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    Hydraulic Design of Energy Dissipators for Culverts andChannelsHydraulic Engineering Circular Number 14, Third Edition

    Chapter 8 !tilling "asinsStilling basins are external energy dissipators placed at the outlet of a culvert, chute, or rundown.These basins are characterized by some combination of chute blocks, baffle blocks, and sillsdesigned to trigger a hydraulic jump in combination with a required tailwater condition. ith therequired tailwater, velocity leaving a properly designed stilling basin is equal to the velocity in thereceiving channel.!epending on the specific design, they operate over a range of approach flow "roude numbers from#.$ to #$ as summarized in Table %.#. This chapter includes the following stilling basins& 'S() Type***, 'S() Type *+, and S". The 'nited States (ureau of )eclamation -'S() basins weredeveloped based on model studies and evaluation of existing basins -'S(), #/%$. The St. nthony"alls -S" stilling basin is based on model studies conducted by the Soil 0onservation Service atthe St. nthony "alls 1ydraulic 2aboratory of the 'niversity of 3innesota -(laisdell, #/4/.

    Table 8#1# $pplicable %roude Number &anges for !tilling "asins

    !tilling "asin 'inimum $pproach %roudeNumber

    'a(imum $pproach %roudeNumber

    'S() Type *** 5.4 #$

    'S() Type *+ 6.4 5.4

    S" #.$ #$

    The selection of a stilling basin depends on several considerations including hydraulic limitations,constructibility, basin size, and cost. The design examples in this chapter all use the identical siteconditions to provide a comparison between the size of basins and a free hydraulic jump basin forone case. Table %.6 summarizes the results of these examples with the incoming "roude number,the required tailwater at the exit of the basin along with basin length and depth. "or this example, theS" stilling basin results in the shortest and shallowest basin. !etails of the design procedures andthis design example are found in the following sections.

    Table 8#)# E(ample Comparison of !tilling "asin Dimensions

    "asin Type1 %roude Number&e*uired Tail+ater,

    m -ft."asin /ength,m -ft. "asin Depth,m -ft.

    "ree jump $.7 8.# -#9.# 88.$ -#9/.6 5.% -#4.4

    'S() Type *** 7./ 8.9 -/.7 69.7 -7$.8 8.% -#6.4

    'S() Type *+6 %.9 8.4 -##.6 8%.# -#6#.% 4.4 -#$.5

    S" 7.# 6.5 -$./ #6.5 -8/.$ 6.$ -%.7

    #(ased on a 8 m by #.% m -#9 ft by 7 ft box culvert at a design discharge of ##.% m8:s -5#$ ft8:s. ll basinshave a constant width equal to the culvert width. !etailed description of the example is found in Section%.#.

    6The 'S() Type *+ approach "roude number is outside of the recommended range, but was included forcomparison.

    8)equired tailwater influences basin depth. +elocity leaving each of these basins is the same anddepends on the tailwater channel.

    8.1 Expansion And Depression For Stilling Basinss explained in 0hapter 5, the higher the "roude number at the entrance to a basin, the moreefficient the hydraulic jump and the shorter the resulting basin. To increase the "roude number asthe water flows from the culvert to the basin, an expansion and depression is used as is shown in

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    "igure %.#. The expansion and depression converts depth, or potential energy, into kinetic energy byallowing the flow to expand, drop, or both. The result is that the depth decreases and the velocityand "roude number increase.

    %igure 8#1# Definition !0etch for !tilling "asin

    The "roude number used to determine jump efficiency and to evaluate the suitability of alternativestilling basins as described in Table %.# is defined in ;quation %.#.

