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Hydraulic design of culverts Driss, Slim 1988

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H Y D R A U L I C D E S I G N O F C U L V E R T S B y S l i m Dr i s s B s c a ( C i v i l E n g i n e e r i n g ) U n i v e r s i t y of O t t a w a , 1986 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F APPLIED SCIENCE in T H E F A C U L T Y O F G R A D U A T E STUDIES CIVIL E N G I N E E R I N G W e accept this thesis a.s c o n f o r m i n g to the required s t a n d a r d T H E UNIVERSITY O F BRITISH C O L U M B I A A p r i l 1988 © S l i m D r i s s , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia 1956 Main Mall Vancouver, Canada Department V6T 1Y3 DE-6(3/81) A b s t r a c t C u l v e r t s are designed to car ry water f r o m one side of an e m b a n k m e n t to another . T h e r e are m a n y culverts u n d e r a t y p i c a l h ighway a n d they a d d s igni f icant ly to i ts cost. T h e h y d r a u l i c design of a culvert is su rpr i s ing ly complex a n d since its p r i m a r y pur-pose is to convey water , i t is i m p o r t a n t tha t it has the f u l l in tended flow capac i ty . T h e ob jec t ive of this thesis was to develop a c o m p u t e r p r o g r a m to help an engineer w i t h the h y d r a u l i c design of cu lver t s . T h e user of the p r o g r a m can choose between des igning a new cu lver t or checking the adequacy of an ex i s t ing cu lver t f rom a hydraul ic , p o i n t of v i e w . T h e p r o g r a m handles the p r o b l e m of sediment depos i t ion that can occur a n d reduce the capac i ty of cu lver t s h a v i n g gentle slopes. T h e most w i d e l y used culvert shapes are i n c l u d e d in the p r o g r a m and in thi s thesis. C o m m e n t s are p r o v i d e d on the cond i t ions \mder w h i c h cer ta in shapes are best. C u l v e r t inlets are g iven , and some i m p r o v e d in le t designs are presented since the in le t design can have a m a j o r i m p a c t on the cost of the cu lver t . A l s o , erosion at the culver t out let is discussed a n d suggestions are p r o v i d e d on how to prevent i t or cope w i t h i t . 11 T a b l e o f C o n t e n t s A b s t r a c t i i L i s t of Tab le s v i L i s t o f F i g u r e s v i i A c k n o w l e d g e m e n t v i i i 1 I N T R O D U C T I O N 1 2 C U L V E R T O P E R A T I O N 3 2.1 I N L E T C O N T R O L : 4 2.2 O U T L E T C O N T R O L : 6 2.3 T Y P E S O F C U L V E R T F L O W : 8 2.4 O U T L E T V E L O C I T Y : 11 3 P R O B L E M O F S E D I M E N T D E P O S I T I O N 12 4 C I R C U L A R C U L V E R T S 13 4.1 C I R C U L A R C U L V E R T S F R E E O F S E D I M E N T : 13 4.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D R O U N D S E C -T I O N : 15 4.3 P R O G R A M O P E R A T I O N : 16 5 B O X C U L V E R T S 18 ii i 5.1 B O X C U L V E R T S F R E E O F S E D I M E N T : 18 5.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D B O X S E C T I O N : 19 6 A R C H C U L V E R T S 20 6.1 A R C H C U L V E R T S F R E E O F S E D I M E N T : 21 6.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D A R C H S E C T I O N : 23 7 E L L I P T I C C U L V E R T S 25 7.1 E L L I P T I C C U L V E R T S F R E E O F S E D I M E N T : 26 7.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D E L L I P T I C A L C U L V E R T : 29 8 I N L E T T Y P E S 31 8.1 P R O J E C T I N G I N L E T S : 31 8.2 F L U S H I N L E T S : 32 8.3 W I N G W A L L S : 33 9 I M P R O V E D I N L E T D E S I G N S 35 9.1 B O X C U L V E R T : 37 9.2 C I R C U L A R C U L V E R T : 38 10 S C O U R A T C U L V E R T O U T L E T S 39 10.1 S C O U R C O N T R O L A T C U L V E R T O U T L E T S : 39 10.2 S C O U R E S T I M A T I O N : 41 11 O T H E R C O N S I D E R A T I O N S : 44 12 S U M M A R Y A N D C O N C L U S I O N : 48 i v B i b l i o g r a p h y Lis t of Tab les 2.1 Inlet, c o n t r o l p e r f o r m a n c e coefficients • • • • 5 2.2 E n t r a n c e loss coefficients for submerged c i rcu la r p ipe culverts 7 10.3 S u m m a r y of coefficients a a n d b for equa t ion 10.84 43 11.4 S u m m a r y of the results o b t a i n e d f r o m c o m p u t e r output-1 47 v i L i s t of F i g u r e s 2.1 Factors in f luenc ing culvert d ischarge 7 4.2 C i r c u l a r cu lver t 13 4.3 C i r c u l a r cu lver t w i t h sediment i n the sect ion 15 5.4 B o x culver t 18 5.5 B o x culver t w i t h sediment i n the sect ion 19 6.6 A r c h cu lver t 21 6.7 A r c h cu lver t w i t h sediment i n the sect ion 23 7.8 H o r i z o n t a l e l l i p t i c a l culvert 26 7.9 E l l i p t i c a l cu lver t w i t h sediment i n the sect ion 29 8.10 C o m m o n p r o j e c t i n g culvert inlets 31 8.11 R o u n d e d - l i p entrance w i t h radius of r o u n d i n g = 0 .15D 32 8.12 C o m m o n types of w i n g w a l l entrance 34 9.13 1 Bevel-edge inlets 36 9.14 S ide-tapered inlets . . . 36 9.15 S lope- tapered inlets 36 9.16 H y d r a u l i c elements at t apered inlets 37 v i i A c k n o w l e d g e m e n t , I w o u l d l i k e to t h a n k D r . S . O . (Deni s ) R u s s e l l for his va luab le gu idance and adv ice t h r o u g h o u t this research. S incere t h a n k s go to D r . W . C a s e l t o n for his comment s r egard ing th i s thesis . I a m grate ful to D a v i d T o w n s e n d ( C o m p u t i n g C e n t r e at U B C ) for his assistance in the c o m p u t i n g aspects of this research. F i n a l l y , I w o u l d l ike to t h a n k m y parents a n d m y fr iends for the i r suppor t and encour-agement. v n i C h a p t e r 1 I N T R O D U C T I O N C u l v e r t s are c o n s t r u c t e d to carry water f r o m one side of an e m b a n k m e n t to the o ther under a h ighway, c a n a l or r a i l r o a d . H i g h w a y culverts are no longer cons idered m i n o r s t ructures as they are b e c o m i n g much m o r e expensive w i t h increa s ing s t r u c t u r a l s t rength a n d cross sec t iona l d imens ions due to the use of wider pavements , flatter grades and higher fills. A c h i e v i n g the most e c o n o m i c a l design of h ighway cu lver t s requires an a t tent ive e x a m i n a t i o n of the i r h y d r a u l i c s , a l i g n m e n t , e leva t ion , slope, l o c a t i o n and struc-t u r a l des ign. If the channel crosses the road at a s ignif icant skew, it is adv i sab le to reduce the skew by a l te r ing the c h a n n e l at the inlet or out le t or b o t h to d i m i n i s h the l ength of the cu lver t . In th i s case, the m a i n t e n a n c e cost of the channe l should be c o m p a r e d to the cost of the cu lver t . T h e s lope of the cu lver t w h i c h is genera l ly equal to the channe l slope is one of the most i m p o r t a n t factors i n cu lver t design. D u r i n g h i g h flood and if the culver t is steep enough , depos i t ion of m a t e r i a l s ins ide the cu lver t is prevented due to h i g h flow veloci ty . However , on m i l d slopes, depos i t i on can take place , hence c rea t ing m a i n t e n a n c e prob-lems. In thi s case, headwater pools should be p r o v i d e d at the inlets to p r o d u c e a higher flow ve loc i ty t h r o u g h the cu lver t , and prov i s ions against poo l s i l t a t i o n s h o u l d be made . W h e n a culvert has its in let invert p laced at a ce r ta in e levat ion above, the n a t u r a l b e d , a p o n d u p s t r e a m f r o m the culvert w o u l d be fo rmed . T h e p o n d can be used for recreat ion purposes whenever the s t ream is p e r m a n e n t . B u t if the s t r e a m is d r y at t imes , 1 Ch apter 1. INTROD UCTION 2 there is a risk of c rea t ing a s t i l l poo l g a t h e r i n g debris a n d sed iment , therefore it is be t ter to place the cu lver t in le t invert at c h a n n e l bed e l eva t ion . H y d r a u l i c ana lys i s assists i n f i n d i n g the m i n i m u m d imens ions of the culvert tha t ensure m i n i m u m cost a n d m i n i m u m f lood dama,ge. U n f o r t u n a t e l y , most of the present d o c u m e n t s dea l ing w i t h the h y d r a u l i c design of cu lver t s refer the user to numerous charts a n d most of the t i m e the concepts b e h i n d these charts are not s h o w n to the user. In this thesis , the hydraul ic , design of cu lver t s is t reated a n a l y t i c a l l y for var ious culver t shapes, a n d a c o m p u t e r p r o g r a m was w r i t t e n i n the B a s i c language to help the cu lver t designer choose the a p p r o p r i a t e cu lver t d imens ions or check the per formance of an e x i s t i n g cu lver t w i t h o u t the help of the charts . T h e c o m p u t e r p r o g r a m relies heav i ly on m a t h e m a t i c a l c o m p u t a t i o n s needed for the hy-d r a u l i c ana lys i s . T h e t r i a l a n d error p rocedure was carr ied out n u m e r i c a l l y i n order to f ind the a p p r o p r i a t e cu lver t d imens ions a n d the most l i ke ly t y p e of flow t h r o u g h it . V a r -ious approaches such as the use of an E x p e r t S y s t e m were cons idered but because of the c o m p l e x i t y of cu lver t des ign, it was dec ided tha t a s t r a i g h t f o r w a r d p r o g r a m w r i t t e n i n B a s i c w o u l d be the m o r e a p p r o p r i a t e first step. C h a p t e r 2 C U L V E R T O P E R A T I O N F l o w enter ing a cu lver t is genera l ly subject to a severe c o n t r a c t i o n at the entrance. T h e c o n t r a c t i o n is less severe w i t h s m o o t h a n d r o u n d e d inlet sect ion. T h e cont rac t ion creates a loss t e r m e d an entrance loss, He. A s a d d i t i o n a l head is lost a long the length of the cu lver t as f r i c t i o n loss, Hf, the l ength of the culvert is the m a i n var iab le d e t e r m i n i n g whether or not the cu lver t w i l l flow f u l l . If the cu lver t is l o n g enough to p e r m i t the increas ing d e p t h of flow to fill the barre l , the culvert is ca l led a hydraulically long culvert. O t h e r w i s e , the culvert does not r u n fu l l and is ca l led a hydraulically short culvert [ l] . After the des ign discharge has been d e t e r m i n e d , the cu lver t designer has to choose the m i n i m u m cu lver t size t h a t has the capac i ty to carry the flow w i t h o u t exceeding the a l lowable h e a d w a t e r d e p t h and not caus ing eros ion problems d o w n s t r e a m . U n d e r inlet c o n t r o l c o n d i t i o n s , the geometry of the in le t , cross-section of the culvert barre l and the d e p t h of water at the cu lver t inlet are the essential factors de te rmin ing the flow t h r o u g h the c u l v e r t . U n d e r outlet, c o n t r o l c o n d i t i o n s , a l l the design variables must be t aken into account. These inc lude b a r r e l cross-sect ion, l eng th , s lope and roughness , in let geometry, depth of water at the in le t and at the out le t . For design purposes , headwater depths for b o t h in le t , HWI, and out let c o n t r o l , HWO, s h o u l d be c a l c u l a t e d , and the higher va lue , HWC, determines the t y p e of cont ro l . 