HYDRAULIC STRUCTURES
CHAPTER 7 -- ROBERSON ET AL., WITH ADDITIONS

FUNCTIONS OF HYDRAULIC STRUCTURES
CHANNELS CONVEY WATER WITH FREE SURFACE.

Junction of fresh water with irrigation-return water, La Cano, Peru.

Bypass between irrigation and drainage canals, near Georgetown, Guyana.

PIPES CONVEY WATER UNDER PRESSURE.

Orange County Sanitation District's ocean outfall pipe, Huntington Beach, California.

CULVERTS PASS WATER UNDER HIGHWAY OR RAILWAY WITH FREE SURFACE OR UNDER PRESSURE.

Culvert under railroad embankment, Cañada Joe Bill, Tecate, Baja California.

SPILLWAYS TRANSPORT WATER AROUND, THROUGH, OR OVER DAMS, USUALLY AT HIGH SPEED.

Spillway under operation at Itaipu Dam, Brazil.

LEGACY TALE: THE PARANA RIVER.
SPECIAL ATTENTION SHOULD BE GIVEN TO ACCELERATION, DECELERATION, AND TURNING OF THE FLOW.
INTAKE AND OUTLET STRUCTURES SHOULD BE DESIGNED TO CAREFULLY CHANGE FLOW VELOCITY.

Outlet from diversion tunnel, Cuajone Dam, Peru.

Five Gates sluice, outlet from East Demerara Conservancy, Guyana.

Waramia sluice, outlet from Boeraserie Conservancy, Guyana.

OTHER CATEGORIES:
-- CONTROL AND MEASUREMENT OF FLOW: GATES, SURGE TANKS
-- SEWAGE SYSTEMS
-- FISH PASSES (FISH LADDERS)
-- ENERGY DISSIPATION

Surge tanks at ocean outfall, Orange County Sanitation District,
Huntington Beach, California.

Fish ladder at Bonneville Dam, Washington.

Crossing of Tinajones feeder canal with Chiriquipe Wash, Peru.

Creek bypass on Wellton-Mohawk Canal, near Yuma, Arizona.

Drop structure at Tinajones Feeder Canal.

HIGH-VELOCITY FLOW CAN PRODUCE UNWANTED PHENOMENA SUCH AS VIBRATION AND CAVITATION.
HIGH-VELOCITY FLOW IN SPILLWAYS AND CHUTES MUST BE DISSIPATED.

World largest spillway (110,000 m³/s) at Tucurui Dam, Brazil.

CULVERTS
A CULVERT IS A CONDUIT PLACED UNDER A FILL, SUCH AS A HIGHWAY EMBANKMENT, TO CONVEY STREAMFLOW.

Culvert at intersection of Campo Creek with Highway 94, San Diego County.

Culvert at road crossing near La Paz, Baja California Sur.

CULVERTS ARE DESIGNED TO PASS THE DESIGN DISCHARGE WITHOUT OVERTOPPING.
THE DESIGN STORM MAY BE A 50-YR STORM.
THE FLOW IN A CULVERT IS A FUNCTION OF:
-- CROSS-SECTIONAL SIZE AND SHAPE
-- SLOPE
-- LENGTH
-- ROUGHNESS
-- ENTRANCE AND EXIT DESIGN.
FLOW IN A CULVERT MAY BE FREE SURFACE (OPEN CHANNEL), CLOSED CONDUIT (PIPE FLOW), OR BOTH.
HEADWATER AND TAILWATER ARE MAJOR FACTORS THAT DICTATE WHETHER THE CULVERT FLOWS PARTIALLY OR COMPLETELY FULL.
HEADWATER (HW) IS THE DEPTH OF WATER ABOVE THE INVERT OF THE CULVERT AT THE INLET.
TAILWATER (TW) IS THE DEPTH OF WATER ABOVE THE INVERT OF THE CULVERT AT THE OUTLET.
DESIGN OBJECTIVE: MOST ECONOMICAL DESIGN THAT WILL PASS THE DESIGN DISCHARGE WITHOUT EXCEEDING A SPECIFIED HEADWATER ELEVATION.
DESIGN DEPENDS ON WHETHER THE CULVERT IS UNDER INLET OR OUTLET CONTROL.
INLET CONTROL
ASSUME DIAMETER D, LENGTH L, AND SLOPE S OF CULVERT (SLOPE OF ORIGINAL STREAM) ARE KNOWN.
COMPUTE NORMAL DEPTH y_n AND CRITICAL FLOW DEPTH y_c.
FIND THE TAILWATER DEPTH TW FROM STREAMFLOW RECORDS.
IF TW < D, AND D > y_c > y_n, THE FLOW IS OPEN CHANNEL, SUPERCRITICAL, WITH OUTLET OPEN TO THE ATMOSPHERE.
BECAUSE THE FLOW IS SUPERCRITICAL, THE TAILWATER HAS NO INFLUENCE ON THE UPSTREAM CONDITIONS.
THE HEADWATER IS SOLELY CONTROLLED BY THE CONDITIONS AT THE INLET.
DISCHARGE DEPENDS ONLY ON CONDITIONS AT THE INLET.