    -%.#

    where,"r#< "roude number at the entrance to the basin+#< velocity entering the basin, m:s -ft:sy#< depth entering the basin, m -ftg < acceleration due to gravity, m:s6-ft:s6

    To solve for the velocity and depth entering the basin, the energy balance is written from the culvertoutlet to the basin. Substituting =:-y#( for +#and solving for = results in&

    -%.6

    where,

    (< width of the basin, m:s -ft:s+o< culvert outlet velocity, m:s -ft:sy#< depth entering the basin, m -ftyo< culvert outlet depth, m -ftz#< ground elevation at the basin entrance, m -ftzo< ground elevation at the culvert outlet, m -ft

    ;quation %.6 has three unknowns y#, (, and z#. The depth y#can be determined by trial and error if(and z#are assumed. (should be limited to the width that a jet would flare naturally in the slopedistance 2.

    -%.8

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    where,2T< length of transition from culvert outlet to basin, m -ftST< slope of the transition, m:m -ft:ft

    "ro< outlet "roude numberSince the flow is supercritical, the trial y#value should start near zero and increase until the design =is reached. This depth, y#, is used to find the sequent -conjugate depth, y6, using the hydraulic jumpequation&

    -%.5

    where,y6< conjugate depth, m -fty#< depth approaching the jump, m -ft0 < ratio of tailwater to conjugate depth, T:y6"r#< approach "roude number

    "or a free hydraulic jump, 0 < #.9. 2ater sections on the individual stilling basin types provideguidance on the value of 0 for those basins. "or the jump to occur, the value of y6> z6must beequal to or less than T > z8as shown in "igure %.#. *f z6> y6is greater than z8>T, the basin mustbe lowered and the trial and error process repeated until sufficient tailwater exists to force the jump.*n order to perform this check, z8and the basin lengths must be determined. The length of thetransition is calculated from&

    -%.4

    where,2T< length of the transition from the culvert outlet to the bottom of the basin, m -ftST< slope of the transition entering the basin, m:m -ft:ft

    The length of the basin, 2(, depends on the type of basin, the entrance flow depth, y#, and the

    entrance "roude number, "r#. "igure %.6 describes these relationships for the free hydraulic jump aswell as several 'S() stilling basins.

    %igure 8#)# /ength of Hydraulic ump on a Hori2ontal %loor

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    The length of the basin from the floor to the sill is calculated from&-%.7

    where,

    2S< length of the basin from the bottom of the basin to the basin exit -sill, m -ftSS< slope leaving the basin, m:m -ft:ft

    The elevation at the entrance to the tailwater channel is then calculated from&-%.$

    where,z8< elevation of basin at basin exit -sill, m -ft

    "igure %.# also illustrates a radius of curvature between the culvert outlet and the transition to thestilling basin. *f the transition slope is 9.4+ or steeper, use a circular curve at the transition with aradius defined by ;quation %.% -3eshgin and 3oore, #/$9. *t is also advisable to use the samecurved transition going from the transition slope to the stilling basin floor.

    -%.%

    where,r < radius of the curved transition, m -ft"r < "roude numbery < depth approaching the curvature, m -ft

    "or the curvature between the culvert outlet and the transition, the "roude number and depth aretaken at the culvert outlet. "or the curvature between the transition and the stilling basin floor, the"roude number and depth are taken as "r#and y#.

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    8.2 General Design ProcedureThe design procedure for all of these stilling basins may be summarized in the following steps. (asinspecific variations to these steps are discussed in the following sections on each basin.!tep 1#!etermine the velocity and depth at the culvert outlet. "or the culvert outlet, calculate culvertbrink depth, yo, velocity, +o, and "ro. "or subcritical flow, use "igure 8.8 or "igure 8.5. "orsupercritical flow, use normal depth in the culvert for yo. -See 1!S 4 -?ormann, et al., 699# for

