruptly expanding basin. The gradually expanding basinrequires less tailwater depth and can be used for highly variable tailwater. This type ofbasin is suitable for approach flow with Froude numbers less than 4. Very few basinsof this type have been built. An abruptly expanding basin has been studied and report-ed by Vischer and Hager (Novak et al., 1990). No practical applications have beenreported.

18.2.7 Fluctuating Pressures on Stilling Basin Floors

When designing a stilling basin to achieve highest possible hydraulic efficiency in terms ofenergy dissipation, one should also consider the structural aspects of the stilling basin. Theeffect of transient pressures caused by turbulence in the jump can be significant and shouldbe considered in the design of the structure. Extensive discussions of this subject have beenprovided by International Commission on Large Dams (ICOLD, 1987), Toso and Bowers(1988), and Visher and Hager (1995), and so on. The hydromechanic characteristics and theturbulence level of the jump in a stilling basin depends not only on the relative tailwaterlevel but also on the geometry and the concrete finish conditions of the basin floor andtraining walls. The pressure fluctuations resulting from intense macro-scale turbulence inthe jump must be carefully considered during the design of the structure. The pressure fluc-tuations vary widely in amplitude at all locations within the jump. The maximum half-amplitude of the fluctuation has been determined to be approximately 40 percent of themean approach velocity head with a frequency of about 1 Hz. The dominant pulsatingcomponents have frequencies between 0 and 10 Hz. When the pressure becomes negative






at a point on the apron surface, a dangerous local instability may develop with respect tothe uplift pressure at the bottom of the concrete slab. Some projects have experienced highuplift pressures under large areas of the basin floor and resulted in complete floor concreteslabs being torn up (Bowers and Toso, 1988; ICOLD, 1987; Toso and Bowers, 1988). Inaddition, cavitation, abrasion, and vibration due to intense turbulence and pressure fluctu-ations can also contribute significantly to the damage of a stilling basin.

Based on the model studies of USBR Type II and Type III stilling basins, Toso andBowers (1988) obtained the following useful conclusions:

1. The pressure fluctuations in the jump tend to approach a definite limit, on the order of80 to 100 percent of the approach velocity head. This is on the order of 10–20 timesthe root-mean square (rms) of the pressure fluctuation.

2. Addition of chute blocks, intermediate blocks, and end sills did not result in signifi-cantly higher maximum negative and positive deviations than those for basins withoutblocks and sills. The energy dissipation was quicker.

3. Side-wall pressure fluctuations are very significant, and peak at one to two inflowdepths above the floor.

4. The longitudinal extent of extreme pressure pulsation in the zone of maximum turbulenceis on the order of eight times the inlet flow depth. The lateral extent of a characteristicpulse is approximately 1.6 times the longitudinal extent or 13 times the inlet flow-depth.

ICOLD (1987) recommended, as a minimum precaution, that the following two con-ditions be considered when designing the stilling basin apron:

1. Full downstream uplift pressure applied over the entire area of the floor with basin empty.

2. Full uplift pressure equals 12 percent of the approach velocity head applied under thewhole basin, with the basin full.

If necessary, the basin floor can be strengthened by providing anchors or using thick-er slabs which may be held in place by the side walls.

ICOLD (1987) also recommended following structural arrangements to minimizepotential uplift damages due to undesirable turbulent flow induced pressure fluctuations.

1. All contraction joints should be fitted with properly located and embedded seals.

2. There should be no drain openings in the training wall inside the basin. However, drainoutlets in a dentated sill at the beginning of a stilling basin have performed satisfactorily.

3. Keep the areas of the floor slabs as large as possible.

4. Connect slabs by means of dowels, shear keys, and reinforcement across the joints.

5. Keep horizontal construction joints to a minimum, with dowels across them.

6. If drainage is necessary, keep it well away (1–1.5 m at least) from the wetted surfacesso that abrasion or cavitation erosion will not make it accessible to the turbulent flow.

18.3 DROP-TYPE ENERGY DISSIPATORS

For small drops in canals with values of the Froude number between 2.5 and 4.5, adrop–type energy dissipator which is in the form of a grating is particularly applicable toreduce wave actions and dissipating energy. The device causes the over falling water jetto separate into a number of long, thin sheets of water which falls nearly vertical into thecanal below. It has excellent capability in dissipating energy and eliminating wave prob-lems. Guidelines for developing a drop-type energy dissipator are given as follows(Peterka, 1964):





1. The device is highly recommended for approach flow with the Froude number below 3.0.

2. The Froude number is computed at the top of the drop.

3. The dissipator consists of a series of steel rails, channel irons, or timber beams in theform of grating installed at the drop (Fig. 18.12).