3 Chapter 2. CULVERT OPERATION 4 2.1 I N L E T C O N T R O L : W i t h thi s t y p e of contro l , the cu lver t runs par t fu l l a n d the discharge t h r o u g h the culver t is c o n t r o l l e d by the shape of in le t entrance and the in le t headwater d e p t h . Var i ab le s such as roughness , slope and l e n g t h of the cu lver t have p r a c t i c a l l y no inf luence on the discharge capac i ty of the cu lver t ; b u t they p lay a m a j o r role i n the cont ro l of out le t ve loc i t ies s w i t c h i n g the culver t o p e r a t i o n f r o m in le t cont ro l to out le t c o n t r o l . E x p e r i m e n t s have shown that the character i s t ic s of flow ins ide the cu lver t vary f r o m a submerged in le t to an u n s u b m e r g e d one. If the entrance is unsubmerged , the flow w i l l enter the cu lver t w i t h a d e p t h a lmost equal to the c r i t i c a l d e p t h . W i t h some c o r r e c t i o n factors , the e q u a t i o n for inlet cont ro l flow for u n s u b m e r g e d in le t has been proposed as [2]: where : HWI — inlet headwater So — cu lver t s lope He = c r i t i c a l energy head D - equiva lent culvert d iameter T h e e m p i r i c a l r e l a t ionsh ip re l a t ing He and the discharge factor O/D2/5, is g iven by [2]: W h e r e , K a n d m are g iven in t ab le 2.1 for var ious entrance shapes. If the inlet is submerged , the flow equa t ion becomes: HjD-\- .5So = hl/D-r Kl{Q / D25)2 HWI/D + .5So = Hc/D + He/D 2.1) He/D = A ' (1 .2730/Z> 2 - 5 ) ' (2.2) Chapter 2. CULVERT OPERATION 5 E m p i r i c a l factors such as hl/D a n d Kl are given in tab le 2.1 for various entrance shapes. N . B : T h e same relat ionships are used for non c i rcu lar cu lver t s us ing the fact tha t : D = 4RH (2.3) where: RH = H y d r a u l i c radius . Table 2.1: Inlet cont ro l per formance coefficients Entrance shape Submerged inlet Mow Nonsubmergcd inlet flow ht/D k Ml H./n\ With headwall Groove edge, .05Dx.07D Rounded edge, .15/) radius Square edge 0.74 0.74 0.67 0.0468 0.04 I'J 0.0645 3.3 2.58 2.5S 0.00 IS 0.00065 0.0098 2.5 2.67 2.0 0.035 0.016 0.105 Headwall and 45" wingwalls Groove edge, .05Dx.07D Square edge 0.73 0.70 0.0472 0.0594 3.0 3.5 0.0018 0.0030 2.50 2.67 0.035 0.072 Headwall and parallel wingwalls Groove edge, .0oD\.07D 0.74 0.0528 4.0 0.0020 2.67 0.04 S Miter (square edge) 2:1 embankment slope 0.74 0.0750 4.0 0.0210 1.33 0.091 Projecting entrance Groove edge, .05Z)x.07P Square edge (thick wall) Thin edge 0.70 0.04 0.53 0.0514 0.0668 0.0924 2.58 3.5 4.0 0.0045 0.0145 0.0420 2.0 1.75 1.33 0.049 0.116 0.205 "The equation (or inlet control with submerged inlet only applies when Q/DS/' is larger than the listed values. tTlie equation for inlet control with nonsubmcrged inlet only applies when II./D is less than the listed values. Chapter 2. CULVERT OPERATION 6 2 . 2 O U T L E T C O N T R O L : W i t h thi s type of c o n t r o l , the flow is a lways s u b c r i t i c a l . R e f e r r i n g to F i g 2.1, the t o t a l head loss, HOT, is the s u m of entrance head loss, He, f r i c t i o n head loss, Hf, a n d out let head loss Hv. HOT = He + Hf + Hv (2.4) w i t h : He = Ke * V2/(2g) = Ke * Q 2/[{ir * D 2/4) 22g] = Ke * 2 . 5 2 0 4 / D 4 * (Q/10) 2 (2.5) V a l u e s for Ke are shown in table 2.2 . Hf = {29N 2L/RH 1- 33)V 2/(2g) = ( 4 6 6 . 1 8 . / V 2 J L / J D 1 6 / 3 ) ( O / 1 0 ) 2 • (2.6) Hv = V2/2g = 2 . 5 2 0 4 / J D 4 ( O / 1 0 ) 2 (2.7) W h e r e is the M a n n i n g roughness of the c u l v e r t , V is the mean water v e l o c i t y inside the cu lver t , and L is the culver t l e n g t h . There fore , HOT = (2.5204 * (1 + Ke)/D 4 + 466ASN 2L/D 16/3)(O/l0) 2 (2.8) T h e headwater depth HWO is ca lcu la ted by : HWO = HO +HOT - LSo (2.9) If the t a i lwater dep th TW submerges the out let of the cu lver t , then HO = TW; o therwise HO is t aken as [DC + D)/2. See [3] for further detai l s , where : DC — c r i t i c a l d e p t h in the cu lver t . Chapter 2. CULVERT OPERATION 7 Figure 2.1: Factors influencing culvert discharge Table 2.2: Entrance loss coefficients for submerged circular pipe culverts Type of entrance Entrance head loss coefficient, KC Pipe entrance with hcadwall Grooved edge Hounded edge (0.150 radius) Hounded edge (0.25D radius) Square edge (corrugated metal pipe) 0.10 0.15 0.10 0.43 Pipe entrance with hcadwall and 45° wingwall Grooved edge Square edge (corrugated metal pipe) 0.20 0.35 Hcadwall with parallel wingwalls spaced 1.25/3 apart Grooved edge Square edge (corrugated metal pipe) 0.30 0.40 Miter entrance for 2:1 embankment slope 0.(52 Projecting entrance Grooved edge, thick wall Square- edge, thick wall Sharp edge, thin wall (corrugated metal pipe) 0.25 0.41) 0.1)2 Chapter 2. CULVERT OPERATION 8 2.3 T Y P E S O F C U L V E R T F L O W : Let HEIGHT designates the height of the culvert, and HE the uniform depth of flow inside the culvert. Type 1: HWC < l.bHEIGHT TW < DC HE < DC Supercritical Flow N . B : If the tailwater T W exceeds the uniform depth, a hydraulic jump wil l form and move upstream filling the culvert from the downstream end. If the tailwater depth and culvert roughness are high enough; the hydraulic jump wi l l move all the way up to the culvert inlet, thus making the culvert flowing ful l . In this case, the computer program wil l print a warning message and informs the user that a hydraulic jump is likely to occur. Chapter 2. CULVERT OPERATION Type 2: HWC < 1.5HEIGHT TW < DC HE > DC S u b c r i t i c a l flow C r i t i c a l d e p t h at the out let Type 3: HWC < l.bHEIGHT TW > DC HE > DC Chapter 2. CULVERT OPERATION Type 4: HWC > 1.5HEIGHT TW > HEIGHT Ful l flow HWC 1_. Type 5: HWC > l.bHEIGHT TW < HEIGHT HE < HEIGHT Rapid flow at inlet, culvert running partly ful l , outlet unsubmerged. HWC Type 6: — r — f " HWC > 1.5HEIGHT TW < HEIGHT Ful l flow, . free outfall. 1 Chapter 2. CULVERT OPERATION 11 See [l, pages J, 93-^99] for further details. 2.4 O U T L E T V E L O C I T Y : If in let c o n t r o l governs, it is assumed i n the computer p r o g r a m t h a t u n i f o r m flow occurs near the out le t . However , the culver t designer should take this a s s u m p t i o n w i t h c a u t i o n since often i n h y d r a u l i c a l l y short cu lver t s , u n i f o r m flow doesn' t h a p p e n a n d the real out let v e l o c i t y is s igni f icant ly higher t h a n the u n i f o r m veloc i ty . If out let c o n t r o l governs; then if the t a i l w a t e r submerges the out l e t , the out let v e l o c i t y w i l l be equa l to the discharge d i v i d e d b y the culvert cross sect ion area; o therwise i t is a s sumed tha t the out let ve loc i ty corresponds to an out let d e p t h equa l to the average of the c r i t i c a l d e p t h a n d the culvert height [3]. Chapter 3 P R O B L E M O F S E D I M E N T D E P O S I T I O N In fiat areas, the water ve loc i ty in the channe l is genera l ly not great enough to p r o d u c e the requ i red cu lver t self c leaning ve loc i ty , thus sediment d e p o s i t i o n can occur and culverts become p a r t i a l l y filled w i t h sed iment . A s a resul t , the net cross-sectional area of the cu lver t is decreased caus ing a decrease in its h y d r a u l i c flow rate capaci ty . In thi s s i t u a t i o n , the c u l v e r t cross-sect ional d imens ions m i g h t have to b e increased i n size so tha t the area after s i l t i n g can carry the design f low, o therwise consequences such as erosion of the embankment , and flooding of the road might h a p p e n . D u e to the c o m p l e x i t y of the p r o b l e m of sediment, t ranspor t - type of sediments , g rad ing , pe rmeab i l i ty . . . - , it was dec ided in the c o m p u t e r p r o g r a m to ask the user for a value of the sediment d e p t h r e s u l t i n g f rom his o w n judgement , and the value entered represents a u n i f o r m i m p e r m e a b l e sediment d e p t h a l l a long the cu lver t l eng th . 12 C h a p t e r 4 C I R C U L A R C U L V E R T S C i r c u l a r culverts are w i d e l y used as they are m o r e read i ly avai lable a n d cheaper than other shapes despite the fact that often they do not m a t c h the shape of mos t dra inage channels . W h e r e h y d r a u l i c efficiency is i m p o r t a n t , as in a l o n g culvert , a c i r c u l a r sect ion m a y be best. T h e use of a c i rcu lar section also results i n m a x i m u m economy i n mater ia l s since for a given per imeter a c irc le has a greater cross-sectional area t h a n any other shape. 