OCCURRENCE OF INLET CONTROL
INLET CONTROL OCCURS WHEN THE MAIN PART OF THE CULVERT IS CAPABLE OF CONVEYING MORE DISCHARGE THAT THE INLET WILL ALLOW.
THE FLOW PASSES THROUGH CRITICAL DEPTH AT THE INLET AND BECOMES SUPERCRITICAL DOWNSTREAM OF THE INLET.
THE INLET CONFIGURATION AND DISCHARGE RATE ARE THE MAIN FACTORS THAT CONTROL THE WATER SURFACE ELEVATION U/S OF THE INLET.
IF INLET IS OPEN TO THE ATMOSPHERE, CONDITIONS ARE LIKE WEIR FLOW.
IF INLET IS SUBMERGED (A COMMON DESIGN SITUATION), CONDITIONS ARE LIKE ORIFICE FLOW.
IF THE HEADWATER IS LESS THAN 1.2D, THE INLET WILL BE UNSUBMERGED.
IF INLET IS OPEN TO THE ATMOSPHERE, BUT THE OUTLET IS SUBMERGED, A HYDRAULIC JUMP WILL FORM INSIDE THE CULVERT.

OUTLET CONTROL
IF TW > 1.2D, THE CULVERT WILL BE COMPLETELY FULL OF WATER.
THE HEADWATER CAN BE COMPUTED BY APPLYING THE ENERGY EQUATION FROM THE U/S POOL TO THE D/S POOL.
THE HEADWATER IS DIRECTLY CONTROLLED BY THE WATER SURFACE ELEVATION AT THE OUTLET.
DISCHARGE DEPENDS ON THE ENTIRE CULVERT AND CONDITIONS AT THE OUTLET.
OCCURRENCE OF OUTLET CONTROL
OUTLET CONTROL OCCURS WHEN INLET AND OUTLET ARE SUBMERGED.
OUTLET CONTROL ALSO OCCURS WHEN THE PIPE HAS A MILD SLOPE AND BOTH TW AND HW ARE LESS THAN D.
IN THIS CASE IT IS BEST TO CALCULATE THE W.S.P.
CULVERT DESIGN
STEPS:
1. ASSEMBLE INITIAL DESIGN DATA
-- DESIGN DISCHARGE
-- TAILWATER ELEVATION
-- SLOPE OF CULVERT
2. MAKE INITIAL CHOICE OF CULVERT
-- LENGTH
-- CROSS-SECTIONAL SHAPE (CIRCULAR, SQUARE, RECTANGULAR, ARCH)
-- SIZE (D IF CIRCULAR)
-- KIND OF MATERIAL (CONCRETE, CORRUGATE STEEL)
-- TYPE OF ENTRANCE (SQUARE EDGED OR ROUNDED)
3. TRY TO ASCERTAIN THE TYPE OF CONTROL (INLET OR OUTLET), BASED ON HW, TW, D AND SLOPE.
4 (A). IF INLET CONTROL PREVAILS, CALCULATE THE REQUIRED WATER SURFACE ELEVATION IN THE HEADWATER TO PASS THE DESIGN DISCHARGE.
4 (B). IF OUTLET CONTROL PREVAILS, CALCULATE THE REQUIRED WATER SURFACE ELEVATION IN THE UPSTREAM POOL BY THE ENERGY EQUATION OR W.S.P. COMPUTATIONS.
5. IF WATER SURFACE ELEVATION IN THE HEADWATER IS GREATER THAN ALLOWED, CHOOSE A LARGER SIZE CULVERT AND REPEAT THE PROCESS.
FOR SOME DATA IT MAY BE HARD TO DETERMINE A PRIORI THE TYPE OF CONTROL.
IN THIS CASE MAKE BOTH CALCULATIONS.
THE ONE YIELDING THE GREATEST WATER SURFACE ELEVATION U/S WILL BE THE CONTROLLING ONE.
OTHER DESIGN FACTORS:
-- PIPING IN EMBANKMENT.
-- LOCAL SCOUR AT OUTLET.
-- EROSION OF FILL MATERIAL NEAR INLET (METAL CULVERTS ARE PARTICULARLY SUSCEPTIBLE).
-- FISH PASSAGE.
-- CLOGGING BY DEBRIS.

Fish-passage channel at restored Ferris Creek, Plumas County, California.

EXAMPLE
A CONCRETE CULVERT IS TO BE DESIGNED FOR THE 25-YR FLOOD.
THE DESIGN DISCHARGE IS: Q = 200 CFS.
THE INLET INVERT ELEVATION IS: z₁ = 100 FT.
THE NATURAL STREAM BED SLOPE IS: S₀ = 0.01.
THE TAILWATER DEPTH ABOVE OUTLET INVERT IS: y₂ = 3.5 FT.
THE CULVERT LENGTH IS: L = 200 FT.
ROADWAY SHOULDER ELEVATION IS 110 FT.
SOLUTION
ASSUME A 2 FT FREEBOARD BETWEEN U/S DESIGN W.S. ELEVATION AND ROAD SHOULDER.
THEREFORE, THE DESIGN ELEVATION FOR U/S POOL IS: 110 - 2 = 108 FT.
ASSUME A CIRCULAR CONCRETE PIPE, SQUARE EDGE WITH HEADWALLS.
CULVERT END TREATMENTS
FIRST ASSUME OUTLET CONTROL.
ASSUME THAT THE HGL IS AT THE ELEVATION OF THE D/S POOL.
CALCULATE OUTLET INVERT ELEVATION: z₂ = 100 - (0.01 × 200) = 100 - 2 = 98 FT.
CALCULATE D/S POOL ELEVATION: 98 + 3.5 = 101.5 FT.
SET UP ENERGY EQUATION: z₁ + y₁ + V₁²/(2g) = z₂ + y₂ + V₂²/(2g) + ∑h_L