4. The spacing beams may vary from 2/3 to the full width of the beams. The narrowerspacing is more effective. Use the following expression to compute the length ofbeams:

L � �CSN

Q

�2�� g�� y��

where Q�total discharge (ft3/s or m3/s, C � experimental coefficient (dimensionless),S � width of a space in feet or meters, N � the number of spaces, g � the accelera-tion of gravity (ft/s2 or m/sec2), and y � the depth of flow in the canal upstream (ft orm). The value of C is about 0.245.

5. The length of the beams varies from about 2.9 to 3.6 times the depth of the approachflow.

6. The rails or beams may be tilted downward at an angle of 3º or more to provide someself-cleaning capability. It may also be made adjustable and tilted upward to act as acheck to maintain a certain level in the canal upstream. However, more frequent clean-ing of the device may be required.

18.4 WAVE SUPPRESSORS

A wave suppressor is used to provide greater wave reduction to a proposed structure or anexisting waterway. Two types of wave suppressors may be considered. They are raft-typeand underpass-type wave suppressors. Both are applicable to most open-channel water-ways having rectangular, trapezoidal, or other cross-sectional shapes. Both types may beused without regard to the Froude number. The underpass-type suppressor providesgreater degrees of wave reduction but may be less economical than the raft-type.

FIGURE 18.12 Drop-type energy dissipator for small dropcanals.(From Pterka, 1964)





18.4.1 Raft-Type Wave Suppressors

A number of rafts of different designs were tested by USBR (Peterka, 1964). The mosteffective raft arrangement was found to consist of two rigid stationary rafts 20 ft (6.10m) long by 8 ft (2.45 m) wide, made from 6- by 8-in timbers, placed in the canal down-stream from the stilling basin as shown in Fig. 18.13. The arrangement is also applicablefor suppressing waves having a regular period such as wind waves or waves produced byoperation of pumps. Guidelines for designing a raft–type wave suppressor are providedas follows:

1. A space should be left between timbers and lighter crosspieces are placed on the raftsparallel to the flow. It creates many open spaces resembling rectangular holes.

2. The rafts should be perforated in a regular pattern and there should be some depth tothese holes.

3. The ratio of hole area to total area of the raft may vary from 1:6 to 1:8.

4. The 8 ft (2.5 m) width, W, as shown in Fig. 18.13, is a minimum dimension.WW

5. The raft must have sufficient thickness so that the troughs of the waves do not breakfree from the underside.

6. At least two rafts should be used, and the rafts should be rigid and held stationary.

7. The top surfaces of the rafts are set at the mean water surface in a fixed position so thatthey cannot move.

8. Spacing between rafts should be at least three times the raft dimension, measured par-allel to the flow. Each raft can decrease the wave height about 50 percent.

FIGURE 18.13 Raft-type wave suppressor. (From Peterka, 1964)




9. For suppressing waves having regular periods, the second raft should be placed down-stream at some fraction of the wave length to maintain its effectiveness. It may be nec-essary to make the second raft portable for narrow canals.

18.4.2 Underpass-Type Wave Suppressors

Based on numerous studies conducted, USBR determined that the most effective wavedissipator to be located downstream from a stilling basin is the short-tube type underpasswave suppressor (Peterka, 1964). When it becomes necessary to make the raft-type wavesuppressors adjustable or portable, or a moderate increase in depth in the stilling basin canbe tolerated, consideration should be given to the underpass-type wave suppressors. Itmay be added to an existing structure or included in the original construction. It can beused to prevent wave overtopping of the canal lining or bank erosion due to waves. Thestructure consists of a horizontal roof placed in the flow channel with a headwall suffi-ciently high to cause all flow to pass beneath the roof as shown in Fig. 18.14a. Three mainfactors should be considered when designing an underpass-type suppressor. They are thesubmergence of the roof, the length of the underpass, and the increase in flow depthupstream of the underpass. The following guidelines may be used to design an underpass-type suppressor:

1. The height of the roof above the channel floor may be set to reduce wave heights effec-tively for a considerable range of flows or channel stages.

2. The maximum wave reduction occurs when the roof is set 33 percent of the flow depthbelow the water surface for maximum discharge. The submergence and the percentreduction in wave height becomes less, in general, for smaller-than-maximum dis-charges.

3. Fig. 18.14c can be used to estimate the wave reduction. The upper curve shown in thefigure was obtained from the study conducted for the short tube underpass wave sup-pressor of the Carter Lake Dam No.1 Outlet Works. The lower curve shows the modeltest results of the Friant-Kern Canal (Fresno, California) underpass type suppressor forless than maximum discharges with smaller wave heights and shorter periods. Thewave period greatly affects the performance of a given underpass. The suppressor pro-vides a greater percentage reduction on short period waves. The wave action below astilling basin usually has no measurable period and the water surface is choppy andconsists of generated and reflected waves. The waves found downstream fromhydraulic jumps or energy dissipators usually have a period of not more than 5 s. Thereis a tendency for the wave period to become less with decreasing discharge.