4.1 C I R C U L A R C U L V E R T S F R E E O F S E D I M E N T : U T J r H , I>'»A , F i g u r e 4.2: C i r c u l a r culvert. 13 Chapter 4. CIRCULAR CULVERTS 14 For any water d e p t h H, H = DIA/2 + DIA/2 * cos(NX) =4> NX = a rccos [ (# - DIA/2)/{DIA/2)} (4.10) T h e c o r r e s p o n d i n g flow area AR w i l l be : AR = (TT - NX + sm(27V.Y) /2 ) * DIA 2/A (4.11) T h e wet ted p e r i m e t e r P : P = DIA(ir -\NX\) (4.12) T h e top w i d t h T: T = 2(H - DIA/2)tan(NX) (4.13) T h e c r i t i c a l d e p t h DC is ca lcu la ted after so lv ing by t r i a l and error the f o l l o w i n g equat ion : Q^-T/igAR 3) - 1 = 0 (4.14) RH designates the h y d r a u l i c rad ius : RH = AR/P (4.15) A g a i n , us ing t r i a l and error procedure , the u n i f o r m depth HE can be found after so lv ing the subsequent e q u a t i o n : O - l/N(AR/P) 2/3(AR)So- 5 = 0 (4.16) N . B : T h e same t r i a l and error p rocedure shown above for c a l c u l a t i n g the u n i f o r m d e p t h and the c r i t i c a l d e p t h for c i r cu la r cu lver t is used for a l l o ther culver t shapes, except i n the c a l c u l a t i o n of the c r i t i c a l d e p t h for box culverts where a s imple f o r m u l a can be used. Chapter 4. CIRCULAR CULVERTS 15 4.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D R O U N D S E C -T I O N : H st> _1_ 0 •9 Figure 4.3: Circular culvert with sediment in the section Denoting by SD the sediment depth, the following relations can be written: SD = DIA/2 - DI A/2cosV V = arccos(l - 2SD/DIA) (4.17) H = DIA/2 + DIA/2cosNX — SD = > i V X = arccos[(# - + SD)/.(DIA/2)] (4.18) Area of sediment plus water (bcdefb): A = [ir-NX + SIN{2NX)/2]DIA 2/4 (4.19) Area of sediment (cdec): SA = DIA 2/4\V - .5sin(2V)] (4.20) Chapter 4. CIRCULAR CULVERTS 16 ==' F l o w area (bcefb) : AR= A - SA = DIA 2{n - NX + sm(2NX)/2 - V + .5 s i n ( 2 V ) ) (4.21) T h e por t ions i n contact w i t h water are arc lengths be, fe a n d c h o r d l e n g t h ce. =t> W e t t e d P e r i m e t e r : P = DIA(ir - NX - V + s in V) (4.22) It is clear tha t equat ions 4.10, 4.11 and 4.12 are respect ive ly equiva lent to 4.18, 4.21 a n d 4.22 i n the case where sediment depth is zero. In the case of c i r cu l a r culvert-as i n a l l other shapes-the p r o g r a m asks the user w h e t h e r he wants to design a new culver t or to s tudy the hydraul ic , propert ies of an e x i s t i n g c i rcu la r cu lver t . If the choice is to des ign a new culver t , t h e n the p r o g r a m starts w i t h a tenta t ive va lue of a cu lver t d i amete r DIA equa l to ha l f the a l lowable headwater HW. If the sediment d e p t h SD was entered as zero, then the equivalent cu lver t d iameter D is s i m p l y equal to DIA . O t h e r w i s e , D is c a l c u l a t t e d us ing formulas 4.17, 4.18, 4.21, 4.22, 4.15 a n d 2.3. T h e culver t d i a m e t e r w i l l be increased or decreased u n t i l the c o m p u t e d headwater for b o t h in le t cont ro l and out let contro l is less t h a n the a l lowable headwater but greater t h a n 3 /4 of i t s value. T h i s is to m i n i m i z e the chances of flooding the road w i t h o u t the expense of overdes igning the cu lver t . For the a p p r o p r i a t e cu lver t a n d us ing the basic equat ions of sect ion 4-1 and 4-2; c r i t i c a l d e p t h , u n i f o r m d e p t h a n d o ther relevant h y d r a u l i c propert ies , such as out le t ve loc i ty , fu l l flow ve loc i ty a n d discharge are c o m p u t e d . See c o m p u t e r ou tput -2 . 4.3 P R O G R A M O P E R A T I O N : ('hauler 4. CIRCULAR CULVERTS 17 H o w e v e r , i f the user deci s ion is to check the h y d r a u l i c proper t ie s of the cu lver t ; t h e n after a sk ing the user for ex i s t ing cu lver t d imens ions , the c o m p u t e r p r o g r a m checks tha t the a l lowable headwater is not exceeded a n d also gives a l l the detai ls of the h y d r a u l i c proper t ie s of the flow a n d its t y p e ins ide the cu lver t . See c o m p u t e r o u t p u t - 1 . C h a p t e r 5 B O X C U L V E R T S Severe flow contraction occurs at the entrance in such type of culverts where generally inlet control governs. The resulting high head losses the flow suffers during expansion makes such culverts useful to control outlet velocities in case where downstream erosion has to be avoided. 5.1 B O X C U L V E R T S F R E E O F S E D I M E N T : T H HEIGHT Figure 5.4: Box culvert The .flow area A R for any given depth H is given by: AR = B*H (5.23) 18 Chapter 5. BOX CULVERTS 19 T h e w e t t e d p e r i m e t e r P is c a l c u l a t e d as: P = B + 2H (5.24) T h e c r i t i c a l d e p t h DC is d i r e c t l y f o u n d f rom the f o l l o w i n g r e l a t i o n : DC = \(Q/B)2/g}^ (5.25) 5 . 2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D B O X S E C -T I O N : T h e same h y d r a u l i c r e l a t ionsh ip s shown for a b o x cu lver t free of sediment are used here w i t h the t o p of the sediment layer t a k e n as reference. T _L I// / // 1 ^ SD T F i g u r e 5.5: B o x culver t w i t h sediment i n the sect ion C h a p t e r 6 A R C H C U L V E R T S A r c h culver t s are r e c o m m e n d e d where m i n i m u m cover is needed or where v e r t i c a l c learance p r o b l e m s p r e v a i l . T h e y c a r r y greater flow t h a n most other culver t s of equivalent w a t e r w a y area for the same depth of flow. T h e use of open b o t t o m arch culverts is s t rong ly advised where f ishery resources are present. Bes ides , arch culverts are used w h e n it is more e c o n o m i c a l to support the weight of the e m b a n k m e n t on an arch t h a n on other shapes. 20 Chapter 6. ARCH CULVERTS 21 6.1 A R C H C U L V E R T S F R E E O F S E D I M E N T : H£i'GHT Figure 6.6: A r c h culvert Having, ' R(l + cos69/2) = HEIGHT 2/2 sin 5/2 = SPAN and as: cos 0 + cos 9/2 = 2 cos 2 9/4 2.RCOS2 9/4 = HEIGHT 4R sin 9/4 cos 9/4 = S P A / V Div id ing 6.26 by 6.25, get: (6.26) (6.27) 2 tan 5/4 = SPAN/HEIGHT = ? 5 = 4 s,rct<m(SP AN/(2H EIGHT)) (6.28) = > i2 = HEIGHT/{I + cos 0/2) (6.29) The full flow area Chapter 6. ARCH CULVERTS 2 2 AF = TTR- - Area(nwk) (6.30) ' Area(nwk) = Area(cnwk) - Area(cnk) = irR 2 * 6/(2w) - SPAN(HEIGHT - R)/2 (6.31) AF = TTR 2 - R26/2 + SPAN(HEIGHT - R)/2 (6.32) T h e f u l l wet ted per imeter PF is g iven by : PF = 2Ra + SPAN (6.33) where , a = (2*-6)12 (6.34) T h e flow area A T for any given d e p t h H : H = HEIGHT - (R - i ? c o s 7 ) (6.35) AT = AF - [Area(clvu) - Area(clu)} = AF - TTR 2(2^/2TT) + . 5 T i ? c o s 7 (6.36) =^> AT = AF - i ? 2 7 + T i ? c o s 7 / 2 (6.37) where T designates the top w i d t h of flow: T = 2 i ? s m 7 . (6.38) cos 7 = (H - Rcos(theta/2))/R. => 7 = a rccos [ ( i J - R cos{6/2))/R] (6.39) T h e wetted per imeter P for any g iven d e p t h H: P = PF -2Rry (6,40) C h a p t e r 6. ARCH CULVERTS 23 6.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D A R C H S E C -T I O N : Denoting by SD the sediment depth inside the culvert ,with SD < (HEIGHT -R), we have: where: Figure 6.7: A r c h culvert with sediment in. the section R[l + cos(0 s/2)] + SD = HEIGHT => cos(0,/2) = HEIGHT IR - SD/R - 1 => 9S = 2 a.rccos[{HEIGHT - SD)/R - 1] R = HEIGHT l\\ + cos(c?/2)] 0 = 4 arctan[5PAN/(2HEIGHT)] (6.41) (6.42) (6.43) (6.44) (6.45) Calculating the full flow area AF: AF = irR 2 - Area(xnwky) (6.46) Chapter G. ARCH CULVERTS 24 Area(xnwky) = Area(cxnwky) — Area(cxy) = R2 * 6s/2 - (2Rsm(8s/2))(HEIGHT - R - SD)/2 (6.47) ==- AF = TTR2 - R2 * 6J2 + (HEIGHT - R - SD)Rsm(0s/2) (6.48) T h e f u l l wet ted p e r i m e t e r PF : PF = 2Ras + 2R sm(Os/2) (6.49) w i t h : as = (2TT -es)/2 (6.50) T h e flow area AR for any g iven d e p t h H: • H = HEIGHT - (R - 72cos7 + SD) (6.51) AR = AF - [Area(clvu) - Area(clu)) = AF - TTR221/(27T) + .5TRcos-y (6.52) =4- AR = AF - i ? 2 7 + TRcos-y/2 (6.53) T h e wet ted p e r i m e t e r P for any given d e p t h H : P = PF -2RJ (6.54) C h a p t e r 7 E L L I P T I C C U L V E R T S E l l i p t i c cu lver t s are in s t a l l ed w i t h the m a j o r axis e i ther h o r i z o n t a l -horizontal elliptical culvert - or v e r t i c a l -vertical elliptical culvert . W h e r e m i n i m u m cover cond i t ions are required or where v e r t i c a l c learance is l i m i t e d by e x i s t i n g s t ructures , a h o r i z o n t a l e l l i p t i c a l culvert is r e c o m m e n d e d as it achieves a greater c a p a c i t y for the same d e p t h of flow t h a n most o ther culver t s of equivalent w a t e r w a y area. H o w e v e r , where m i n i m u m h o r i z o n t a l clearances are des i red , a ver t i ca l e l l i p t i c a l cu lver t is preferred . It also achieves higher flushing veloc i t ies under m i n i m u m flow cond i t ions b u t carries less flow at the same depth than an equiva lent h o r i z o n t a l e l l i p t i c a l or c i r c u l a r c u l v e r t . 