    additional information on culvert brink depths.!tep )#!etermine the velocity and T depth in the receiving channel downstream of the basin.?ormal depth may be determined using Table (.# or other appropriate technique.!tep #;stimate the conjugate depth for the culvert outlet conditions using ;quation %.5 todetermine if a basin is needed. Substitute yoand "rofor y#and "r#, respectively. The value of 0 isdependent, in part, on the type of stilling basin to be designed. 1owever, in this step the occurrenceof a free hydraulic jump without a basin is considered so a value of #.9 is used. 0ompare y6and T.*f y6@ T, there is sufficient tailwater and a jump will form without a basin. The remaining steps areunnecessary.!tep 4#*f step 8 indicates a basin is needed -y6A T, make a trial estimate of the basin bottomelevation, z#, a basin width, (, and slopes STand SS. slope of 9.4 -9.4+ or 9.88 -9.88+ issatisfactory for both STand Ss. 0onfirm that (is within acceptable limits using ;quation %.8.!etermine the velocity and depth conditions entering the basin and calculate the "roude number.Select candidate basins based on this "roude number.!tep 3#0alculate the conjugate depth for the hydraulic conditions entering the basin using ;quation%.5 and determine the basin length and exit elevation. (asin length and exit elevation are computedusing ;quations %.4, %.7, and %.$ as well as "igure %.6. +erify that sufficient tailwater exists to forcethe hydraulic jump. *f the tailwater is insufficient go back to step 5. *f excess tailwater exists, thedesigner may either go on to step 7 or return to step 5 and try a shallower -and smaller basin.!tep #!etermine the needed radius of curvature for the slope changes entering the basin using;quation %.%.!tep 5#Size the basin elements for basin types other than a free hydraulic jump basin. The detailsfor this process differ for each basin and are included in the individual basin sections.Design Example: Stilling Basin wit Free !"draulic #ump $S%&"ind the dimensions for a stilling basin -see "igure %.# with a free hydraulic jump providing energydissipation for a reinforced concrete box culvert. Biven&

    = < ##.% m8:s

    Culvert

    ( < 8.9 m

    ! < #.% m

    n < 9.9#4

    So< 9.974 m:m

    zo< 89.49 m

    !ownstream channel -trapezoidal

    ( < 8.#9 m

    C < #+&61

    n < 9.989

    Solution

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    !tep 1#!etermine the velocity and depth at the culvert outlet. (y trial and error using 3anningDs;quation, the normal depth is calculated as&

    +o< %.49 m:s, yo< 9.578 m

    Since the "roude number is greater than #.9, the normal depth is supercritical and thenormal depth is taken as the brink depth.!tep )#!etermine the velocity and depth -T in the receiving channel. (y trial and error using3anningDs ;quation or by using Table (.#&

    +n< 5.%5 m:s, yn< T < 9.4$5 m!tep #;stimate the conjugate depth for the culvert outlet conditions using ;quation %.5. 0 < #.9.

    Since y6-6.5 m A T -9.4$5 m a jump will not form and a basin is needed.!tep 4#Since y6E T < 6.75 E 9.4$5 < 6.9$ m, try z#< zoE 6.9$ < 6%.5 m

    lso, choose (< 8.9 m -no expansion from culvert to basin and slopes ST< 9.4 and SS 6%.5 A z8> T -6/.94> 9.4$5, tailwater is not sufficient to force a jumpin the basin. Bo back to step 5.

    !tep 4 -)nd iteration.#Try z#< 64.$ m. 3aintain (, ST, and SS.

    (y using ;quation %.6 or other appropriate method by trial and error, the velocity and depthconditions entering the basin are&+#< #8.96 m:s, y#< 9.896 m

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    !tep 3 -)nd iteration.#0alculate the conjugate depth for a free hydraulic jump -0z6-8.#9>64.$ @ z8> T -6%.89> 9.4$5, tailwater is sufficient to force a jump inthe basin. 0ontinue on to step 7.

    !tep #"or the slope change from the outlet to the transition, determine the needed radius ofcurvature using ;quation %.% and the results from step #.

    !tep 5#Size the basin elements. Since this is a free hydraulic jump basin, there are no additionalelements and the design is complete. The basin is shown in the following sketch.

    Total basin length < /.7 > #%./ > 4.6 < 88.$ m!0etch for %ree Hydraulic ump !tilling "asin Design E(ample -!6.