4. The underpass is most effective when the velocity beneath the underpass is less thanabout 10 ft/s or 3 m/s and the channel length downstream from the underpass is threeto four times the length of the underpass.

5. The minimum length of underpass required depends on the amount of wave reductionconsidered necessary. For nominal wave reduction to prevent canal lining overtoppingor bank erosion due to waves, a length 1.0–1.5D2 will provide about 60 to 75 percentwave height reduction. For greater wave reduction, a longer underpass is necessary.






FIGURE 18.14 Underpass-type wave suppressor (From Peterka, 1964)

For wave periods up to about 5 s, an underpass 2.0–2.5D2 long may provide up to 88percent wave reduction. Up to about 93 percent of wave height reduction can beachieved by using an underpass 3.5–4.0D2 long. This length includes a 4:1 sloping roofextending from the underpass roof elevation to the tail water surface. The sloping por-tion should not exceed one-quarter of the total underpass length and slopes flatter than4:1 provide better draft tube action and are more desirable.

6. The greatest wave reduction occurs in the first D2 of underpass length, the constructionof two short underpasses rather than one may be considered. An additional wave reduc-





FIGURE 18.15 Basic design of an impact-type stilling basin (From Peterka, 1964)

tion of 10 percent may be achieved but the extra cost of an additional headwall shouldbe considered.

7. The backwater effect of the underpass can be determined based on Fig. 18.14b.

8. For design purposes, pressures along the underside of the roof may be considered tobe atmospheric. The average pressures on the headwall and the downstream verticalwall may be considered as hydrostatic.

18.5 IMPACT-TYPE STILLING BASIN FOR PIPE OR OPEN

CHANNEL OUTLETS

This is an impact-type energy dissipator equipped with a hanging-type �-shaped baffle,contained in a relatively small boxlike structure, which requires no tail water for success-ful performance (Fig. 18.15). The energy dissipation is accomplished by flow striking thevertical hanging baffle and being turned upstream by the horizontal portion of the baffleand by the floor, in vertical eddies, and is greater than in a hydraulic jump of the sameFroude number. It may be used to substitute Basin IV-type stilling basin for low Froude





FIGURE 18.16 Selection of width for an impact-type stilling basin. (From Peterka, 1964)

FIGURE 18.17 Comparison of energy losses – impact basin andhydraulic jump.(From Peterka, 1964)





number applications as discussed in Sec. 18.2.4. The impact-type stilling basin generallyprovides greater efficiency than that of a jump on horizontal floor (Fig. 18.17). Based onhydraulic model test results, generalized design rules and procedures have been developedby USBR (Peterka, 1964) and are given below to allow determination of the proper basinsize and all critical dimensions for a range of discharges up to 339 ft3/s (9.6 m3/s) andvelocities up to about 30 ft/s (9.1 m/s).

1. The use of the impact-type stilling basin discussed in this section is limited to instal-lation where the velocity at the entrance to the stilling basin does not greatly exceed30 ft/s (9.1 m/s).

2. The basin operates as well whether a small pipe flows full or a larger pipe flows par-tially full is used. An open channel having a width less than the basin width will per-form equally well.

3. Determine the stilling basin dimensions using Figs. 18.15 and 18.16 and Table 18.1,Columns 3–13 for the maximum expected discharge. For discharges exceeding 339ft3/s (or 10 m3/s), it may be more economical to consider multiple units side by side.

4. Compute the necessary pipe area from the velocity and discharge. The values inTable 18.1, Columns 1 and 2, are suggested sizes based on a velocity of 12 ft/s (3.7m/s) and the desire that the pipe run full at the discharge given in Column 3. Therelationship between discharge and basin size given in the table should be main-tained regardless of the pipe size chosen. An open–channel entrance may be used inplace of a pipe. The approach channel should be narrower than the basin with invertelevation the same as the pipe.

5. A moderate depth of tail water will improve the performance although tail water isnot a key factor for successful operation. For best operation, set the basin so thatmaximum tail water does not exceed d � g/2.

6. Recommended thickness of various parts of the basin are given in Columns 14-18,Table 18.1.

7. Determine the minimum size of individual riprap protective stones which will resistmovement when critical velocity occurs over the end sill. Most of the riprap shouldconsist of the sizes given in Table 18.1, Column 19 or larger. The following empiri-cal equation, which was developed based on studies performed by Marvis andLaushey, and Berry as reported by USBR (Peterka, 1964), may also be used to deter-mine the stone size with reasonable accuracy.