ASSUME V₁ = 0 [VELOCITY IS ZERO IN THE U/S POOL]
ASSUME V₂ = 0 [VELOCITY DISSIPATES TO ZERO IN THE D/S POOL]
∑h_L = [K_e + K_E + f(L/D)] V²/(2g)
ASSUME K_e = 0.5; K_E = 1. [TABLE 5-3]
ASSUME f = 0.018
ENERGY EQUATION: 108 = 101.5 + [0.5 + 1.0 + 0.018 (200/D)] V²/(2g)
6.5 = [1.5 + 3.6/D] V²/(2g)
V = Q/A = 200/A = 200/[(π/4)D²]
V²/(2g) = { 200²/[(π/4)²D⁴] } / (2g)
6.5 = 200² [1.5 + 3.6/D] / [(π/4)²D⁴ (2g)]
SOLVE BY TRIAL AND ERROR: D = 4.36 FT.
CHOOSE NEXT LARGER SIZE: D = 4.5 FT.
WITH Q = 200, AND D = 4.5 FT = 54 IN, ENTER FIG. 7-5 TO FIND RATIO HEADWATER DEPTH OVER DEPTH HW/D = 2.1

HW DEPTH = 2.1 × 4.5 = 9.45 FT.
U/S POOL ELEVATION = 100 + 9.5 = 109.5 LARGER THAN 108. TOO LARGE.
THE CHOSEN D = 4.5 FT IS TOO SMALL.
TRY D = 5 FT.
WITH Q = 200, AND D = 5.0 FT = 60 IN, ENTER FIG. 7-5 TO FIND RATIO HEADWATER DEPTH OVER DEPTH HW/D = 1.5
HW DEPTH = 1.5 × 5 = 7.5 FT.
U/S POOL ELEVATION = 100 + 7.5 = 107.5 SMALLER THAN 108. OK.
CHECK CRITICAL DEPTH.
COMPUTE THE SECTION FACTOR: Q/(g^1/2d_o^5/2) = 200 / [32.2)^1/2(5)^5/2] = 0.63
ENTER FIG. 4-15, WITH SECTION FACTOR 0.63: y_c/d_o = 0.8

THUS: y_c = 4 FT.
CHECK NORMAL DEPTH.
ASSUME n = 0.012.
COMPUTE THE SECTION FACTOR: Qn/(1.49 × S_o^1/2 × d_o^8/3 ) = 200 × 0.012 / (1.49 × 0.1 × 73.1) = 0.22
ENTER FIG. 4-7, WITH SECTION FACTOR 0.22: y_n/d_o = 0.6

THUS: y_n = 3 FT.
BECAUSE y_n < y_c, THE FLOW IS SUPERCRITICAL.
BECAUSE TW < y_c, THERE WILL BE NO HYDRAULIC JUMP NEAR THE OUTLET.
BECAUSE THE FLOW IS SUPERCRITICAL IN THE PIPE AND THE OUTLET IS OPEN TO THE ATMOSPHERE (TW DEPTH < D) WE CAN CONCLUDE THAT THERE IS INLET CONTROL.
DESIGN DIAMETER: D = 5 FT = 60 IN.

DAM APPURTENANCES
-- SPILLWAYS
-- ENERGY DISSIPATORS
-- DIVERSION WORKS
-- OUTLET WORKS
-- INTAKE STRUCTURES
SPILLWAYS
SPILLWAYS ARE NEARLY ALWAYS REQUIRED TO PASS FLOW BY A DAM.
FOR DIVERSION DAMS, THE SPILLWAY MAY OPERATE CONTINUOUSLY.

Diversion intake at Cuajone Dam, Peru.

Diversion spillway at Cabana intake, Peru.

SAFE OPERATION OF SPILLWAY IS THE MAIN OBJECTIVE IN DESIGN.
FAILURE OF THE SPILLWAY MAY LEAD TO DAMAGE AND FAILURE OF THE DAM WITH POSSIBLE LOSS OF LIVES AND PROPERTY.
EARTH AND ROCKFILL DAMS CANNOT WITHSTAND OVERTOPPING.
SPILLWAYS MUST DE DESIGNED FOR HIGH VELOCITY FLOW.
DISSIPATOR MUST RELEASE FLOW AT SMALL ENOUGH VELOCITY TO REDUCE POSSIBILITY OF SCOURING DOWNSTREAM.
DAMS CAN ATTENUATE THE FLOOD WAVE.
SMALL DAMS HAVE LITTLE ATTENUATING CAPACITY.
SPILLWAY SHOULD SPILL INCOMING FLOW.
LARGER DAMS HAVE HIGH ATTENUATING CAPACITY.
SPILLWAY MAY BE DESIGNED FOR ATTENUATED FLOW.
SERVICE SPILLWAY PASSES FREQUENTLY OCCURRING SMALLER FLOWS.
AUXILIARY SPILLWAY CAN PASS THE LARGE FLOWS.
ENERGY DISSIPATION IS OFTEN NEEDED DOWNSTREAM.
OVERFLOW SPILLWAYS CAN BE CLASSIFIED INTO TWO CATEGORIES:
-- STRAIGHT DROP DESIGN, SUCH AS DOWNSTREAM OF AN ARCH DAM
-- SCHEME THAT PROVIDES A CONTINUOUS CHANNEL SHAPED IN S-SHAPE, OGEE SPILLWAY.
SHAPE OF OGEE SPILLWAY CONFORMS TO THE UNDERSIDE OF WATER FLOWING OVER A WEIR.

Closeup of ogee-section emergency spillway,
El Capitan Dam, Dan Diego County.

Closeup of ogee-section emergency spillway,
Oroville Dam, California.

Ogee-section emergency spillway,
Turner Dam, San Diego County.