    Design Example: Stilling Basin wit Free !"draulic #ump $'(&"ind the dimensions for a stilling basin -see "igure %.# with a free hydraulic jump providing energydissipation for a reinforced concrete box culvert. Biven&

    = < 5#$ ft8:s

    Culvert

    ( < #9.9 ft

    ! < 7 ft

    n < 9.9#4

    So< 9.974 ft:ft

    zo< #99 ft

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    Downstream channel (trapezoidal)

    ( < #9.6 ft

    C < #+&61

    n < 9.989

    Solution!tep 1#!etermine the velocity and depth at the culvert outlet. (y trial and error using 3anningDs;quation, the normal depth is calculated as&

    +o< 6$.% ft:s, yo< #.49 ft

    Since the "roude number is greater than #.9, the normal depth is supercritical and thenormal depth is taken as the brink depth.

    !tep )#!etermine the velocity and depth -T in the receiving channel. (y trial and error using3anningDs ;quation or by using Table (.#&

    +n< #4./ ft:s, yn< T < #.%% ft!tep #;stimate the conjugate depth for the culvert outlet conditions using ;quation %.5. 0 < #.9.

    Since y6-$.% ft A T -#.%% ft a jump will not form and a basin is needed.!tep 4#Since y6E T < %.44 E #.%% < 7.7$ ft, try z#< zoE7.7$ < /8.8 ft, use /8.

    lso, choose (< #9.9 ft -no expansion from culvert to basin and slopes ST< 9.4 and SS /8 A z8> T -/4.64>#.%%, tailwater is not sufficient to force a jump inthe basin. Bo back to step 5.

    !tep 4 -)nd iteration.#Try z#< %5.4 ft. 3aintain (, ST, and SS.

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    (y using ;quation %.6 or other appropriate method by trial and error, the velocity and depthconditions entering the basin are&+#< 56.4 ft:s, y#< 9./% ft

    !tep 3 -)nd iteration.#0alculate the conjugate depth for a free hydraulic jump -0 z6-#9.# > %5.4 @ z8> T -/6./9 > #.%%, tailwater is sufficient to force a jump inthe basin. 0ontinue on to step 7.

    !tep #"or the slope change from the outlet to the transition, determine the needed radius ofcurvature using ;quation %.% and the results from step #.

    !tep 5#Size the basin elements. Since this is a free hydraulic jump basin, there are no additionalelements and the design is complete. The basin is shown in the following sketch.

    Total basin length < 8#.9 > 7#.5 > #7.% < #9/.6 ft!0etch for %ree Hydraulic ump !tilling "asin Design E(ample -C7.

    8.) (SB* +"pe %%% Stilling BasinThe 'S() Type *** stilling basin -'S(), #/%$ employs chute blocks, baffle blocks, and an end sillas shown in "igure %.8. The basin action is very stable with a steep jump front and less wave actiondownstream than with the free hydraulic jump. The position, height, and spacing of the baffle blocksas recommended below should be adhered to carefully. *f the baffle blocks are too far upstream,

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    wave action in the basin will resultH if too far downstream, a longer basin will be requiredH if too high,waves can be producedH and, if too low, jump sweep out or rough water may result.The baffle blocks may be shaped as shown in "igure %.8 or cubesH both are effective. The cornersshould not be rounded as this reduces energy dissipation.The recommended design is limited to the following conditions&

    #. 3aximum unit discharge of #%.7 m8:s:m -699 ft8:s:ft.

    6. +elocities up to #%.8 m:s -79 ft:s entering the basin.

    8. "roude number entering the basin between 5.4 and #$.

    5. Tailwater elevation equal to or greater than full conjugate depth elevation. This provides a #4 to#% percent factor of safety.