VbVV � 2.6 �d��

where VbVV � bottom velocity (ft/s), and d � diameter of rock (in). The rock isassumed to have a specific gravity of about 2.65. The accuracy of the equation forvelocities above 16 ft/s (4.9 m/s) is not known.

8. The entrance pipe or channel may be tilted downward about 15º without affectingperformance adversely. For greater slopes use a horizontal or sloping pipe (up to 15º)two or more diameters long just upstream from the stilling basin. Proper elevation ofthe invert at entrance is maintained as shown in Fig. 18.15.




TA

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18.32





9. The invert of the entrance pipe, or open channel, should be held at the elevation inline with the bottom of the baffle and the top of the end sill, regardless of the size ofthe pipe selected.

10. If a hydraulic jump is expected to form in the downstream end of the pipe and thepipe is sealed by the incoming flow, install a vent about one-sixth the pipe diameterat any convenient location upstream from the jump.

11. For the best possible operation of basin, use an alternative end sill and 45º walldesign as shown in Fig. 18.15. Erosion tendencies will be reduced.

18.6 BAFFLED APRON FOR CANAL OR SPILLWAY

DROPS (BASIN IX)

Baffled aprons or chutes have been used in many irrigation projects for being practical andeconomical. The chute is constructed on an excavated slope, 2:1 or flatter, extending tobelow the channel bottom. The multiple rows of baffle piers on the chute prevent exces-sive acceleration of the flow and provide a reasonable terminal velocity. Initial tailwateris not a prerequisite for the structure to be effective. Backfill is placed over one or morerows of baffles to restore the original streambed elevation. It prevents excessive accelera-tion of the flow entering the channel when scour or downstream channel degradationoccur. Through extensive model studies, the hydraulic design of the energy dissipators

FIGURE 18.18 Basic design of a baffled chute (From Peterka, 1964)





with baffled aprons have been generalized (Peterka, 1964). Basic proportions of a baffledchute are given in Fig. 18.18 and a simplified design procedure has been developed and isoutlined as follows:

1. The baffled apron should be designed for the maximum expected discharge, Q.

2. The unit discharge q � Q/W may be as high as 60 ft3/s/ft [or 5.6 m3/s/m] based onchute width, W.W

3. Approach velocity, V1VV , should as low as practical. Use recommended approach veloc-ity (Curve D) shown in Fig. 18.19.

4. The vertical offsets between the approach channel floor and the chute is used to cre-ate a stilling pool or desirable V1VV and will vary in individual installations. See Fig.18.20 for examples of approach pool arrangements. Use a short-radius curve to pro-vide a crest on the sloping chute. Place the first row of baffle piers close to the topof the chute no more than 12 inches or 30 cm in elevation below the crest.

5. Use the recommended height for baffled pier Curve B, Fig. 18.19.

6. Baffle pier widths and spaces should be equal and about 1.5 H but not less than H.Partial blocks, width 1/3 H to 2/3 H, should be placed against the training walls inRows 1, 3, 5, 7, and so forth, alternating with spaces of the same width in Rows 2,4, 6, and so on.

7. The slope distance (along a 2:1 slope) between rows of baffle piers should be 2H,twice the baffle height H. When the baffle height is less than 3 ft (or 91.5 cm), therow spacing may be greater than 2 H but should not exceed 6 ft or 183 cm.

8. The baffle piers may be constructed with their upstream faces normal to thechute surface.

FIGURE 18.19 Recommended baffle pier heights and allowable velocities for baffled chutes (FromPeterka, 1964)





FIGURE 18.20a Examples of existing baffled chute designs (From Peterka, 1964)





FIGURE 18.20a Examples of existing baffled chute designs (From Peterka, 1964)





FIGURE 18.20b Examples of existing baffled chute designs (From Peterka, 1964)





9. Four rows of baffle piers are required to establish full control of flow. The chuteshould be extended to below the normal downstream channel elevation and at leastone row of baffles should be buried in the backfill.

10. The chute training wall should be three times as high as the baffle piers to containthe main flow and splash.

11. Riprap consisting of (6 to 12-in) (15 to 38-cm) stone should be placed at the down-stream ends of the training walls to prevent eddies from working behind the chute.The riprap should not extend appreciably into the flow area.

18.7 RIPRAP FOR STILLING BASIN DOWNSTREAM PROTECTIONS

Riprap stones are placed on the channel bottom and bank downstream of a stilling basinto prevent bank erosion caused by surges and residual energy from the stilling basin toreduce the possible undermining of the structure by the erosive currents. Factors affect-ing design of the riprap include size or weight of the individual stones, the shape of thelarge stones, the gradation of the entire mass of riprap, the thickness of the layer, thetype of filter or bedding material placed beneath the riprap, the slope of the riprap layer,velocity and direction of currents, and eddy action and waves, etc. Based on publishedmaterial, laboratory observations and field experience, a design curve (Fig. 18.21) wasdeveloped for the determination of the individual stone size to resist a range of veloci-ties (Reference 3). Use the estimated bottom velocity or the average velocity at the endsill of the stilling basin to find the maximum stone size in Fig. 18.21. Specify riprap sothat most of the graded mixture consists of this size. Place the riprap in a layer at least1.5 times as thick as the maximum stone size. It is recommended that the riprap beplaced over a filter, or bedding, composed of gravel or graded gravel having the largerparticles on the surface.