25 C h a p t e r 7. ELLIPTIC CULVERTS 26 7.1 E L L I P T I C C U L V E R T S F R E E O F S E D I M E N T : Ellipse equation: x2/a2 + y 2/b 2 = 1 a = SPAN/2 b = HEIGHT/2 (7.55) (7.56) (7.57) T H F i g u r e 7.8: H o r i z o n t a l e l l i p t i c a l cu lver t F l o w area A R for any g iven flow d e p t h H : H = y0 + b (7.58) AR = 2 x d y = 2a /6 ^ ( i 2 - y 2)' 5<fy = 2a/b[y/2(b2 - y2)5 + b2/2 arcsm(y/b)}% AR = 2a/b[y0/2(b2 - y 20)b + b 2/2arcsin(y0/6) + T T 6 2 / 4 ] (7.59) (7.60) Chapter 7. ELLIPTIC CULVERTS 27 R e p l a c i n g yc by b, the f u l l f low area AF c an be o b t a i n e d : AF = ir*a*b (7.61) T h e wet ted per i me te r P for any given flow depth H : let : x — a cost => dx/dt = — a s i n t (7.62) y = bsint dyjdt = bcost (7.63) P = 2 * length f r o m t = —TT/2 to £ = ta where : y0 = bsmt0 => t0 = arcsin(j/ c , /6) (7-64) P = 2 jl^Sdx/dtf + (dy/dty-}*dt P = 2 / ! ; / 2 [ a 2 s i n 2 < + fe2 cos 2 t\bdt = 21 W h e r e / is an e l l i p t i c i n t e g r a l that can be f o u n d to any accuracy w i t h n u m e r i c a l inte-g r a t i o n . U s i n g S impson ' s ru le : L e t : gso(t) = ( a 2 s i n 2 1 -f 6 2 cos 2 /.)'5 (7.65) C h o o s e a large even n u m b e r ND, say ND = 10 (7.66) L e t : h = (t0 + */2)/ND (7.67) Chapter 7. ELLIPTIC CULVERTS 28 s0 = —7r /2 , SI = s0 + / i , , sk = —7r/2 + / J i , , sn = sn_1 + h (7.68) = - P = 2(h/3)[gsp(s0) + 4 ^ 5 o ( 5 i ) + 2gso(s2) + 4c?so(53) + ... + 4gso(sn-i) + gso(sn)} (7.69) T h e top w i d t h T is g iven by : T = 2 a c o s i 0 (7.70) Chapter 7. ELLIPTIC CULVERTS 29 7.2 H Y D R A U L I C E L E M E N T S O F A P A R T I A L L Y S I L T E D E L L I P T I -C A L C U L V E R T : Denoting by SD the sediment depth in the ell iptical section which is represented by the same equation in the plane xy . For point S: 4.* x. H Figure 7.9: El l ipt ica l culvert with sediment in the section xl — a cos t yl = b sin t with , y i = SD - HEIGHT/2 = SD -b (7.71) The wetted perimeter P for any flow depth H: P = 2 * length from t = arcsin(y a /6) to t = t0 Chapter 7. ELLIPTIC CULVERTS 30 where : y0 = bs'mtc ==> tc, — a r c s i n ( y 0 / 6 ) (7.72) H = y0 + b- SD (7.73) P = 2 F°[(dx/dt)2 + (dy/dtffdt (7.74) R e f e r r i n g to equat ions 7.62 a n d 7.63, a n d us ing S impson ' s rule as i n the prev ious sect ion, see equat ions 7.65 to 7.68, the wet ted per imeter P is eventua l ly : P = 2{H/3)[gso(s0) + Agso(si) + 2gso(s2) + .. + gso(sn)] + 2 a | c o s t 1 | ] (7.75) T h e flow area AR for any g iven flow d e p t h H: AR = 2 jV° xdy = 2a/b F'\b 2-y2)*dy = 2a / b[y/2(b2-y2)5+ b 2 / 2 a,rcsm{y/b)] yy° (7.76) ==- AR = 2a/b[yc./2(b2 - y;) 5 + b 2/2 arcsin(t/0/6) - yi/2(b2 - y 2) 5 - b 2/2 a r c s i n ^ / i ) ] C h a p t e r 8 I N L E T T Y P E S W h e t h e r the culver t operates w i t h inlet c o n t r o l or w i t h out le t c o n t r o l , the hydraul ic , propert ies of flow are i n b o t h cases very dependent u p o n the shape of the entrance. T h e idea l design has an in le t such that no flow c o n t r a c t i o n occurs , w i t h the b a r r e l d o w n s t r e a m f r o m the entrance f lowing just fu l l . A special s t u d y should be made on w h i c h inlet to use for l o n g cost ly culver t s as use of the proper in le t shape can result in cons iderable savings. 8.1 P R O J E C T I N G I N L E T S : P r o j e c t i n g inlets represent the s implest t y p e of culvert entrance ; however their use is restr icted to culverts t h a t are in l ine w i t h the approach f low-otherwise , serious scour problems might occur w h i c h could affect the embankment- . A t the entrance , the flow is contracted to a lmost .6DIA. F i g u r e 8.10: C o m m o n p r o j e c t i n g cu lver t inlets 31 Chapter 8. INLET TYPES 32 8.2 F L U S H I N L E T S : W i t h f lush inlets , the cu lver t entrance is level led w i t h a h e a d w a l l w h i c h provides a guide to the flow a n d enhances the h y d r a u l i c efficiency of the c u l v e r t . T h e flow c o n t r a c t i o n at the entrance of the culver t c an be kept to a m i n i m u m using a well rounded in le t , the most efficient s t a n d a r d type of in l e t . Headwal l s also re ta in the fill and prov ide s t a b i l i t y to the e m b a n k m e n t by p r o t e c t i n g i t f r o m eros ion, however the i r use is also res t r ic ted to culverts a l i gned w i t h the d i rec t ion of the approach flow. T h e height of the headwal l above the c r o w n of the cu lver t should be a m i n i m u m of lft or .2D I A, whichever is greater. T h e headwa l l f o u n d a t i o n must be p laced below the pred ic ted m a x i m u m scour d e p t h . "?—LJ. : • 1 — rounded-lip entrance with radius of rounding =0.150 F i g u r e 8.11: R o u n d e d - l i p entrance w i t h rad ius of r o u n d i n g = 0 .15D Chapter S. INLET TYPES 33 8 . 3 W I N G W A L L S : W i n g w a l l s are m a i n l y used to pro tec t the e m b a n k m e n t . T h e y are i m p o r t a n t i n secur ing the e m b a n k m e n t f r o m scour ing eddies w h i c h often develop at the entrance , as a consequence of the nona l i gnement of the cu lver t w i t h the approach f low. In the case of a skewed dra inage c h a n n e l , the wal l s c an be qui te useful to guide the flow and c o n t r o l the water f r o m a t t a c k i n g the e m b a n k m e n t f i l l . A l s o , i n areas where s treams carry bou lder s , branches , a n d o ther f loa t ing debris d u r i n g severe f loods, w i n g w a l l s he lp a l ign the flow of th i s m a t e r i a l t h r o u g h the cu lver t and hence avo id c logg ing of the entrance . P r a c t i c e i n the select ion of headwal l s a n d w i n g w a l l s depends large ly on the engineer's j udgement a n d the specia l requirements of the p a r t i c u l a r l o c a t i o n . T h e o r i en ta t ion and size of the a p p r o a c h c h a n n e l , its res istance to eros ion , and general t o p o g r a p h i c features are factors to be cons idered . Tab le 2.2 ind ica te s tha t 4 5 ° w i n g w a l l are h y d r a u l i c a l l y m o r e efficient t h a n pa ra l l e l w i n g w a l l s . H o w e v e r , para l l e l w ingwa l l s are desirable when the requi red l e n g t h of the wingwal l s has to be reduced and dra inage is not a n i m p o r t a n t factor . C h a p t e r S, INLET TYPES 34 F i g u r e 8.12: C o m m o n types o f w i n g w a l l entrance C h a p t e r 9 I M P R O V E D I N L E T D E S I G N S It has been s h o w n tha t w h e n a cu lver t operates w i t h inlet c o n t r o l , the inlet be-haves as an orif ice, as the b a r r e l resistance has p r a c t i c a l l y no inf luence o n the f low. In thi s case, the culver t doesn't r u n ful l and most of the cross sec t iona l area is f i l l ed w i t h air . O b v i o u s l y , this represents a waste of money since the bar re l of the cu lver t represents the m a j o r and most expensive component . In order to increase the h y d r a u l i c efficiency of cu lver t s , m a n y studies have been m a d e to improve the i r inlets . T h r e e m a i n designs of i m p r o v e d inlets are {17]: - )bevel edge inlets [F ig 9.13] -)side t apered inlets [Fig 9.14] -)slope t apered inlets [Fig 9.15] T h e above inlets m i n i m i z e the flow c o n t r a c t i o n at the in le t and increase the hydraul ic , c apac i ty of the cu lver t . For ex i s t ing unders ized cu lver t s , t apered inlets can be used to increase the capac i ty , hence sav ing the cost of c o n s t r u c t i n g a larger cu lver t . A d d i t i o n a l benefits can be o b t a i n e d w i t h raised-inlet cu lver t s , as they help c o n t r o l degra-d a t i o n of the channe l u p s t r e a m of the culvert and b a n k eros ion, and p rov ide s m a l l ponds for r ec rea t ion purposes . T h e use of slope tapered in le t s fur ther increases the a m o u n t of w a t e r h e a d app l ied due to the lower ing of the inlet cross sect ion. T h e h y d r a u l i c design of culverts us ing s lop ing t apered inlets is i n c l u d e d in the c o m p u t e r p r o g r a m for b o t h box and c i r c u l a r culver t s . In the c o m p u t e r p r o g r a m , the savings i n cross sect ion is also shown to the user. 35 Chapter 9. IMPROVED INLET DESIGNS 36 F i g u r e 9.13: Bevel-edge in le t s ELEVATION VIEW F i g u r e 9.14: S ide- tapered in le t s CULVIHT SAflRCL F i g u r e 9.15: S lope- tapered in le t s C U V A T t O N VltW Chapter 9. IMPROVED INLET DESIGNS 37 9.1 B O X C U L V E R T : TrcLrtSihon /ess 0--0 r _« o 4* in Bo.rrd F i g u r e 9.16: H y d r a u l i c elements at tapered inlets Referr ing to F i g 9.16 and as suming that c r i t i c a l flow occurs at the entrance of the in le t , the fo l lowing equa t ion can be w r i t t e n between sect ion 1 a n d sec t ion 2 as: Z + DC + Vc 2/2g = d2 + V2/2g + HL (9.78) where Hi represents the to ta l head loss between sect ion 1 a n d 2; d2 and V2 represent respect ively the d e p t h and flow ve loc i ty at sect ion 2. Hi is due to the f r i c t i o n loss plus a t r a n s i t i o n c o n t r a c t i o n loss. T a k i n g Kc = .1 where A'c represents a c o n t r a c t i o n loss coefficient, get: HL = .5L(Sn + Sf2) + A(V2 2/2g - Vc 2/2g) (9.79) W h e r e Sji and 5 / ; represent respect ively the f r i c t ion s lope at sec t ion 1 a n d 2 - B o t h can be easi ly ca lcu la ted us ing M a n n i n g equat ion- . For p r a c t i c a l purpose , Hi is assumed to be .5ft; th i s is due to the fact tha t f r i c t i o n loss C h a p t e r 9. IMPROVED INLET DESIGNS 38 u s u a l l y varies f r o m .1 — .2ft. and t r ans i t ion ' s c o n t r a c t i o n loss varies f r o m .1 — .3ft. Therefore , the requ i red d r o p Z can be ca l cu l a t ed as: Z = [d2 + V2/2g + .5] - [DC + Vc 2/2g] (9.80) A l s o , do is a s sumed to be between .8 — .9 the height of the b o x c u l v e r t . [6] F r o m the M a n n i n g e q u a t i o n , the b a r r e l s lope can be c a l c u l a t e d : Sb = [QN/(1A9AR 2/3) 2} (9.81) N . B : F r o m equat ions 9.80 a n d 9.81, i t is deduced that as the fa l l Z is increased , the b a r r e l s lope decreases. T h e increased excavat ion cost f r o m us ing s lop ing t apered inlets shou ld be c o m p a r e d to the savings achieved f r o m a reduced bar re l cross sec t ion . 