    4. The basin sidewalls should be vertical rather than trapezoidal to insure proper performance of thehydraulic jump.

    %igure 8## 7!"& Type 666 !tilling "asin

    The general design procedure outlined in Section %.# applies to the 'S() Type *** stilling basin.Steps # through 5 and step 7 are applied without modification. "or step 4, two adaptations to thegeneral design procedure are made&

    #. "or computing conjugate depth, 0

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    where,?c< number of chute blocks

    (lock width and block spacing are determined by&

    -%.#9

    where,#< block width, m -ft6< block spacing, m -ft

    ;quations %./ and %.#9 will provide ?cblocks and ?cE# spaces between those blocks. The remainingbasin width is divided equally for spaces between the outside blocks and the basin sidewalls. iththese equations, the height, width, and spacing of chute blocks should approximately equal thedepth of flow entering the basin, y#. The block width and spacing may be reduced as long as#continues to equal 6.The height, width, and spacing of the baffle blocks are shown on "igure %.8. The height of the bafflesis computed from the following equation&

    -%.##

    where,h8< height of the baffle blocks, m -ft

    The top thickness of the baffle blocks should be set at 9.6h8with the back slope of the block on a #slope. The number of baffle blocks is as follows&

    -%.#6

    where,?(< number of baffle blocks -rounded to an integer

    (affle width and spacing are determined by&-%.#8

    where,8< baffle width, m -ft5< baffle spacing, m -ft

    s with the chute blocks, ;quations %.#6 and %.#8 will provide ?(baffles and ?(E# spaces betweenthose baffles. The remaining basin width is divided equally for spaces between the outside bafflesand the basin sidewalls. The width and spacing of the baffles may be reduced for narrow structuresprovided both are reduced by the same amount. The distance from the downstream face of thechute blocks to the upstream face of the baffle block should be 9.%y6.The height of the final basin element, the end sill, is given as&

    -%.#5

    where,h5< height of the end sill, m -ft

    The fore slope of the end sill should be set at 9.4 -+&1.*f these recommendations are followed, a short, compact basin with good dissipation action willresult. *f they cannot be followed closely, a model study is recommended.Design Example: (SB* +"pe %%% Stilling Basin $S%&!esign a 'S() Type *** stilling basin for a reinforced concrete box culvert. Biven&

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    = < ##.% m8:s

    Culvert

    ( < 8.9 m

    ! < #.% m

    n < 9.9#4

    So< 9.974 m:m

    zo< 89.49 m

    Downstream channel (trapezoidal)

    ( < 8.#9 m

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T

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    "or the chute blocks, the height of the chute blocks, h# %.9 > 5./ < 69.4 m. The basin is shown in the following sketch.!0etch for 7!"& Type 666 !tilling "asin Design E(ample -!6.

    Design Example: (SB* +"pe %%% Stilling Basin $'(&!esign a 'S() Type *** stilling basin for a reinforced concrete box culvert. Biven&

    = < 5#$ ft8:s

    0ulvert

    ( < #9.9 ft

    ! < 7 ft

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    n < 9.9#4

    So< 9.974 ft:ft

    zo< #99 ft

    Downstream channel (trapezoidal)

    ( < #9.6 ft

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T

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    ith 4 blocks at #.9 ft and 5 spaces at #.9 ft, #.9 ft of space remains. This is divided equallyfor spaces between the outside blocks and the basin sidewalls."or the baffle blocks, the height of the baffles is computed from ;quation %.##&

    The number of baffles blocks is calculated from ;quation %.#6&

    (affle width and spacing are determined by ;quation %.#8&

    ith 5 baffles at #.8 ft and 8 spaces at #.8 ft, 9./ ft of space remains. This is divided equallyfor spaces between the outside baffles and the basin sidewalls. The distance from thedownstream face of the chute blocks to the upstream face of the baffle block should be9.%y6

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    6. "or obtaining the length of the basin, 2(, use "igure %.6 -dashed portion of the free jump curvebased on the "roude number calculated in step 5.

    "or step $, sizing the basin elements -chute blocks and an end sill, the following guidance isrecommended. The height of the chute blocks, h#, is set equal to 6y#. The top surface of the chuteblocks should be sloped downstream at a 4 degree angle.