18.8 SUBMERGED DEFLECTOR BUCKETS

There are occasions that it is desirable to deliver the spillway discharge directly to theriver without additional streambed protection works, the jet may be projected beyond thestructure by a deflector bucket which acts as an energy dissipator at the base of a steepopen chute spillway. USBR had developed both slotted and solid deflector buckets(Fig. 18.25) for high, medium, and low dam spillways. Both types require a greater depthof tailwater than a hydraulic jump stilling basin. However, the hydraulic action and theresulting performance of the two buckets are different. In general, the slotted bucket isan improvement over the solid type, particularly for lower ranges of tail water depths.USBR (Peterka, 1964) developed a simplified seven-step design procedure for the slot-ted bucket as follows:

1. Determine Q, q (per foot or meter of bucket width), V1VV , D1; compute Froude numberfrom F � V1VV /(g D1)

1/2 for maximum flow and intermediate flows.

2. Enter Fig. 18.22 with F to find bucket radius parameter R/(D1� V1VV 2/2g) from whichminimum allowable bucket radius, R, may be computed.





FIGURE 18.21 Curve to determine maximum stone size in riprap mixture. (From Peterka, 1964)





FIGURE 18.22 Minimum allowable bucket radius for slotted and solid buckets. .(From Peterka, 1964)





FIGURE 18.23 Minimum tail waterlimit for slotted and solid buckets..(From Peterka, 1964)





FIGURE 18.24 Maximum tail water limit for slotted and solid buckets. .(From Peterka, 1964)





FIGURE 18.26 Average water surface profilesfor submerged buckets. (From Peterka, 1964)

FIGURE 18.25 Examples of submerged bucket designs..(From Peterka, 1964)





FIGURE 18.27 Water surface profile characteristicsfor slotted buckets (From Peterka, 1964).

3. Enter Fig. 18.23 with R/(D1� V1VV 2/2g) and F to find TminTT /D// 1 from which minimum tail-water depth limit TminTT , may be computed.

4. Enter Fig. 18.24 as in Step 3 above to find maximum tailwater depth limit, TmaxTT .

5. Set bucket invert elevation so that tail water curve elevations are between tailwaterdepth limits determined by TminTT and TmaxTT . Keep apron lip and bucket invert aboveriverbed, if possible. For best performance, set bucket so that the tailwater depth is nearTminTT . Check factor of safety against sweep out.

6. Complete the design of the bucket, using Fig. 18.25 to obtain tooth size, spacing,dimensions, and so on.

7. Use Figs. 18.26 and 18.27 to estimate the water surface profile in and downstreamfrom the bucket.

18.9 FLIP BUCKETS

Flip bucket or ski-jump energy dissipators are often used in association with high over-flow dams to reduce the project cost when spray from the jet can be tolerated and the ero-sion by the plunging jet can be controlled. Most of the energy is dissipated when the jetplunges into the tailwater. Factors affecting the horizontal throw distance from the bucketlip to the point of jet impact are the exit velocity of the jet at the bucket lip, the bucket lip





(a)

angle, and the difference in elevation between the lip and the tailwater. With the origin ofthe coordinates taken at the lip of the bucket, the trajectory of the jet may be expressed bythe following equation:

(b)





Exhibit 18.3: Strontia springs project, Colorado (Courtesy Denver Water Department, Denver, Colorado)(a) General view of the spillway with low-level-outlet-work in operation.(b) General view of the spillway with low-level-outlet-work in operation.(c) Close-up view of the spillway in operation showing free trajectory and impact at the

plunge pool.

(c)

(a)





(b)

Exh

ibit

18.

4M

ossy

rock

Hyd

roel

ectr

ic P

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ct,M

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,Was

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(a) A

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illw

ay in

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ee ta

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ory

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way

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,pow

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iver

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els.