PRESSURE ON CREST IS CLOSE TO ATMOSPHERIC FOR THE SELECTED FLOW RATE.
THE HEAD ABOVE THE SPILLWAY CREST IS THE DESIGN HEAD H_D.
FLOW RATES LESS THAN DESIGN HEAD WILL PRODUCE PRESSURES GREATER THAN ATMOSPHERIC.
FLOW RATES GREATER THAN DESIGN HEAD WILL PRODUCE PRESSURES LESS THAN ATMOSPHERIC.
NEGATIVE PRESSURES SHOULD BE AVOIDED BECAUSE IT COULD LEAD TO CAVITATION.
ANALYTICAL METHODS ARE AVAILABLE TO COMPUTE THE NAPPE COORDINATES.
THE [BROAD-CRESTED] WEIR EQUATION IS:
Q = C (2g) ^1/2 L H ^3/2
C = DISCHARGE COEFFICIENT, DIMENSIONLESS
H = TOTAL HEAD, INCLUDING APPROACH VELOC ITY.
THE THEORETICAL VALUE OF C = 0.385.
FOR OGEE-TYPE SPILLWAYS:
Q = C_D (2g) ^1/2 L H_D^3/2
FIGURE 7-10 (a) GIVES THE VARIATION OF C_D, THE VALUE OF C WHEN H EQUALS THE DESIGN HEAD H_D.
NOTE THAT ACTUAL C_D RANGES FROM 0.40-0.49, GREATER THAN THE THEORETICAL VALUE C = 0.385.
THIS MEANS THAT THE OGEE SPILLWAY IS VERY EFFECTIVE IN PASSING THE FLOW.
FIGURE 7-10 (b) GIVE VARIATION OF C/C_D AS A FUNCTION OF H/H_D

THIS MEANS THAT THE DISCHARGE COEFFICIENT VARIES DIRECTLY WITH THE HEAD.
A SPILLWAY CREST BECOMES MORE EFFICIENT AT HEADS THAT EXCEED THE DESIGN HEAD, BUT THIS COMES AT THE EXPENSE OF SUBATMOSPHERIC PRESSURES ON THE SPILLWAY, WHICH LEADS TO CAVITATION.
EXAMPLE: SPILLWAY RATING CURVE
DETERMINE THE RATING CURVE FOR AN OGEE-TYPE SPILLWAY WITH LENGTH L = 100 FT. THE DESIGN HEAD IS 30 FT, AND THERE ARE NO PIERS. THE CREST IS AT ELEVATION 1,200 FT, AND THE RIVERBED IS AT ELEVATION 1,110 FT. NEGLECT THE APPROACH VELOCITY.
SOLUTION
H_D = 30
P = 1200 - 1110 = 90
P/H_D = 3
FROM FIG. 7-10 (a): C_D = 0.492
Q = C (2g)^1/2 L H^3/2 = 802 C H^3/2 IN THE FOLLOWING RATING TABLE, CALCULATE C/C_D FROM FIG. 7-10 (b), BASED ON H/H_D.

Elevation (ft) H (ft) H/H_D C/C_D C Q (cfs)
1200 0 0.000 0.00 0.00 0
1205 5 0.167 0.83 0.41 3660
1210 10 0.333 0.88 0.43 10900
1215 15 0.500 0.92 0.45 21000
1220 20 0.667 0.95 0.47 33400
1225 25 0.833 0.97 0.48 47900
1230 30 1.000 1.00 0.49 64900
1235 35 1.166 1.02 0.50 83400
1240 40 1.333 1.04 0.51 104000
1245 45 1.500 1.06 0.52 126000

ONLINE OGEE RATING H_D = 30 FT; P = 90 FT, L = 1200 FT, FB = 15 FT; SPILLWAY CREST ELEVATION = 1200 FT.

RADIAL GATES
OVERFLOW SPILLWAYS FREQUENTLY USE TAINTER OR RADIAL GATES.

Tainter gate at La Puntilla, Chancay river, Peru.

THE PRESENCE OF THE GATE PRODUCES ORIFICE-TYPE FLOW.
DRUM GATES ARE USED IN CERTAIN CASES.

Cresta Dam, Feather river, California.

Operation of a drum gate such as that used in Cresta Dam.

FAILURE OF THE DRUM GATE AT CRESTA DAM, JULY 5, 1997

A drum gate failed at Cresta Dam, which is located on the North Fork of the Feather River, approximately 30 miles east of Oroville, California.
The failure occurred at 12:30 on Saturday, July 5, 1997, during the busy July 4th weekend.
The mean daily flows in the days prior to the failure were approximately 70 ft³/s.
The maximum discharge during the gate failure was about 15,000 ft³/s.
Pacific Gas and Electric, the owner of the dam, estimated that over a 40-minute period, the river stage increased 13.5 feet at a location approximately 1 mile downstream from Cresta Dam.
The peak discharge released from the dam, although greater than the reservoir inflow at the time, was far less than the highest flows that have occurred on this river.
On January 1, 1997, a record discharge of 115,000 ft³/s was recorded at a gauge located 2.1 miles downstream from Cresta Dam.
Flows greater than 15,000 ft³/s occurred in 7 of the 13 years between 1986 and 1998.
The gate failure did not impact any structures or highways (Water Commission Report, 1997). The flooding did impact recreationists downstream from the dam. Rafters were capsized, and fishermen, campers, and picnickers were scattered by the surge. In two cases, people left stranded had to be rescued by helicopter. A local newspaper reported: "Many anglers and swimmers were alerted to the danger by a woman who drove down the canyon honking her horn and yelling "Get out! Get out! ..." at everyone she saw.
The chain of events that led to the failure of the drum gate at Cresta Dam follows (Water Commission Report, August 1997):

Siltation in the reservoir blocked the 54-inch diameter water supply pipe to the flotation chamber.