    The number of chute blocks is determined by ;quation %.#4a and rounded to the nearest integer.-%.#4a

    where,?c< number of chute blocks

    (lock width and block spacing are determined by&-%.#4b

    -%.#4c

    where,#< block width, m -ft6< block spacing, m -ft

    %igure 8#4# 7!"& Type 6 !tilling "asin

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    ith ;quation %.#5, the block width, #, should be less than or equal to the depth of the incomingflow, y#. ;quations %.#5 and %.#4 will provide ?cblocks and ?cE# spaces between those blocks. Theremaining basin width is divided equally for spaces between the outside blocks and the basinsidewalls.The height of the end sill, is given as&

    -%.#7

    where,h5< height of the end sill, m -ft

    The fore slope of the end sill should be set at 9.4 -+&1.Design Example: (SB* +"pe %- Stilling Basin $S%&!esign a 'S() Type *+ stilling basin for a reinforced concrete box culvert. Biven&

    = < ##.% m8:s

    0ulvert

    ( < 8.9 m

    ! < #.% m

    n < 9.9#4

    So < 9.974 m:m

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    zo < 89.49 m

    Downstream channel (trapezoidal)

    ( < 8.#9 m

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T64.99 @ z8> T -6%.99>9.4$5, tailwater is sufficient to force a jump inthe basin. *f this had not been the case, repeat step 5 with a lower assumption for z#.

    !tep #!etermine the needed radius of curvature for the slope changes entering the basin. See thedesign example Section %.# for this step. *t is unchanged.!tep 5#Size the basin elements. "or the 'S() Type *+ basin, the elements include the chuteblocks and end sill.

    "or the chute blocks&The height of the chute blocks, h#

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    ith 5 blocks at 9.6# m and 8 spaces at 9.48 m, 9.4$ m of space remains. This is dividedequally for spaces between the outside blocks and the basin sidewalls."or the sill&The height of the end sill, is given by ;quation %.#7&

    Total basin length < ##.9 > 6#.# >7.9 < 8%.# m. The basin is shown in the following sketch.!0etch for 7!"& Type 6 !tilling "asin Design E(ample -!6.

    Design Example: (SB* +"pe %- Stilling Basin $'(&!esign a 'S() Type *+ stilling basin for a reinforced concrete box culvert. Biven&

    = < 5#$ ft8:s

    Culvert

    ( < #9 ft

    ! < 7 ft

    n < 9.9#4

    So< 9.974 ft:ft

    zo< #99.9 ft

    Downstream channel (trapezoidal)

    ( < #9.6 ft

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T

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    (y using ;quation %.6 or other appropriate method by trial and error, the velocity and depthconditions entering the basin are&+#< 58./ ft:s, y#< 9./4 ft

    *t should b"r sub # equals + sub # divided by square root of -g times y sub # equals 58./divided by square root of -86.6 times 9./4 equals $./e noted that this "roude number isoutside the applicability range for the Type *+ basin, therefore the Type *+ is not appropriatefor this situation. 1owever, we will proceed with the calculations in order to compare basindimensions with the other basin options.

    !tep 3#0alculate the conjugate depth in the basin -0z6-##.#4>%6.79 @ z8> T -/6.#9>#.%%, tailwater is sufficient to force a jump inthe basin. *f this had not been the case, repeat step 5 with a lower assumption for z#.

    !tep #!etermine the needed radius of curvature for the slope changes entering the basin. See thedesign example Section %.# for this step. *t is unchanged.!tep 5#Size the basin elements. "or the 'S() Type *+ basin, the elements include the chuteblocks and end sill.

    "or the chute blocks&The height of the chute blocks, h#

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    8. SAF Stilling BasinThe Saint nthony "alls -S" stilling basin, shown in "igure %.4, provides chute blocks, baffleblocks, and an end sill that allows the basin to be shorter than a free hydraulic jump basin. *t isrecommended for use at small structures such as spillways, outlet works, and canals where the"roude number at the dissipator entrance is between #.$ and #$. The reduction in basin lengthachieved through the use of appurtenances is about %9 percent of the free hydraulic jump length.The S" stilling basin provides an economical method of dissipating energy and preventing streambed erosion.