9.2 C I R C U L A R C U L V E R T : T h e same procedure o u t l i n e d in box culvert, is used. H o w e v e r , due to the increase i n f r i c t i o n loss; Hi is a s sumed to be .6ft. T h e d e p t h of water at sect ion 2 is t aken as .ID. See [6] for fur ther detai l s . See c o m p u t e r o u t p u t - 3 . C h a p t e r 10 S C O U R A T C U L V E R T O U T L E T S A t the cu lver t i n l e t , the p o t e n t i a l energy of flow is t r a n s f o r m e d i n t o k i n e t i c energy as the bar re l cross sect ion is m u c h smal ler t h a n the non c o n s t r i c t e d s t ream sect ion. T h e r e s u l t i n g h i g h flow ve loc i t ies can p r o d u c e large scour holes benea th the out let a n d as a result a s u b s t a n t i a l a m o u n t of sediments is t r a n s p o r t e d d o w n s t r e a m . If th i s scour p r o b l e m is left unchecked , the flow at the out let m i g h t u n d e r m i n e the culvert s t ruc ture a n d cause f a i lure of the barre l and the e m b a n k m e n t ; besides aggradat ion of the channe l , l a n d areas a n d propert ies d o w n s t r e a m of the out let c o u l d result i n severe and cos t ly damages . 10.1 S C O U R C O N T R O L A T C U L V E R T O U T L E T S : O f t e n , scour p r o b l e m s are not due to excessively h i g h out le t ve loc i t ie s , but ins tead they result f r o m c h a n n e l d e g r a d a t i o n d o w n s t r e a m f r o m the c u l v e r t . Therefore , i t is wise in out let des ign, to expect channel eros ion and select a lower e levat ion for the culvert out le t s t ruc ture . In the case of h i g h flow veloci t ies , i t is w o r t h w i l e to r e m e m b e r tha t scour at culvert out let s resul t m a i n l y f r o m concentra ted flow emerg ing f rom the barre l caus ing eddies a n d waves w h i c h a t t ack the channe l banks at the sides of the cu lver t . B a n k scour is accentua ted where the channe l w i d t h is re l a t ive ly nar row compared to the cu lver t out let- . So, the idea is to t r y to d i s t r i b u t e the flow and e i ther t r ans fo rm the h i g h k i n e t i c energy i n t o p o t e n t i a l energy or jus t d i s s ipate i t . 39 Chapter 10. SCOUR AT CULVERT OUTLETS 40 F l o w d i s t r i b u t i o n can be real ized w i t h the use of a n apron and a w i n g w a l l . W i n g w a l l s protect the banks f r o m eddies p r o d u c e d i n the t a i l w a t e r ; however, aprons must be p r o v i d e d to secure the wingwa l l s f r o m u n d e r c u t t i n g . D e n o t i n g by x the h o r i z o n t a l d i r e c t i o n , by y the v e r t i c a l d i r e c t i o n , by t the t i m e , a n d cons ider ing the f low f r o m the out let as a free jet w i t h v e l o c i t i y V0, we have: T h e d i s tance L r equ i red for the jet to fa l l a d i s tance equal to the d i a m e t e r HEIGHT of the culver t p ipe is t h e n : F r o m w h i c h , and a l l o w i n g a safety factor , the a p p r o x i m a t e l eng th of a p r o n La was pro-posed as: O n e of the means of d i s s ipa t ing k i n e t i c energy is by e s t ab l i sh ing a h igh t a i lwa te r d e p t h . H i g h roughness and f lat ter channe l slope play an i m p o r t a n t part in increas ing the water dep th d o w n s t r e a m f r o m the cu lver t out let . I n th i s case, i f the flow was super-c r i t i c a l ins ide the cu lver t and s u b c r i t i c a l d o w n s t r e a m , a h y d r a u l i c j u m p occurs caus ing a s u b s t a n t i a l energy loss. A n e c o n o m i c a l energy diss ipator can often be real ized b y p l a c i n g l o c a l l y avai lable large rocks or boulders at the culvert out let [12]. (10.82) La = 37V0s/HEIGHT (10.83) Chapter 10. SCOUR AT CULVERT OUTLETS 41 1 0 . 2 S C O U R E S T I M A T I O N : V a r i o u s exper iment s have been done i n thi s field [10]. Scour holes were p r o d u c e d by us ing different discharges on different b e d mater i a l s , a n d us ing different, cu lver t shapes and t a i lwa te r c o n d i t i o n s . A n a l y s i s of the e x p e r i m e n t a l results led to the f o l l o w i n g con-clus ions : - ) A p p r o x i m a t e l y 80% of the m a x i m u m d e p t h , w i d t h a n d length of scour is a t t a i n e d i n the first ha l f h o u r of scour. - ) T h e m a x i m u m scour d e p t h was loca ted between .3 a n d .4 of the m a x i m u m scour l e n g t h . - ) T h e use of h e a d w a l l has no not iceable inf luence on the m a x i m u m d e p t h of scour a n d on the rate of scour. H o w e v e r , headwal l s i f p r o p e r l y c o n s t r u c t e d , prevent u n d e r m i n i n g of the culver t b a r r e l and protect the e m b a n k m e n t f r o m u n d e r c u t t i n g on b o t h sides of the culver t out le t . - ) T h e m a x i m u m dimens ions of the scour hole increase w h e n the cu lver t discharges on a bed of u n i f o r m m a t e r i a l . O n the other h a n d , graded mater i a l s t end to a r m o u r the scour hole , hence r e d u c i n g the u l t i m a t e scour hole d imens ions f r o m those of more u n i f o r m m a -terials . - )Scour hole d imens ions are larger w h e n the t a i lwa te r e levat ion is between the invert a n d the culver t centre l ine . - ) A t the e q u i l i b r i u m stage, scour hole acts as an excel lent energy d i s s ipator . Scour hole d imens ions are g iven by the c o m p u t e r p r o g r a m , u s ing the fo l lowing e m p i r i c a l formulas [10]: dsni k V s r n L s m Vsm O ^ /-in o A\ R l i ^ - m i 0 r R m = Ayi'RH ( 1 0 " 8 4 ) W H E R E : dsm= M a x i m u m d e p t h of scour Wsm = M a x i m u m w i d t h of scour Chapter 10. SCOUR AT CULVERT OUTLETS Lsm= M a x i m u m length of scour Vsm~ M a x i m u m v o l u m e of scour Coeff ic ients a and b are g iven i n tab le 10.3 . Chapter 10. SCOUR AT CULVERT OUTLETS Tab le 10.3: S u m m a r y of coefficients a a n d b for e q u a t i o n 10.84 S o i l tu j j^C- De.jtencjcnl' /afv'aij]c ex. b cls^v / R H 0.^ 3 o .63 / • ^ G roAzA o.£?> \ 3 r\i9o T m 0-27 Ws>* /KV\ 6 . 0.53 / r\V\3 /-hi o-Z7 Wsv. / R V4 0. £3 o-53 ) o 2*5 4 (3 - \ \ Ls>- /R H C h a p t e r 11 O T H E R C O N S I D E R A T I O N S : G e n e r a l l y , culverts are costly. However , m a j o r savings can often be achieved by careful h y d r a u l i c design i n order to choose o p t i m a l b a r r e l d imens ions . In most cases, the engineer k n o w s the design discharge a n d the a l lowable head at the in le t . H o w e v e r , he t h e n faces the ques t ion of w h i c h culver t shape is most e c o n o m i c a l and m o r e convenient to use. C o m p u t e r ou tput -1 i l lus t ra tes var ious culverts tha t differ i n shape but have the same equiva lent d i a m e t e r of 10ft. T h e design discharge is 1000ft 3/s a n d the a l lowable head-water level is 14ft. T h e results are s u m m a r i z e d in tab le 11-4. T h e la t ter shows that the m a x i m u m d e p t h of scour at the out let is greater w i t h c i r cu l a r culverts . However , the m a x i m u m w i d t h and l e n g t h of scour are greater w h e n box cu lver t s are used . A n exper ienced design engineer c o u l d ant i c ipa te the above result since jets discharged f r o m square out le t s t r y to disperse a n d i m p a c t over a wider area t h a n the m o r e concen-t r a t e d jets f r o m c i r cu l a r cu lver t s . T h e use of arch culver t s or v e r t i c a l e l l i p t i c a l culvets leads to m i l d e r erosion values , m a i n l y because of the apprec iab le flow d i s t r i b u t i o n that takes effect i n t h e m . There fore , i f ero-sion at the out le t . represent s a severe p r o b l e m for the designer, c i rcu lar culver t s should be avo ided a n d the best choice is e i ther to use an a rch or a ve r t i c a l e l l i p t i c a l culvert . U n f o r t u n a t e l y , as table 11-4 shows, the c i rcu la r culverts are able to car ry a higher ful l d i scharge c a p a c i t y t h a n o ther culver t s . A l s o , where sediment, depos i t ion occurs inside the c u l v e r t , the a l lowable headwater can more read i ly be exceeded w i t h arch or ver t i ca l 44 Chapter 11. OTHER CONSIDERATIONS: 45 e l l i p t i c a l cu lver t s , w h i c h might result in f lood ing the road a n d damage to the embank-m e n t . E v e n t h o u g h the c o m p u t e r p r o g r a m carries out most of the h y d r a u l i c ca l cu la t ions re levant to the des ign, the culvert designer shou ld also be aware of the adverse effects on cu lver t capac i ty r e su l t ing f r o m air en t ra inment t h a t happens m a i n l y w i t h low in le t submergence . A l s o , the engineer shou ld use his o w n j u d g e m e n t ' o n whether to use a con-crete or a corrugated steel cu lver t . C o n c r e t e pipes are s m o o t h e r and h y d r a u l i c a l l y m o r e efficient, however they p r o d u c e h i g h outlet veloci t ies tha t m i g h t result i n scour p rob lems d o w n s t r e a m . T h e service life of the culver t can be grea t ly ex tended when the b a r r e l is p ro tec ted f r o m eros ion . Serious corros ion u s u a l l y starts f r o m the out s ide of a cu lver t a n d t h e n moves t o w a r d the ins ide , so i t m a y not be n o t i c e d i f the culvert is not exposed or if samples are not cut f r o m the ins ide . E n c l o s i n g the cu lver t in an i n o r g a n i c f i l l zone of low p e r m e a b i l i t y is preferred since organic e n v i r o n m e n t s support, the g r o w t h of b a c t e r i a w h i c h can grea t ly enhance the corros ion process. G a l v a n i z i n g and increased thickness of m e t a l lengthens the life of steel culverts against corros ion , however i t has to be checked tha t p r o t e c t i v e oxides w h i c h are expected to f o r m i n contact w i t h the air do indeed de-ve lop . G e n e r a l l y , precast concrete p i p e of good q u a l i t y is h i g h l y resistant to erosion but care m u s t be t aken against the abras ive ac t ion of s t ream bed load . T h e c o m p u t e r p r o g r a m assumes that the designer has l ooked at the s t ream h y d r o l -ogy a n d the watershed area, and that the des ign discharge that the culver t has to carry is a l ready k n o w n . T h e r e is no p a r t i c u l a r p h i l o s o p h y i n w h a t type of f l ood to choose i n d e t e r m i n i n g the design discharge, however the f o l l o w i n g two ex t reme cases are genera l ly agreed u p o n : A low fill on a secondary road p o s i n g no threat to p r o p e r t y damage up-s t r e a m or d o w n m i g h t suppor t a design for 5 year or 10 year s to rm. In the o ther h a n d , a h i g h fill on a m a j o r h ighway w i t h developed p r o p e r t y m i g h t require a design f lood w i t h C-ha.pt.er 11. OTHER CONSIDERATIONS: 46 a 100 year r e t u r n p e r i o d or longer. U n c e r t a i n t i e s i n d e t e r m i n i n g the exact runoff t h a t the cu lver t m u s t car ry mus t not prec lude the designer f r o m c a r r y i n g out the necessary h y d r a u l i c ana lys i s . O t h e r w i s e a large safety factor has to be used and the culver t w i l l p r o b a b l y be overdes igned. Chapter 11. OTHER CONSIDERATIONS: T a b l e 11.4: S u m m a r y of (he results o b t a i n e d f rom c o m p u t e r o u t p u t - ] CUL V€fiT (FtV.) Hwc (••*«=) C PV) \ s j > = | f t \ S D - . I ft \ S D , J Ft \ i C - . l Vt SD = 0 \ SD= 0 5 b = o \ CiVculcx . r-X Mf3 X 25.