Limited flow capacity of the 24-inch backup supply pipe restricted flow into the flotation chamber.

A severed atmospheric drain hose fitting from the drum gate permitted the drum gate to partially fill with water.

A steel plate placed over the downstream end of the atmospheric drain prevented drainage from the drum.

A failed check valve permitted water to flow into the drum gate through the severed hose fitting.

Severely worn gate seals permitted excess leakage from the flotation chamber.

The weight of the partially flooded drum gate overcame the buoyant lift supplied by the flotation chamber.

Gate seal leakage exceeded the water supply from the 24-inch diameter backup pipe.

OTHER GATES ARE RUBBER GATES: ARROYO PASAJERO, CALIFORNIA.

Rubber gate at emergency spillway at sediment detention basin, Arroyo Pasajero, near Coalinga, California.
THE GOVERNING EQUATION FOR RADIAL (TAINTER GATE) GATED FLOW IS (SEE FIG. 7-11):
Q = (2/3) (2g)^1/2 C L (H₁^3/2 - H₂^3/2)
C IS GIVEN IN FIGURE 7-11.

PIERS REDUCE THE EFFECTIVE FLOW-PASSING LENGTH BY THE WIDTH OF THE PIERS BUT ALSO CAUSE LOCAL CONTRACTIONS THAT FURTHER REDUCE THE EFFECTIVE LENGTH, PARTICULARLY IF THE NOSE OF THE PIER IS NOT ROUNDED.
REDUCTION AMOUNTS TO UP TO 4% WHEN HEAD ON THE CREST IS EQUAL TO THE OPENING BETWEEN PIERS.

Barrett dam and spillway, San Diego County.

SHAFT SPILLWAYS
SHAFT SPILLWAYS ARE SPILLWAYS UNDER PRESSURE.
THEY ARE NOT GENERALLY RECOMMENDED DUE TO THE POSSIBILITY OF CAVITATION.
FURTHERMORE, SHAFT SPILLWAYS CAN CLOG READILY WITH DEBRIS, AND THIS CAN LEAD TO FAILURE OF THE DAM.
The possibility of clogging is real and, for most part, unpredictable.
One way to minimize the possibility of clogging is to build the shaft of a diameter large enough to pass all large trees or logs.
In this respect, the guidelines of the French National Committee of ICOLD (International Committee on Large Dams) specify that all Morning Glory (shaft) spillways should have a minimum throat diameter of 6 m.

CLOSE VIEW OF MORNING GLORY SPILLWAY, ON THE BARRAGEM NORTE COFFERDAM SITE, ITAJAI, RIVER. IN SANTA CATARINA, BRAZIL.
THE SPILLWAY GOT PLUGGED WITH VEGETATIVE DEBRIS (VISIBLE ON THE LEFT SIDE) DURING A FLOOD EVENT IN DECEMBER 1982, AND LED TO THE BREACH OF THE COFFERDAM.

TERMINAL STRUCTURES
FLOW IN A SPILLWAY MUST BE EITHER DEFLECTED OR DECELERATED BEFORE BEING RELEASED TO THE DOWNSTREAM CHANNEL.
OTHERWISE, EROSION OF THE STREAMBEDS AND SIDEBANKS COULD RESULT IN DANGER TO THE DAM ITSELF.
THE HYDRAULIC JUMP IS A DECELERATING STRUCTURE.
HYDRAULIC JUMP DISSIPATES ENERGY.
FROUDE NUMBER: F² = v₁²/(gy₁)
SEQUENT-DEPTH RELATION FOR THE HYDRAULIC JUMP:
y₂/y₁= (1/2) [(1 + 8F²)^1/2 - 1]
THE HEAD LOSS THROUGH THE JUMP FOR A RECTANGULAR CHANNEL IS:
ΔE = ( y₂ - y₁)³ / (4y₁y₂)

HYDRAULIC STRUCTURES ARE DESIGNED SO THAT HYDRAULIC JUMPS OCCUR UNDER CONTROLLED CONDITIONS IN A STRUCTURE CALLED A STILLING BASIN.
WHERE AND HOW THE ENERGY IS DISSIPATED IS OF OUTMOST IMPORTANCE IN CONTROLLING EROSION.

A CLOSE MATCH OF SEQUENT DEPTH WITH D/S DEPTH IS NEEDED.
IF THE D/S DEPTH MATCHES THE SEQUENT DEPTH, THE HYDRAULIC JUMP WILL OCCUR ON THE APRON.
IF D/S DEPTH IS LESS THAN SEQUENT, THE HYDRAULIC JUMP WILL OCCUR D/S FROM THE APRON: A SWEPT- OUT JUMP.
IF D/S DEPTH IS GREATER THAN SEQUENT DEPTH, THE HYDRAULIC JUMP WILL BECOME SUBMERGED.
SUBMERGED JUMP IS PREFERABLE THAN SWEPT-OUT, BUT CAN ALSO CAUSE DOWNSTREAM SCOUR.
A CAREFULLY DESIGNED STILLING BASIN WILL NOT ONLY IMPROVE THE DISSIPATION CHARACTERISTICS OF THE HYDRAULIC JUMP, BUT WILL ALSO SHORTEN ITS LENGTH AND STABILIZE THE POSITION OF THE JUMP, SO THAT IT IS NOT SENSITIVE TO FLUCTUATIONS IN TAILWATER (D/S) LEVEL.
CHUTE BLOCKS, BAFFLE BLOCKS, SLOTTED BUCKETS, AND END SILLS ARE APPURTENANCES DESIGNED TO CONTROL THE JUMP.