    %igure 8#3# !$% !tilling "asin -"laisdell, 1939.

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    The general design procedure outlined in Section %.# applies to the S" stilling basin. Steps #through 8 and step 7 are applied without modification. s part of step 5, the designer selects a basinwidth, (. "or box culverts, (must equal the culvert width, o. "or circular culverts, the basinwidth is taken as the larger of the culvert diameter and the value calculated according to thefollowing equation&

    -%.#$

    where,(< basin width, m -ft= < design discharge, m8:s -ft8:s!o< culvert diameter, m -ft

    The basin can be flared to fit an existing channel as indicated on "igure %.4. The sidewall flaredimension z should not be greater than 9.4, i.e., 9.4, 9.88, or flatter."or step 4, two adaptations to the general design procedure are made. "irst, for computingconjugate depth, 0 is a function of "roude number as given by the following set of equations.!epending on the "roude number, 0 ranges from 9.75 to #.9% implying that the S" basin mayoperate with less tailwater than the 'S() basins, though tailwater is still required.

    -%.#%a

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    when #.$ @ "r# @ 4.4

    -%.#%b

    when 4.4 @ "r# @ ##

    -%.#%c

    when ## @ "r# @ #$

    The second adaptation is the determination of the basin length, 2(, using ;quation %.#/.-%.#/

    "or step $, sizing the basin elements -chute blocks, baffle blocks, and an end sill, the followingguidance is recommended. The height of the chute blocks, h#, is set equal to y#.The number of chute blocks is determined by ;quation %.69 rounded to the nearest integer.

    -%.69

    where,?c< number of chute blocks

    (lock width and block spacing are determined by&-%.6#

    where,#< block width, m -ft6< block spacing, m -ft

    ;quations %.69 and %.6# will provide ? cblocks and ?cspaces between those blocks. half block isplaced at the basin wall so there is no space at the wall.The height, width, and spacing of the baffle blocks are shown "igure %.4. The height of the baffles,h8, is set equal to the entering flow depth, y#.The width and spacing of the baffle blocks must account for any basin flare. *f the basin is flared asshown in "igure %.4, the width of the basin at the baffle row is computed according to the following&

    -%.66

    where,(6< basin width at the baffle row, m -ft2(< basin length, m -ftz < basin flare, z as defined in "igure %.4 -z

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    where,8< baffle width, m -ft5< baffle spacing, m -ft

    ;quations %.68 and %.65 will provide ?(baffles and ?(E# spaces between those baffles. Theremaining basin width is divided equally for spaces between the outside baffles and the basinsidewalls. ?o baffle block should be placed closer to the sidewall than 8y #:%. +erify that thepercentage of (6obstructed by baffles is between 59 and 44 percent. The distance from thedownstream face of the chute blocks to the upstream face of the baffle block should be 2(:8.The height of the final basin element, the end sill, is given as&

    -%.64

    where,h5< height of the end sill, m -ft

    The fore slope of the end sill should be set at 9.4 -+&1. *f the basin is flared the length of sill -widthof the basin at the sill is&

    -%.67

    where,(8< basin width at the sill, m -ft2(< basin length, m -ftz < basin flare, z as defined in "igure %.4 -z

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    zo< 89.49 m

    Downstream channel (trapezoidal)

    ( < 8.#9 m

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T

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    half block is placed at each basin wall so there is no space at the wall."or the baffle blocks&The height of the baffles, h8

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    zo< #99.9 ft

    Downstream channel (trapezoidal)

    ( < #9.6 ft

    C < #+&61

    n < 9.989

    SolutionThe culvert, design discharge, and tailwater channel are the same as considered for the freehydraulic jump stilling basin addressed in the design example in Section %.#. Steps # through 8 ofthe general design process are identical for this example so they are not repeated here. Thetailwater depth from the previous design example is T

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    half block is placed at each basin wall so there is no space at the wall."or the baffle blocks&The height of the baffles, h8