\ \ sis X £ 1 ^ 151554 \ \ v l 3 . \ \ \ * 6 3. s \ 15553! M - l X iSTtfX \ 155531 \ j\cc\\ X AkX X ^ 3 . 1 \ 425. i \ lu .C X > J U 5 . j \ El i>j*s^-X -?U.t> X 3 X - I ^ l ion'Zon to . I) x J 3 3 . M \ i \ C h a p t e r 12 S U M M A R Y A N D C O N C L U S I O N : C u l v e r t s can be expens ive a n d m a n y cons idera t ions have to be t a k e n in to account i n the i r des ign. T h i s thesis has concentra ted on h y d r a u l i c analys is since i t represents a m a j o r e lement i n cu lver t design where the a i m is to o b t a i n the smallest a n d hence most e c o n o m i c a l s t ruc ture t h a t w i l l ca r ry the design discharge for a f ixed head on the in le t . A c o m p u t e r p r o g r a m for the h y d r a u l i c design of cu lver t s was w r i t t e n i n the B a s i c language. T h e a b i l i t y to check an ex i s t ing culvert is i n c l u d e d i n the p r o g r a m , as it cou ld be useful i n regions where design flows have increased in recent years, perhaps due to changes i n weather pa t terns , a d d i t i o n a l h y d r o l o g i c da ta , or to the increase of u r b a n i z a t i o n a n d i n d u s t r i a l deve lopments . T h e h y d r a u l i c design of cu lver t s is qu i te c o m p l e x since m a n y factors have a n impact, on the final design. G e n e r a l l y , the most efficient, designs are the ones based o n the culver t f lowing fu l l w h i c h requires careful s tudy of the inlet des ign, the slope and the roughness . Inlet design is p a r t i c u l a r l y i m p o r t a n t i n short cu lver t s or i n long culver t s w i t h steep slopes, b u t of lesser i m p o r t a n c e in long culverts w i t h flat slopes. S lope is not i m p o r t a n t w h e n the c o n t r o l sect ion is at the in le t . H o w e v e r , w i t h outlet, c o n t r o l , increas ing the cu lver t s lope results in a h igher discharge. T h e l e n g t h w i l l de te rmine whether a culvert, on a flat s lope w i l l flow fu l l w i t h a p o o r l y des igned in le t . L e n g t h is also a factor in culverts f l owing fu l l as the head loss due to f r i c t i o n increases w i t h l e n g t h . W i t h the c o m p u t e r p r o g r a m a n d the a n a l y t i c a l approach i l l u s t r a t e d i n th i s thesis 48 Chapter 12. SUMMARY AND CONCLUSION: 49 for the h y d r a u l i c ana lys i s of cu lver t s , the engineer has an o p p o r t u n i t y to use a new way of c o m p u t i n g cu lver t c a p a c i t y in s tead of us ing the s t a n d a r d nomograms and charts . T h i s w i l l he lp the engineer save t i m e , and avoid the l i m i t a t i o n s on use of culvert capac i ty charts . For e x a m p l e , these charts do not i n c l u d e curves for a l l cu lver t d imens ions a n d they show di scharge-headwater curves for o n l y s ingle-barre l cu lver t . T h i s thesis gave spec ia l a t t e n t i o n to var ious i m p r o v e d inlet designs as they increase the discharge capac i ty of the cu lver t . However , i t w o u l d be advisable to m a k e a s tudy of the cost a n d benefits at each p a r t i c u l a r cu lver t site to see whether or not m o d i f i c a t i o n to the inlet geometry such as beve l edge, side tapers or slope tapers are w a r r a n t e d . Serious c o n s i d e r a t i o n mus t be g iven to the size and q u a n t i t y of debris w h e n select ing cu lver t sizes. A l s o , the debris s i t u a t i o n can change very q u i c k l y i f the watershed is i n a logg ing area. B e d scour at the out le t of a cu lver t m a y not be as serious as l a te ra l erosion w h i c h u n d e r m i n e s the e m b a n k m e n t , but i f a l lowed to progress unchecked, it m a y u n d e r m i n e the end of the cu lver t p i p e . V a r i o u s scour cont ro l procedures a n d e s t i m a t i o n of scour hole d imens ions were presented i n th i s thesis . However , most of the studies made on the scour at cu lver t out le t s re ly on e m p i r i c a l approaches a n d therefore, the engineer has to use his own j u d g e m e n t and exper ience . T h e engineer s h o u l d also t ry to adjust cer ta in e m p i r i c a l coefficients whenever he feels t h a t such modi f i ca t ions w o u l d suit bet ter his specific culvert des ign or after l o o k i n g at a l ready cons t ruc ted culver t s . B i b l i o g r a p h y [1] Vent Te C h o w (1959) Open-Channel Hydraulics, pages 493-501. [2] P o r t l a n d C e m e n t A s s o c i a t i o n (1964). Handbook of Concrete Culvert Pipe Hy-draulics [3] A m e r i c a n C o n c r e t e A s s o c i a t i o n (1980) Concrete Pipe Handbook . [4] James F . R u f f and Steven R . A b t Culvert Slope Effects on Outlet Scour, A S C E , O c t o b e r 1985, pages 1363-1367, J o u r n a l of the H y d r a u l i c D i v i s i o n . [5] James F . R u f f a n d Steven R . A b t Estimating Culvert Scour in Cohesive Material, A S C E , J a n u a r y 1982, pages 25-33, J o u r n a l of the H y d r a u l i c D i v i s i o n . [6] R o n a l d L . R o s s m i l l e r , and M e r w i n D . D o u g a l Tapered Inlet Design Using Specific Energy Curves, A S C E , J a n u a r y 1982, pages 127-135, J o u r n a l of the H y d r a u l i c D i v i s i o n . [7] F r e d W . B l a i s d e l l Flow in culverts and related design philosophies, A S C E , M a r c h 1966, pages 19-31, J o u r n a l of the H y d r a u l i c D i v i s i o n . [8] L o r e n z G . S t r a u b a n d H e n r y M . M o r r i s Hydraulic Data Comparison of Concrete and Cor.rigat.ed Metal Culvert Pipes. J u l y 1950, M i n n e a p o l i s , M i n n e s o t a . [9] M O E T e c h n i c a l R e p o r t 6 Environmental Objectives and Procedures for Water Crossings, J a n u a r y 1984, V i c t o r i a B . C . [10] James F . R u f f , S . R . A b t a n d F . K . D o e h r i n g Influence of Culvert Shape on Outlet Scour, A S C E , M a r c h 1987, pages 393-399, J o u r n a l of H y d r a u l i c E n g i n e e r i n g . 50 Bibliography 51 (11] D a v i d L . Y a r n e l l and F l o y d A . N a g l e r Flow of Water through Culverts, Iowa studies i n engineer ing , J u n e 1926. [12] B o h a n J . P . Erosion and. Riprap Requirements at Culvert and Storm-Drain Outlets, U . S . A r m y W a t e r w a y s E x p e r i m e n t S t a t i o n , V i c k s b u r g , M i s s . , 1970. [13] M e n d o z a C . Headwall Influence on Scour at Culvert Outlets, M . S . T h e s i s , C o l o r a d o S ta te U n i v e r s i t y , C o l o . , 1980 [14] R u f f J . F . , A b t S .R. , K l o b e r d a n z R . , and S h a i k h C . Scour at Culvert Outlets in Mixed Bed Materials, F e d e r a l H i g h w a y A d m i n i s t r a t i o n , W a s h i n g t o n D . C . , 1981. [15] George K . Y o u n g , M i t c h e l l R . C h i l d r e y , a n d R o y E . T r e n t Optimal Design For High-way Drainage Culverts, A S C E , J u l y 1974, pages 971-993, J o u r n a l of the H y d r a u l i c D i v i s i o n . [16] M a l c o l m H . K a r r and Les l ie A . C l a y t o n Model Studies of Inlet Designs for Pipe Culverts on Steep Grades, B u l l e t i n N o . 3 5 , J u n e 1954, Oregon State Col lege . [17] J e rome M . N o r m a n n Improved Design of Highway Culverts, C i v i l E n g i n e e r i n g , pages 70-73, A S C E , M a r c h 1975. [18] W a y n e T a l b o r t a n d H a r r y J . B r m i d Hydraulics Elements of a Partially Silted Round Section, A S A E T r a n s a c t i o n s , pages 288-292, J u l y 1977. [19] L i n s l e y R . K . and J . B . F r a n z i n i (1972) Water Resources Engineering, pages 531-542, M c G r a w - H i l l . [20] H e n d e r s o n F . M . Open Channel Flow, pages 258-264, 1966. 52 C U r r - I H Y D R A U L I C D E S I G N OF C U L V E R T S L I S T D E S I G N D A T A : D I S C H A R S E C c f s ) = 1OOO SLOPE i= . 0 0 5 T H E A C C E L E R A T I O N DUE TO G R A V I T Y q ( f t / s A 2 ) = 3 2 . 2 A L L O W A B L E WATER HEAD (. f t ) = 14 M A N N I N G R O U G H N E S S OF T H E C U L V E R T - . 0 1 2 T A I L W A T E R D E P T H C f t ) = 4 L E N G T H OF T H E C U L V E R T C f t ) = 3 0 0 S E D I M E N T D E P T H I N T H E C U L V E R T C f t ) = 0 C H E C K E X I S T I N G C I R C U L A R C U L V E R T D I A M E T E R OF E X I S T I N G C U L V E R T (. f t ' ) --• 10 E N T R A N C E S H A P E S E L E C T E D : 2 - - P R O J E C T I N G E N T R A N C E G R O O V E E D G E I N L E T C O N T R O L G O V E R N S A C T U A L I NL.ET H E A D WATER ( f t.1 = 1 2 . 