Chute block spillway dissipator, Oroville Dam, California.

Slotted bucket dissipator downstream of spillway, Gallito Ciego Dam, Peru.

CAVITATION ON THE BAFFLE BLOCKS CAN BE A CONCERN WHEN VELOCITIES ARE HIGH.
THE SILL AT THE END OF THE BASIN LIFTS THE FLOW AWAY FROM THE D/S BED AND PRODUCES A RETURN CURRENT THAT DEPOSITS MATERIAL IMMEDIATELY D/S OF THE STILLING BASIN.
DEFLECTOR BUCKETS CAN CAUSE EROSION IN THE DOWNSTREAM POOL.

Deflector bucket dissipator at Tucurui Dam, Brazil.

THE VERONESE FORMULA (FIG. 7-20) CALCULATES THE DEPTH OF SCOUR D AS A FUNCTION OF TOTAL HEAD AND DISCHARGE PER UNIT OF WIDTH q.
D = 1.9 H^0.225q^0.54
THIS FORMULA IS IN SI UNITS.
NOTE THE IMPORTANCE OF q.

GATES AND VALVES
TWO MAJOR CLASSES OF GATES ARE:
1. SPILLWAY OR OPEN-CHANNEL GATES
• VERTICAL
• RADIAL
• DRUM
2. PIPE OR CLOSED-CONDUIT GATES.
VERTICAL GATES ARE RECTANGULAR, MADE OF STEEL, BETWEEN TWO VERTICAL PIERS.

Gate, road bridge, and creek bypass, Cabana canal, Puno, Peru.

VERTICAL GATES SLIDE IN GUIDES FABRICATED INTO THE PIERS AND ARE RAISED BY HOISTS.
RADIAL GATES CONSIST OF A CYLINDRICAL SKIN SEGMENT CONNECTED BY RADIAL ARMS TO A TRUNNION PIN.
ALL HYDROSTATIC PRESSURE LOADS PASS THROUGH THE PIN.
DRUM GATES ARE DESIGNED TO FILL WITH WATER, FREQUENTLY FOR AUTOMATIC OPERATION.
NEEDLES REST IN A SLOT ALONG THE SPILLWAY CREST, AND THE UPPER END IS SUPPORTED BY A HORIZONTAL BEAM.
FLASHBOARDS ARE RELATIVELY LOW STRUCTURES CONSISTING OF HORIZONTAL BOARDS, USUALLY WOOD, SUPPORTED BY RODS INSERTED INTO THE SPILLWAY CREST.
STOPLOGS ARE HORIZONTAL AND SUPPORTED BY SLOTTED PIERS.
STOPLOGS CAN BE REMOVED BY HAND.

OUTLET WORKS
NORMALLY PROVIDED AT MOST DAMS SO THAT WATER CAN BE RELEASED.
OUTLET WORKS IN CONCRETE DAMS PRIMARILY CONSIST OF A CONDUIT THROUGH THE DAM.

ENTRANCE TO BE PROTECTED BY A TRASHRACK, AND EMERGENCY GATE, A VALVE OR GATE TO CONTROL THE FLOW RATE, AND A TERMINAL STRUCTURE, FREQUENTLY DESIGNED AS AN ENERGY DISSIPATOR.
ELEVATION OF INTAKE SHOULD PROVIDE DESIGN DISCHARGE AT MINIMUM RESERVOIR LEVEL.
SPECIAL INTAKE WITH OPENING AT VARIOUS ELEVATIONS MAY BE REQUIRED TO MEET WATER QUALITY.
OUTLETS FOR EVACUATING THE RESERVOIR, SOMETIMES CALLED SLUICES.
SEPARATE OUTLETS MAY BE REQUIRED AT DIFFERENT LEVELS IF THE RESERVOIR IS TEMPERATURE-STRATIFIED.
INTAKES MAY BE A SUBMERGED OPENING ON THE UPSTREAM FACE, OR AN ELABORATE STANDING TOWER.
OUTLETS ARE USUALLY DESIGNED FOR HIGH VELOCITIES.
HIGH VELOCITY REQUIRES CONSIDERATION OF THE DESIGN OF THE INTAKE FLOW PASSAGES.
NONSTREAMLINED ENTRANCES CAUSE FLOW SEPARATION, AND STRUCTURAL VIBRATION, CAVITATION, NOISE, AND ENERGY LOSS.
SLIDE OR FIXED-WHEEL GATES ARE OFTEN USED FOR CONTROLLING FLOW AT INTAKES AND INTERIOR LOCATIONS.
D/S END REGULATION WITH NEEDLE OR HOLLOW JET VALVE.