FIGURE 18.28 Flip bucket and toe curve pressures. (From USACE, 1998)




y � x tan θ �

where θ � angle of edge of lip with horizontal, K � factor usually assumed as 0.9 to com-pensate for loss of energy, d � depth of water on bucket, hv � velocity head of jet at thelip of the bucket

In general, the exit angle at the lip should not exceed 30º and the minimum radius ofcurvature should not be less than 5 times the depth of water on the bucket. The pressuredistribution on spillway flip buckets associated with high–overflow dams can be estimat-ed based on the Corps of Engineers test data (USACE, 1988) as shown in Fig. 18.28. Fordesign purposes, allowance for spillway energy losses should be included in the compu-tation of the energy head, HT at the invert of the bucket. A discussion of the plungepool hydrulics including scour depth and jet diffusion is given in section 17.3. Photosof several flip bucket type energy dissipators are given in Exhibits 17.2, 17.3, 17.11,18.3, and 18.4

18.9.3 Gas Supersaturation

Gas supersaturation problems occur at dams with spillways designed with deep plungepools and with deep stilling basins that operate submerged hydraulic jumps. When spilledwater with entrained air plunges to depths where the pressures can significantly exceedone atmosphere, the flow becomes supersaturated with gasses. Fish exposed to these gassupersaturated conditions develop gas emboli in the tissues. This condition known as gasbubble disease, cause injury to the fish, and can result in death..

When considering the selection and design of an energy dissipator for use in a damproject, gas supersaturation must be considered. Deflectors that direct discharges alongthe surface and energy dissipating devices that disperse the flow to reduce the depth of theplunge, such as Howell-Bunger valves, are considerations.

Stilling basins that are designed for high unit discharges, but primarily operate for lowerdischarges often have deep basins and excess tailwater depths for the lower discharges. Inthis condition the hydraulic jump is submerged, with the flow plunging to the bottom of adeep pool in the stilling basin. In large spillways these conditions can cause supersatura-tion. In situations where it is not practical to use alternative energy dissipators or design thespillway and stilling basin with lower unit discharges, it may be necessary to divide thespillway and stilling basin with walls. This permits operation of a portion of the structureat higher unit discharge for lower releases, thus effectively reducing the tailwater excess.

18.9.4 Abrasion in Stilling Basins

Many stilling basins are subject to at least some wear due to abrasion from material thatgets washed into the basin and circulates in contact with the concrete surfaces with theflow. To minimize problems due to abrasion, stilling basins should be operated withuniform discharge. Spillways with crest gates should be operated with all gates openedequally to avoid recirculation in the stilling basin. When only one or a few gates areopened on a spillway with a wide stilling basin, circulation patterns develop in the spill-way which can transport streambed material from downstream into the stilling basin. It isnecessary for the designer to consider all conditions under which the spillway and energy

x2

��K[4 (d � hv) cos2 θ]






dissipator will operate. If nonuniform operation of gates is expected to be required to passlow discharges, consideration should be given to dividing the spillway and stilling basinwith guide walls to provide a portion that could be used to pass low discharges withoutcreating recirculation patterns in the stilling basin.

18.10 STILLING BASIN DESIGN EXAMPLES

18.10.1 Design Example 1

The crest of an overfall spillway is 200 ft (61 m) above the horizontal floor of the still-ing basin and the slope of the spillway chute is 0.7:1. The head (H) on the spillway crestHHis 30 ft (9.14 m) and the maximum unit discharge (q) is 480 (ft3/s/ft) [44.6 (m3/s/m]based on the the stilling basin width. Design a Type II stilling basin for these conditions(Peterka, 1964).

Step 1. Determine approach conditions including velocity (V1VV ) of flow entering the basin.

a. Compute the total distance from the reservoir level to the basin floor (total fall)Z.

Z � head on the crest (H) + vertical distance from crest to basin floorHH

� 30 � 200 � 230 ft (70.1 m)

b. Entering Fig. 18.1 with Z ( � 230 ft) and H ( � 30 ft) and determine the ratio ofactual velocity (VAV ) versus theoretical velocity (VTVV ) that is,TT

�VV

AV

TVV�� 0.92

c. Compute the theoretical velocity based on the equation given in Fig. 18.2.

VTVV � �2�� g��

�� 2�� 3�� 0��

3�� 20��

�� 117.6 ft/s (35.8 m/s)

d. Compute the actual velocity VAV (� V1VV of the jump) and the corresponding depthD1 and the approach Froude number F1.

V1VV � VAV � 117.6 � 0.92 � 108.2 ft/s (33.0 m/s)

D1 � �V

q

1VV� � �1

40880.2� � 4.44 ft (1.35 m)

F1 � � ��3�� 2��

1

.2��08

��.2

4�� .4�� 4�� 9.04

Step 2. Set basin apron elevation:

a. Determine tailwater depths. Entering Fig. 18.3b with the Froude number (F1)of 9.04, the heavy dashed line for TW/WW D// 2 � 1.0 gives

V1VV�g�� D�� 1��





TW/WW D// 1 � 12.3

b. Compute D2.

D2 � TW � 12.3 � D1 � 12.3 � 4.44 � 54.6 ft (16.6 m)

c. Check factor of safety (FS) with the minimum tailwater depth required as givenin Fig. 18.3b.