1 1 5 E Q U I V A L E N T D I A M E T E R O F C U L V E R T C f t ) - 10 C R I T I C A L D E P T H I N T H E C U L V E R T ( f t ) = 7 „ 5 8 1 4 8 5 C R I T I C A L S L O P E OF T H E C U L V E R T ^ 8 . 1 6 6 4 4 2 E - 0 3 C R I T I C A L V E L O C I T Y I N T H E C U L V E R T ( f t / s J = 1 5 . 7 3 4 7 6 F U L L FLOW C A P A C I T Y OF T H E C U L V E R T C f t • ' • 3 / s ) = 1 2 7 0 . . 2 0 4 F U L L . FLOW V E L O C I T Y I N T H E C U L V E R T C f t / s ) = 16. 17273 O U T L E T V E L O C I T Y V(ft/s)= 1 3 . 6 7 2 2 2 T Y P E 2 F L O W : C R I T I C A L D E P T H AT O U T L E T , O U T L E T U N S U B M E R G E D S U B C R I T I C A L F L O W . S O I L T Y P E S E L E C T E D AT T H E C U L V E R T O U T L E T : 2 - U N I F O R M S A N D E S T I M A T E D M A X I M U M D E P T H OF S C O U R < f t ) - 2 5 . 8 5 9 1 2 E S T I M A T E D M A X I M U M W I D T H OF S C O U R ( f t ) -- 9 8 . 3 5 8 9 8 E S T I M A T E D M A X I M U M L E N G T H OF S C O U R C f t ) = 2 4 7 . 9 7 2 9 E S T I M A T E D M A X I M U M V O L U M E OF SCOUR ( ft"'" 3 ) =" 1 5 1 5 5 4 . 2 H Y D R A U L I C D E S I G N O F C U L V E R T S L I S T D E S I G N D A T A : D I S C H A R G E (c : f s ) »• 1 0 0 0 S L O P E = . 0 0 5 T H E A C C E L E R A T I O N D U E T O G R A V I T Y q ( f t / s A 2 ) = 3 2 . 2 A L L O W A B L E W A T E R H E A D ( f t ) = 1 4 M A N N I N G R O U G H N E S S O F " T H E C U L V E R T = . , 0 1 2 T A I L W A T E R D E P T H ( f t ) = = 4 L E N G T H O F T H E C U L V E R T ( f t ) = 3 0 0 S E D I M E N T D E P T H I N T H E C U L V E R T C f t ) = 1 C H E C K E X I S T I N G C I R C U L A R C U L V E R T D I A M E T E R O F E X I S T I N G C U L V E R T (. f t ) = 1 0 E N T R A N C E S H A P E S E L E C T E D : 2 - - P R O J E C T I N G E N T R A N C E G R O O V E E D G E I N L E T C O N T R O L G O V E R N S A C T U A L I N L E T H E A D W A T E R i f t ) = 1 2 . 7 2 4 7 1 E Q U I V A L E N T D I A M E T E R O F C U L V E R T < f t > = 9 . 6 1 2 6 6 4 C R I T I C A L D E P T H I N T H E C U L V E R T C f t > = 6 . 9 9 6 0 1 6 C R I T I C A L S L O P E O F T H E C U L V E R T ™ 8 . 5 7 8 4 3 6 E - 0 3 C R I T I C A L V E L O C I T Y I N T H E C U L V E R T C f t / s > = 1 5 . 7 5 1 6 F U L L F L O W C A P A C I T Y O F T H E C U L V E R T C f t ' " - 3 / s > = 1 1 7 2 . 8 F U L L F L O W V E L O C I T Y I N T H E C U L V E R T C f t / s ) = 1 5 . 7 5 2 3 7 O U T L E T V E L O C I T Y V < f t / s ) = 1 4 , , 2 1 4 0 7 T Y P E 2 F L O W : C R I T I C A L D E P T H A T O U T L E T , O U T L E T U N S U B M E R G E D S U B C R I T I C A L F L O W . S O I L T Y P E S E L E C T E D A T T H E C U L V E R T O U T L E T : 2 - L J N I F O R M S A N D E S T I M A T E D M A X I M U M D E P T H O F S C O U R ( f t ' ) =• 2 5 . 0 1 3 1 7 9 E S T I M A T E D M A X I M U M W I D T H O F S C O U R C f t ') •"• 9 7 . 5 2 7 1 7 E S T I M A T E D M A X I M U M L E N G T H O F S C O U R C f t ) = 2 4 4 . 3 3 3 1 E S T I M A T E D M A X I M U M V O L U M E O F S C O U R t f t A 3 ) = 1 4 3 5 2 5 . 6 55 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(cfs)= 1000 SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( f t / s ~ 2 ) = 32 ALLOWABLE WATER HEAD(ft ) = 14 MANNING ROUGHNESS OF THE CULVERT^ .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 300 SEDIMENT DEPTH IN THE C U L V E R T ( f t ) = 0 CHECK EXISTING BOX CULVERT HEIGHT OF EXISTING BOX C U L V E R T ( f t ) = 8.899999 Wl'DTH OF EXISTING BOX C U L V E R T ( f t ) = 8.899999 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(f t ) = 12.07 EQUIVALENT DIAMETER OF C U L V E R T ( f t ) CRITICAL DEPTH IN THE C U L V E R T ( f t ) = CRITICAL SLOPE OF THE CULVERT= 8.7 CRITICAL VELOCITY IN THE CULVERT(f 14.96385 431 = 1 0 . 03 7 . 3190 345 78E-t / s )= 1 f t " 3/s) f t / s) = f t ) = 6. t / s )= 1 OUTLET VELOCITY V ( f t / s ) = 16.88421 TYPE 1 FLOW: CRITICAL DEPTH AT INLET,OUTLET UNSUBMERGED SUPERCRITICAL FLOW. SOIL TYPE SELECTED AT THE CULVERT uUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 24.73178 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 103.4406 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 253.8046 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft~3)= 155597.9 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(c f s ) = 1000 SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( f t / s ^ 2 ) = 32.2 ALLOWABLE WATER HEAD(ft ) = 14 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 30 0 SEDIMENT DEPTH IN THE CULVERT(ft)= 1 CHECK EXISTING BOX CULVERT HEIGHT OF EXISTING BOX CULVERT(ft)= 8.899999 WIDTH OF EXISTING BOX CULVERT*ft)= 8.899999 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 13.07 07 7 EQUIVALENT DIAMETER OF CULVERT(ft)= 9.433257 CRITICAL DEPTH IN THE CULVERT(ft)= 7.31905 CRITICAL SLOPE OF THE CULVERT^ 8.734578E-03 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 15.35166 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 1009.932 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 14.36399 UNIFORM FLOW DEPTH IN THE CULVE R T ( f t ) = 6.654754 UNIFORM VELOCITY THROUGH C U L V E R T ( f t / s ) = 16.8841 OUTLET VELOCITY V ( f t / s ) = 16.8841 TYPE 1 FLOW: CRITICAL DEPTH AT INLET,OUTLET UNSUBMERGED SUPERCRITICAL FLOW. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 24.73179 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 103.4403 ESTIMATED MAXIMUM LENGTH OF SCOUR*ft)= 253.8042 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft"3)= 155597.4 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(cfs)= 1000 SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( f t / s ~ 2 ) = 32.2 ALLOWABLE WATER H E A D ( f t ) = 14 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 300 SEDIMENT DEPTH IN THE C U L V E R T ( f t ) = 0 CHECK EXISTING E L L I P T I C A L CULVERT SPAN OF THE EXISTING E L L I P T I C A L C U L V E R T ( f t ) = 14 HEIGHT OF THE EXISTING E L L I P T I C A L C U L V E R T ( f t ) = 6.8 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 12.09483 EQUIVALENT DIAMETER OF C U L V E R T ( f t ) = 10.01493 CRITICAL DEPTH IN THE C U L V E R T ( f t ) = 5.77586 CRITICAL SLOPE OF THE CULVERT= 7.650096E-03 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 14.83007 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 1117.703 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 14.9 4856 OUTLET VELOCITY V ( f t / s ) = 13.84908 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 24.08939 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 93.44644 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 234.2685 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft~3)= 126646.9 58 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(c f s ) = 1000 SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( f t / s ~ 2 ) = 32.2 ALLOWABLE WATER HEAD(ft)= 14 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 300 SEDIMENT DEPTH IN THE CU L V E R T ( f t ) = 1 CHECK EXISTING ELLIPTICAL CULVERT SPAN OF THE EXISTING ELLIPTICAL C U L V E R T ( f t ) = 14 HEIGHT OF THE EXISTING ELLIPTICAL C U L V E R T ( f t ) = 6 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 13.65128 EQUIVALENT DIAMETER OF CU L V E R T ( f t ) = 9.175669 CRITICAL DEPTH IN THE CU L V E R T ( f t ) = 6.077344 CRITICAL SLOPE OF THE CULVERT= 9.920006E-03 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 15.60958 FULL FLOW CAPACITY OF THE C U L V E R T ( f t " 3 / s ) = 957.9886 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 14.1013 OUTLET VELOCITY V ( f t / s ) = 16.01626 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 23.98978 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 98.81569 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 243.5177 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft~3)= 138398.1 HYDRAULIC DESIGM OF CULVERTS LIST DESIGN DATA: DISCHARGE (cf s ) = 1OOO SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( f t / s A 2 ) = 32.2 ALLOWABLE WATER HEAD(ft) = 15 MANNING ROUGHNESS OF THE CULVERT^ .012 TAILWATER DEPTH <! f t ) := 4 LENGTH OF THE CULVERTCft)= 300 SEDIMENT DEPTH IN THE CULVERTCft)= 0 CHECK EXISTING ELLIPTICAL CULVERT SPAN OF THE EXISTING ELLIPTICAL CULVERTCft)= 6.8 HEIGHT OF THE EXISTING ELLIPTICAL CULVERTCft)= 14 ENTRANCE SHAPE SELECTED: 2--PROJECTIMG ENTRANCE GROOVE EDGE OUTLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 14.59034 EQUIVALENT DIAMETER OF CULVERTCft)= 10.01326 CRITICAL DEPTH IN THE CULVERTCft>= 10.0566 CRITICAL SLOPE OF THE CULVERT^ 1.275839E-02 CRITICAL VELOCITY IN THE CULVERT (ft/s)= 17.34443 FULL FLOW CAPACITY OF THE CULVERT (. f t-""3/&')= 1117.578 FULL FLOW VELOCITY IN THE CULVERTCft/s)= 14.94689 OUTLET VELOCITY V <f t / s ) = 14.63013 TYPE 2 FLOW: CRITICAL DEPTH AT OUTLET, OUTLET UN SUE* ME EG ED SUBCRITICAL FLOW. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(f t ) = 22.58717 ESTIMATED MAXIMUM WIDTH OF SCOUR ( f t ) = 90., 77916 ESTIMATED MAXIMUM LENGTH OF SCOUR ( f t ) = 225.2894 ESTIMATED MAXIMUM VOLUME OF SCOUR ( f t"'"3):- 110825.9 HYDRAULIC DESIGN OF CULVERTS L I S T DESIGN DATA: D I S C H A R G E ( c f s ) ^ XOOO S L O P E - .. 005 THE ACCELERATION DUE TO GRAVITY a ( t t / s - " - 2 ) ^ 32.. 2 ALLOWABLE WATER HEAD ( f t ) == 15 MANNING ROUGHNESS OF THE C U L V E R T - „ 012 TAILWATER D E P T H ( f t ) - 4 LENGTH OF THE C U L V E R T ( f t ) = 300 SEDIMENT DEPTH IN Tl-l!£ CUl._VERT ( f t ) 1 CHECK E X I ST ING EU... I P T I C A L CULVERT SPAN OF THE E X I ST I NG E L L I PT I CAL CULVERT ( f t ) = £., S HEIGHT OF THE E X I S T I N G E L L I P T I C A L CULVERT ( f t ) ••- 14 ENTRANCE SHAPE S E L E C T E D : 2 - P R O J E C T I N G ENTRANCE GROOVE EDGE OUTLET CONTROL GOVERNS ACTUAL INLET HEAD WATER ( f t ) ~ 14.. 