CAVITATION IN HYDRAULIC STRUCTURES
WHEN A LIQUID HAS ITS TEMPERATURE INCREASED UNDER CONSTANT PRESSURE, OR ITS PRESSURE REDUCED UNDER CONSTANT TEMPERATURE, A STATE IS EVENTUALLY REACHED WHERE BUBBLES, OR CAVITIES, BEGIN TO APPEAR AND GROW IN THE LIQUID.
THE GROWTH RATE IS MODERATE IF DISSOLVED GASES ARE DIFFUSING INTO THE BUBBLE, BUT CAN BE EXPLOSIVE IF THE GROWTH IS PRIMARILY A RESULT OF VAPORIZATION OF THE LIQUID INTO THE CAVITY.
THE EXPLOSIVE GROWTH RATE IS CALLED BOILING WHEN RESULTING FROM AN INCREASE IN TEMPERATURE, AND CAVITATION WHEN RESULTING FROM A HYDRODYNAMIC DECREASE IN PRESSURE.
CAVITATION IS A SPEED-RELATED PHENOMENA IN WHICH LOCALLY INCREASED VELOCITIES ARE ASSOCIATED WITH PRESSURE REDUCTIONS.
ITS OCCURRENCE IN A FLOW FIELD USUALLY CAUSES REDUCED PERFORMANCE OR POTENTIAL DAMAGE TO THE FLOW SURFACES.
EARLY OBSERVATIONS OF CAVITATION WERE NOTED IN THE PROPELLERS OF STEAM-DRIVEN VESSELS (WAR SHIPS), WHERE ACHIEVING HIGH SPEEDS WAS A DESIGN OBJECTIVE.
HIGH VELOCITIES WILL PRODUCE CAVITATION WHEN THE AMBIENT PRESSURE IS TOO LOW.
HYDRAULIC STRUCTURES HAVE ALSO FAILED DUE TO CAVITATION.
THESE FAILURES GENERALLY RESULT FROM SOME COMBINATION OF HIGH VELOCITY FLOW AND BOUNDARY DISCONTINUITIES EITHER INTO OR AWAY FROM THE FLOW THAT PRODUCES LOCALLY LOW PRESSURES.
SPILLWAYS, STILLING BASINS, AND GATE SLOTS REQUIRE THAT SEPARATED FLOWS, CONDUIT MISALIGNMENT, AND BOUNDARY ROUGHNESS BE CAREFULLY CONSIDERED.

CAUSES OF CAVITATION
FOR CAVITATION TO OCCUR, THERE MUST BE A SOURCE OF LOW PRESSURE, AND THERE MUST BE NUCLEI (GAS BUBBLES OR OTHER FOREIGN MATERIAL THAT CARRIES GAS) IN THE FLOW.
TO COMPLETE THE CAVITATION PROCESS, THE CAVITY, FORMED UNDER LOW PRESSURE, WILL EVENTUALLY BE EXPOSED TO HIGH PRESSURE AGAIN AT SOME DOWNSTREAM LOCATION, WHEREUPON IT COLLAPSES.
THE COLLAPSE MECHANISM IS LARGELY RESPONSIBLE FOR THE EROSION OF MATERIAL, EXCESSIVE NOISE, DAMAGING VIBRATION, AND OTHER ADVERSE EFFECTS.

CONTROL OF CAVITATION
ONE OBVIOUS WAY TO PREVENT CAVITATION IS TO ELIMINATE THE SOURCE OF LOW PRESSURE.
A LOWER SETTING OF THE TURBINE IN A HYDROPOWER PLANT WILL INCREASE THE PRESSURE AND INHIBIT CAVITATION.
DESIGNS THAT ELIMINATE EDDIES ARE EQUALLY IMPORTANT IN REDUCING SOURCES OF LOW PRESSURE.
LIMITING THE VELOCITY TO A LOW VALUE WILL ALSO REDUCE THE LEVEL OF CAVITATION.
FREQUENTLY, IT IS NEITHER POSSIBLE NOR DESIRABLE TO DESIGN HYDRAULIC STRUCTURES THAT WILL BE FREE FROM CAVITATION.
IN THESE CASES, WHERE EROSION OF MATERIAL IS THE PRIMARY CONCERN, THE EFFECTS OF CAVITATION CAN BE MITIGATED IN SEVERAL DIFFERENT WAYS:
-- THE BOUNDARIES MAY BE DESIGNED SO THAT THE CAVITIES COLLAPSE WELL OUT IN THE FLOW FIELD WHERE HIGH PRESSURES DUE TO COLLAPSE CANNOT ACT ON THE BOUNDARY.
-- CAVITATION-RESISTANT MATERIALS, SUCH AS STAINLESS STEEL, OR FIBER-REINFORCED CONCRETE, CAN BE USED TO GREATLY RETARD THE DAMAGE RATE, EVEN THOUGH THE SYSTEM IS STILL IN A CAVITATING REGIME.
-- INTRODUCING AIR INTO THE FLOW CHANGES THE TYPE OF CAVITATION FROM VAPOROUS TO GASEOUS, WHICH ELIMINATES THE EXPLOSIVE GROWTH AND COMPLETE COLLAPSE OF THE CAVITIES; THUS REDUCES DAMAGES.