For F1 � 9.04, TWminWW /D// 1 � 11.85, TWminWW � 11.85 � 4.44 � 52.6 ft (16.0 m)

FS � (TW � TWminWW )/D// 2 � (54.6 � 52.6) / 54.6

� 4.0 percent � 5 percent (recommended minimum margin of safety)

To satisfy 5 percent minimum margin of safety:

Use TW � TWminWW � 0.05 � D2 � 52.6 � 0.05 � 54.6 � 55.3 ft (16.9 m)

Reposition the stilling basin apron accordingly.

Step 3. Check the effectiveness of the stilling basin:

F1 � 9.04 4.0

The jump should be fully developed for effective energy dissipation.

Step 4. Determine the basin length:

a. Entering Fig. 18.3c with F1 � 9.04 and determine the corresponding valueof L/LL D// 2.

�DL

2� � 4.28

b. LII � L � 4.28 � 54.6 � 234 ft (71.3 m)

Step 5. Determine chute block height, width, and spacing.

Referring to Fig. 18.3a, the recommended height, width, and spacing of thechute block is D1.

Height � width � spacing � D1 � 4.44 ft � 4 ft 5.3 in (use 4 ft 6 in or 1 m35 cm)

Step 6. Determine the height, width, and of the dentated sill based on the recommendeddimensions shown in Fig. 18.3a.

a. Height � 0.2D2 � 0.2 � 54.6 � 10.92 ft (use 11 ft or 3 m 33 cm)

b. Width � spacing � 0.15D2 � 0.15D2 � 0.15 � 54.6 � 8.19 ft (2.50 m) (use8 ft 3 in or 2 m 50 cm)

18.10.2 Design Example 2

In this example (Peterka, 1964), the dimensions of the Type III stilling basin of a smalldam are to be determined. The width of the basin is 50 ft (15.24 m) and the flow is sym-metrical. Based on the design of the spillway, values of V1VV and D1 for the range of dis-charges to be considered have been determined and are given as follows:





Q q V1V D1

ft3tt /s (m3 3/s) ft3 3tt /s/ft [(m3 3/s/m] ft/s (m/s) ft/s (m/s) 3

3,900 (110.5) 78.00 (7.25) 69.0 (21.0) 1.130 (0.344)

3,090 ( 87.5) 61.80 (5.74) 66.0 (20.1) 0.936 (0.285)

2,022 ( 57.3) 40.45 (3.76) 63.0 (19.2) 0.642 (0.196)

662 ( 18.7) 13.25 (0.87) 51.0 (15.5) 0.260 (0.079)

Resulting from a backwater analysis of the downstream channel, the tailwater ratingcurve is also available as shown in Fig. 18.29. The tailwater elevation for 3900 ft3/s (110.5m3/s) is at elevation 617.50 ft (188.22 m).

Step 1. Compute the “jump elevation curve.”

a. Compute F1 based on given V1VV and D1 values.

(computed F1 values are shown in the table below)

b. Determine D2 by entering Fig. 18.4b with the computed values of F1.

c. Assume the most adverse operating condition occurs at the maximum dischargeof 3900 ft3/s (110.5 m3/s) and set the apron elevation accordingly.

D2 � 17.8 ft (5.43 m)

FIGURE 18.29 Tailwater and jump elevation curve for design example 2. (From peterka,1964)





Apron elev. � 617.5 � 17.8 � El. 599.7 ft

� 188.22 � 5.43 � El. 182.8 m

d. Compute jump elevations for the remaining three discharges as shown in the tablebelow for “jump elevation Curve a.”

Q F1 D1 D2 / D1 D2 Jump Elev. Jump Elev.ft3tt /s ft ft Curve a, ft Curve a', ft3

3900 11.42 1.130 15.75 17.80 617.5 615.0

3090 12.02 0.936 16.60 15.54 615.2 612.7

2022 13.85 0.642 19.20 12.33 612.0 609.5

662 17.62 0.260 24.50 6.37 606.1 603.6

or

Q F1F D1 D2 / D1 D2 Jump Elev. Jump Elev.m3/s m m Curve a, m Curve a', m3

110.5 11.42 0.344 15.75 5.43 188.22 187.45

87.5 12.02 0.285 16.60 4.74 187.52 186.75

57.3 13.85 0.196 19.20 3.76 186.54 185.78

18.7 17.62 0.079 24.50 1.94 184.74 183.98

Step 2. Compare the jump elevation curve with the tailwater rating curve as shown inFig. 18.29.

It indicates tailwater depth deficiency for smaller discharges especially at approx-imately 2850 ft3/s (80.7 m3/s) where the curvature of the tailwater rating curve isconcave upward.