47224 EQUI VALIENT DIA METER: OF CULVERT ( f t ) == 9 . S929S9 C R I T I C A L DEPTH IN THE CULVERT ( f t ) -•- 1 0 . 3 8 6 4 5 C R I T I C A L SLOPE OF TI-IE CULVERT'™ 1,. 3211 1 8 E - 0 2 C R I T I C A L VELQCITY IN THE C U L V E R T ( f t / s ) = 1 7 „ 5 5 6 5 3 F U L L FLOW CAPACITY OF THE CULVERT ( f f ' 3 / s ) = 1 0 7 3 . 4 6 3 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 1 4 . 8 2 6 9 7 OUTLET VELOCI TY V ( f t / s ) = 15,. 54182 TYPE 2 FLOW:: C R I T I C A L DEPTH AT O U T L E T , OUTLET UNSUBMERGED S U B C R I T I C A L FLOW. SO IL TYPE S E L E C T E D AT THE CULVERT O U T L E T : 2-UNIFORM SAND EST I MATED MAX I MUM DEPTH OF" SCOUR ( f I; ) - 22. S3109 EST I MATED MAX I MUM WIDTH 0!r' SCUJl.lf? ( f t ) ^ 9 3 . 83968 ESTIMATED MAXIMUM LENGTH OF S C O U R ( f t ) ^ 2 3 1 . 3 9 8 IESTI MATED MAX I MUM VOLUME OF SCOUR ( f t ""S) = 118863.. 2 HYDRAULIC DESIGN OF CULVERTS LIS T DESIGN DATA: DISCHARGE(cfs)= 1000 SLOPE= .005 THE ACCELERATION DUE TO GRAVITY g ( £ t / s ~ 2 ) = 32.2 ALLOWABLE WATER HEAD(£ t ) = 14 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 300 SEDIMENT DEPTH IN THE C U L V E R T ( f t ) = 0 CHECK EXISTING ARCH CULVERT SPAN OF THE EXISTING ARCH C U L V E R T ( f t ) = 12.5 HEIGHT OF THE EXISTING ARCH C U L V E R T ( f t ) = 7.42 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 12.10502 EQUIVALENT DIAMETER OF C U L V E R T ( f t ) = 10.00737 CRITICAL DEPTH IN THE C U L V E R T ( f t ) = 5.56234 CRITICAL SLOPE OF THE CULVERT= 9.198493E-03 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 15.31204 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 769.9998 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 10.02754 OUTLET VELOCITY V ( f t / s ) = 13.76799 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 23.06532 ESTIMATED MAXIMUM WIDTH OF SC O U R ( f t ) = 90.05286 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 225.3452 ESTIMATED MAXIMUM VOLUME OF SCOUR.( f t ~ 3 ) = 112387.3 62 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(cfS)= 1 0 0 0 SLOPE= . 0 0 5 THE ACCELERATION DUE TO GRAVITY g ( f t / s ~ 2 ) = 3 2 . 2 ALLOWABLE WATER HEAD(ft ) = 15 MANNING ROUGHNESS OF THE CULVERT= . 0 1 2 TAILWATER DEPTH( f t) = 4 LENGTH OF THE CU L V E R T ( f t ) = 3 0 0 SEDIMENT DEPTH IN THE CULVERT(ft)= 1 CHECK EXISTING ARCH CULVERT SPAN OF THE EXISTING ARCH CU L V E R T ( f t ) = 12.5 HEIGHT OF THE EXISTING ARCH C U L V E R T ( f t ) = 7.42 ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 14 . 61651 EQUIVALENT DIAMETER OF CULVERT(ft)= 8.829216 CRITICAL DEPTH IN THE CULVERT(ft)= 6.427599 CRITICAL SLOPE OF THE CULVERT^ 1.312817E-02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 16.78214 FULL FLOW CAPACITY OF THE C U L V E R T ( f t " 3 / s ) = 591.9183 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 9.224212 OUTLET VELOCITY V ( f t / s ) = 16.78943 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 21.99001 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 93.98316 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 229.1797 ESTIMATED MAXIMUM VOLUME OF SCOUR ( f t ~ 3 ) = .113433.5 63 HYDRAULIC DESIGN OF CULVERTS L IST DESIGN DATA: DISCHARGE(cfs)= 225 SLOPE= .001 THE ACCELERATION DUE TO GRAVITY g(£t/s " 2 ) = 3 2.2 ALLOWABLE WATER H E A D ( f t ) = 10 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 200 SEDIMENT DEPTH IN THE CULVERT* f t ) = 0 DESIGN OF A CIRCULAR CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE I N L E T CONTROL GOVERNS ACTUAL INLET HEAD W A T E R *ft)= 9 .49 3 42 8 EQUIVALENT DIAMETER OF C U L V E R T *ft)= 5 «» CRITICAL DEPTH IN THE C U L V E R T(ft)= 4 .216719 CRITICAL SLOPE OF THE CULVERT= 1 .320088E-02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 12.63546 FULL FLOW CAPACITY OF THE C U L V E R T ( f t " 3 / s ) = 89.46263 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 4.556294 OUTLET VELOCITY V ( f t / s ) = 11.89114 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF S C O U R *ft)= 13.43342 ESTIMATED MAXIMUM WIDTH OF S C O U R *ft)= 55.15632 ESTIMATED MAXIMUM LENGTH OF S C O U R *ft)= 136.0496 ESTIMATED MAXIMUM VOLUME OF S C O U R(ft " 3 ) = 24169.43 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(c f s ) = 225 SLOPE = .001 THE ACCELERATION DUE TO GRAVITY g ( f t / s " 2 ) = 32.2 ALLOWABLE WATER HEAD( f t ) = 10 MANNING ROUGHNESS OF THE CULVERT= .012 TAILWATER D E P T H ( f t ) = 4 LENGTH OF THE C U L V E R T ( f t ) = 200 SEDIMENT DEPTH IN THE C U L V E R T ( f t ) = .8 DESIGN OF A CIRCULAR CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 9.973086 DIAMETER OF THE CIRCULAR C U L V E R T ( f t ) = 5.3 + EQUIVALENT DIAMETER OF C U L V E R T ( f t ) = 4.925571 CRITICAL DEPTH IN THE CULVERT*ft)= 3.739062 CRITICAL SLOPE OF THE CULVERT= .0133382 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 12.5601 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 90.07378 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 4.510964 OUTLET VELOCITY V ( f t / s ) = 11.68037 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 13.16205 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 53.87346 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 133.004 ESTIMATED MAXIMUM VOLUME OF SCOUR*ft~3)= 22614.61 IV. 8: NoC.c t r ie . i n c r c o J i c i»n si '-£e o P kWe. c o W e c r o s s - s e c t i o n c l ^ e - t « se-c | .Vn«.n t d e r ^ o s . ' h-'o HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(c f s ) = 400 SLOPE= . 0 0 7 THE ACCELERATION DUE TO GRAVITY q ( f t / s ~ 2 ) = 3 2 . 2 ALLOWABLE WATER HEAD(ft)= 9 MANNING ROUGHNESS OF THE CULVERT= . 0 1 2 TAILWATER D E P T H ( f t ) = 3 LENGTH OF THE CULVERT(ft)= 3 5 0 SEDIMENT DEPTH IN THE CULVERT(ft)= 0 DESIGN OF A HORIZONTAL ELLIPTICAL CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE-INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 8.973181 EQUIVALENT DIAMETER OF CULVERT(ft)= 6.578434 CRITICAL DEPTH IN THE CULVERT(ft)= 4.068438 CRITICAL SLOPE OF THE CULVERT= 1.109698E-02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 13.14392 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 425.133 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 13.36533 OUTLET VELOCITY V ( f t / s ) = 12.80007 SPAN OF THE ELLIPTICAL CULVERT(ft)= 9 HEIGHT OF THE ELLIPTICAL C U L V E R T ( f t ) = 4.5 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL, OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF .SCOUR(ft)= 15.88258 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 64.94534 ESTIMATED MAXIMUM LENGTH OF•SCOUR(ft)= 160.3833 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft~3)= 39670.38 HYDRAULIC DESIGN OF CULVERTS LIST DESIGN DATA: DISCHARGE(cfs)= 400 SLOPE- .007 THE ACCELERATION DUE TO GRAVITY g ( f t / s " 2 ) = 32.2 ALLOWABLE WATER HE A D ( f t ) = 9 MANNING ROUGHNESS OF THE CULVERT^ .012 TAILWATER D E P T H ( f t ) = 3 LENGTH OF THE C U L V E R T ( f t ) = 3 50 SEDIMENT DEPTH IN THE CULVERT(ft)= 1.5 DESIGN OF A HORIZONTAL ELLIPTICAL CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE INLET CONTROL GOVERNS ACTUAL INLET HEAD WATER(ft)= 8.97398 EQUIVALENT DIAMETER OF CULVE R T ( f t ) = 6.578029 CRITICAL DEPTH IN THE CULVERT(ft)= 5.205782 CRITICAL SLOPE OF THE CULVERT= 1.098043E-02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 12.98871 FULL FLOW CAPACITY OF THE C U L V E R T ( f t ~ 3 / s ) = 445.795 FULL FLOW VELOCITY IN THE C U L V E R T ( f t / s ) = 13.36478 OUTLET VELOCITY V(£t/s)= 14.28222 SPAN OF THE ELL I P T I C A L C U L V E R T ( f t ) = 9 HEIGHT OF THE EL L I P T I C A L C U L V E R T ( f t ) = 5.900001 TYPE 6 FLOW: FULL FLOW,FREE OUTFALL,OUTLET UNSUBMERGED. SOIL TYPE SELECTED AT THE CULVERT OUTLET: 2-UNIFORM SAND ESTIMATED MAXIMUM DEPTH OF SCOUR(ft)= 16.99549 ESTIMATED MAXIMUM WIDTH OF SCOUR(ft)= 71.67055 ESTIMATED MAXIMUM LENGTH OF SCOUR(ft)= 175.4401 ESTIMATED MAXIMUM VOLUME OF SCOUR(ft~3)= 51198.73 HYDRAULIC DESIGN OF CULVERTS DESIGN DATA: DISCHARGE( c f s ) = 350 SLOPE= .02 THE ACCELERATION DUE TO GRAVITY g ( f t / s ~ 2 ) = 32.2 ALLOWABLE WATER HEAD( £ t ) = 15 MANNING ROUGHNESS OF THE CULVERT= .012 DESIGN OF A CIRCULAR CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE ACTUAL INLET HEAD WATER(It)= 12.82618 EQUIVALENT DIAMETER OF C U L V E R T ( f t ) = 5.100003 CRITICAL DEPTH IN THE C U L V E R T ( f t ) - 4.853127 CRITICAL SLOPE OF THE CULVERT= 2 . 6 4 3534E--02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 17.52197 KATIO OF BARREL AREA TO INLET AREA- .6 REQUIRED DROP(ft)= 16.39385 „ BARREL SLOP.E= 7.671 553E-02 BARREL DIAMETER^ 3.950445 ^ INLET DIAMETER= 5.100003 M  RATIO OF BARREL AREA TO INLET AREA= .5 REQUIRED DROP(ft)= 26.1185 + BARREL SLOPE= .124748 BARREL DIAMETER^ 3.606246 INLET DIAMETER= 5.100003 « K.Q: Trie. K'on c o s h P A slops' toLj^€.reJ /'n L e t s .s>he>olol fce. com^fexl t the Sa-v.Vi^s a-C-A.'evex/ Pfovn a. rl^JoceA ba.rre-1 c r o s s - s e c h ' 70 HYDRAULIC DESIGN OF CULVERTS DESIGN DATA: DISCHARGE(c f s ) = 3 5 0 SLOPE= . 0 2 THE ACCELERATION DUE TO GRAVITY g ( f t / s " 2 ) = 3 2 . 2 ALLOWABLE WATER H E A D ( f t ) = 15 MANNING ROUGHNESS OF THE CULVERT= . 0 1 2 DESIGN OF A BOX CULVERT ENTRANCE SHAPE SELECTED: 2-PROJECTING ENTRANCE GROOVE EDGE ACTUAL INLET HEAD WATER(ft)= 1 3 . 8 3 4 9 5 EQUIVALENT DIAMETER OF C U L V E R T ( f t ) = 4 . 9 5 8 8 0 4 CRITICAL DEPTH IN THE C U L V E R T ( f t ) = 5 . 8 1 3 7 7 3 CRITICAL SLOPE OF THE CUI.VERT= 1.445277E-02 CRITICAL VELOCITY IN THE C U L V E R T ( f t / s ) = 1 3 . 6 8 22 3 R*TIO OF BARREL AREA TO INLET AREA= .6 REQUIRED DROP(ft)= 12.25082 BARREL SLOPE^ 6.437381E-02 BARREL WIDTH(ft)= 3.408228 INLET WIDTH(ft)= 4.400003 RATIO OF BARREL AREA TO INLET AREA-- .5 REQUIRED DROP(ft)= 19.64135 BARREL SLOPE= .1046789 BARREL WIDTH(ft)= 3.111272 INLET WIDTH(ft)= 4.400003 

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