Step 3. Shift the apron elevation curve downward such that the full conjugate depth isrealized at the most adverse 2850 ft3/s (80.7 m3/s) tailwater condition. A down-ward shift of 2.5 ft (0.76 m) is required as indicated by “jump elevation Curve a'”in Fig. 18.29 and the accompanying table.

Step 4. Reset the apron elevation:

Apron elev. � 599.7 � 2.5 � El. 597.20ft

� 182.79 � 0.76 � El. 182.03 m

Step 5. Determine the remaining stilling basin details based on the maximum dischargeof 3900 ft3/s (110.5 m3/s).

Step 6. Determine basin length based on conjugate depth:

Entering Fig. 18.4c with F1 � 11.42.




�LD

II

2

I� � 2.75

The basin length � LIII � 2.75 � 17.80 � 48.95 ft (14.9 m)

Step 7. Determine the height, width, and spacing of chute blocks in accordance withFig. 18.4a.

h1 � W1WW � S1 � 1.0D1 �1.13 ft (use 13 or 14 in) (35 cm)

Step 8. Determine height of the baffle piers in accordance with Fig. 18.4d.

h3 � 2.5D1 � 2.5 � 1.13 � 2.825 ft (use 34 in) (86 cm)

Step 9. Compute the spacing of the baffle piers as 0.75h3.

Baffle pier spacing � 0.75 � 34 � 25.5 in (65 cm)

Step 10.Compute the distance between the baffle piers and the chute blocks as 0.8D2.

Distance � 0.8 � 17.8 � 14.24 ft (4.34 m)

Step 11.Compute the height of the solid end sill h4 based on Fig. 18.4d.

h4 � 1.60D1 � 1.60 � 1.13 � 1.81 ft (use 22 in) (55 cm)

The final dimensions of the Type III stilling basin are shown in Fig. 18.29.

REFERENCES

Blaisdell, F. W., “Develop and Hydraulic Design—Saint Anthony Falls Stilling Basin,”Transactions, ASCE, 113, P.334 1948.

Bowers, C. E., and J. W. Toso, “Karnafuli Project, Model Studies of Spillway Damage,” Journal ofHydraulic Engineering, ASCE, 114 (5), 1988.

Bowers, C. E., and F. Y. Tsai, “Fluctuating Pressures in Spillway Stilling Basins,” Journal ofHydraulic Engineering, ASCE, 95 (HY6), 1969.

Chadwick, A. J., and J. C. Morfett, Hydraulics in Civil Engineering, Allen & Unwin, London,1986.

Chaudhry, M. H., Open-Channel Flow, Prentice-Hall, Englewood Cliffs, NJ, 1993.

Chow, V. T., Open-Channel Hydraulics, McGraw-Hill, New York, 1959.

French, R. H., Open-Channel Hydraulics, McGraw-Hill, New York, 1985.

George, R. L., Low Froude Number Stilling Basin Design, REC-ERC-78-8, U.S. Bureau ofReclamation, 1978.

Henderson, F. M., Open Channel Flow, Macmillan, New York, 1966.

International Commission on Large Dams (ICOLD), Spillways for Dams, Bulletin 58, ICOLD,Paris, 1987.

Novak, P., A. I. B. Moffat, C. Nalluri, and R. Narayanan, Hydraulic Structures, Unwin Hyman,London, 1990.

Peterka, A. J., Hydraulic Design of Stilling Basins and Energy Dissipators, Engineering





Monograph No. 25, U.S. Bureau of Reclamation, Denver, Co, 1964.

Roberson, J. A., J. J. Cassidy, and M. H. Chaudhry, Hydraulic Engineering, Houghton Mifflin,Boston, 1988.

Senturk, F., Hydraulics of Dams and Reservoirs, Water Resources Publications, Highlands Ranch,COl 1994.

Toso, J. W., and C. E. Bowers, “Extreme Pressures in Hydraulic-Jump Stilling Basins,” Journal ofHydraulic Engineering, ASCE, 114 (8), 1988.

U.S. Army Corps of Engineers (USACE), Hydraulic Design Criteria, U.S. Army Corps ofEngineers Waterways Experiment Station, Vicksburg, MS, 1988.

U.S. Bureau of Reclamation (USBR), Small Canal Structures, U.S. Bureau of Reclamation,Denver, CO, 1974.

U.S. Bureau of Reclamation (USBR), Design of Small Dams, U.S. Bureau of Reclamation, Denver,CO, 1987.

Vischer D. L., and W. H. Hager, Energy Dissipators—Hydraulic Design Considerations, IAHRHydraulic Structures Design Manual No. 9, A. A. Balkema, Rotterdam, Netherlands, 1995.

Vischer D. L., and W. H. Hager, Dam Hydraulics, John Wiley & Sons, New York, 1998.





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