CAVITATION INDEX
TO PREDICT CAVITATION, THE HYDRAULIC ENGINEER USES A DIMENSIONLESS PARAMETER THAT CORRELATES THE FORCES PREVENTING CAVITATION (AMBIENT PRESSURE p_o) WITH THOSE CAUSING CAVITATION (DYNAMIC PRESSURE, OR VAPOR PRESSURE OF THE FLUID p_v).
A CAVITATION INDEX IS DEFINED AS FOLLOWS:
σ = (p_o - p_v) / (ρV_o² /2)
-- σ = cavitation index
-- p_o = ambient pressure
-- p_v = vapor pressure
-- ρ = mass density of fluid
-- V_o = (reference) velocity of fluid relative to the body.
SINCE p_o (ABS) > p_V, &sigma IS POSITIVE.
HIGH VALUES OF σ CORRESPOND TO LOW CAVITATION POTENTIAL.
WHEN p_o (ABS) ≅ p_V CAVITATION STARTS TO DEVELOP.
CAVITATION PARAMETER IS A FORM OF PRESSURE COEFFICIENT.
WHEN σ = 0, THE AMBIENT PRESSURE IS REDUCED TO VAPOR PRESSURE AND BOILING SHOULD OCCUR.
NUCLEI MUST BE PRESENT AROUND WHICH VAPOR BUBBLES FORM AND GROW.
HIGH PRESSURES RESULTING FROM COLLAPSE ARE ON THE ORDER OF GIGAPASCALS.
AS σ DECREASES, EITHER FROM A DECREASE IN AMBIENT PRESSURE OR AN INCREASE IN VELOCITY, A VALUE OF σ_i IS EVENTUALLY REACHED WHERE CAVITATION BEGINS.
THE VARIATION OF PRESSURE BETWEEN POINTS 0 (UNDISTURBED FLOW) AND A POINT OF LOW PRESSURE AND HIGH VELOCITY IS:
p/γ - p_o/γ = (V_o² - V²)/2g
WHICH CAN BE WRITTEN AS:
p - p_o= ρ(V_o² - V²)/2 [NEGATIVE IN INLET]
DEFINE A PRESSURE COEFFICIENT C_p SUCH THAT V² = (1 - C_p)V_o²
p - p_o= ρ[V_o² - (1 - C_p)V_o²]/2
p - p_o = ρ C_p V_o²/2
THEN:
C_p = (p - p_o)/ [ρV_o²/2] [NEGATIVE IN INLET]
WHEN THE PRESSURE p IS LOWERED TO THE POINT OF CAVITATION INCEPTION, IT ATTAINS A VALUE CLOSE TO THE VAPOR PRESSURE p_v, AT WHICH POINT THE CAVITATION INDEX IS AT THE POINT OF INCEPTION: σ = σ_i,
C_p = (p_v - p_o)/ [ρV_o²/2]
THUS:
σ_i = (p_o - p_v) / (ρV_o² /2) = - C_p
SEPARATED FLOWS
THE ROLE OF EDDIES (TURBULENCE) IN PRODUCING CAVITATION.
IN FIG. 7-40, A SLOT HAS BEEN INSTALLED IN A STREAMLINED STRUT.
AN EDDY SETS UP IN THE SLOT.
THE PRESSURE IN THE CENTER OF THE EDDY IS REDUCED FROM THE REFERENCE PRESSURE p_o BECAUSE OF BOTH THE GEOMETRY OF THE STRUT AND THE PRESENCE OF THE EDDY.
THE VELOCITY V_s ADJACENT TO THE SLOT CAN BE EXPRESSED IN TERMS OF THE REFERENCE VELOCITY:
V_s = V_o(1 - C_p)^1/2
BY ASSUMING THE VELOCITY DISTRIBUTION IN THE SLOT EDDY IS APPROXIMATED BY THAT OF A FREE VORTEX, THE PRESSURE AT THE CENTER OF THE EDDY, p_min IS GIVEN BY:
p_min = p_s - ρV_s²/ 2

IN THIS CASE, THE CAVITATION INDEX IS:
σ_i (separated flow) = (p_o - p_min) / (ρV_o² /2)
σ_i (separated flow) = (p_o - p_s + ρV_s²/ 2) / (ρV_o² /2)
V_s² = (1 - C_p)V_o²
σ_i (separated flow) = [p_o - p_s + ρ(1 - C_p)V_o²/ 2] / (ρV_o² /2)
σ_i (separated flow) = (p_o - p_s)/(ρV_o² /2) + 1 - C_p
σ_i (separated flow) = - C_p + 1 - C_p
σ_i (separated flow) = 1 - 2 C_p
THIS EQUATION PREDICTS σ_i QUITE WELL FOR HIGH REYNOLDS NUMBERS.
IT IS AN UPPER LIMIT FOR LOW REYNOLDS NUMBERS.

EXAMPLE
ASSUME THE CONDITIONS IN THE SKETCH, WITH V_o = 5 FPS; V_A= 10 FPS, p_o= 20 PSIA
THE CONVERGING BOUNDARY IS IN A HORIZONTAL PLANE.
DETERMINE VALUE OF V_o THAT WILL JUST BEGIN TO CAUSE CAVITATION IN THE SLOT.

SOLUTION:
FOR POINT A, THE PRESSURE COEFFICIENT IS OBTAINED FROM:
V_A = V_o(1 - C_p)^1/2
C_p = 1 - (V_A²/V_o²)
C_p = 1 - (10²/5²) = -3
σ_i_B = 1 - 2 C_p = 1 - 2 (-3) = 7
σ_i_B = (p_o - p_v) / (ρV_o² /2)
ASSUME T= 60^oF: p_v = 0.256 PSIA
7 = (20 × 144 in²/ft² - 0.256 × 144 in²/ft²) / (ρ V_o² /2)
7 = (2880 - 37) / (1.94 V_o² /2)
V_o = 20.5 FPS.

CAVITATION IN SPILLWAYS
FOR MANY YEARS, THE DESIGN OF SPILLWAYS HAS USED CREST PROFILES THAT MINIMIZE LOW PRESSURES.
SPILLWAYS ASSOCIATED WITH HIGH DAMS, HOWEVER, PRODUCE HIGH VELOCITIES THAT COMBINE WITH MODERATE ROUGHNESS OR OTHER IRREGULARITIES, SUCH AS CONSTRUCTION JOINTS ON THE SURFACE, TO PRODUCE CAVITATING CONDITIONS.
SERIOUS DAMAGE OCCURRED AT GLEN CANYON DAM DUE TO CAVITATION, WHEN IT WAS FIRST USED.

Glen Canyon Dam, Colorado River, Arizona.

The Flood at Glen Canyon Dam
In 1984, an unusually heavy snow pack and a prolonged extremely warm early spring produced a huge flood, which threatened to top Glen Canyon Dam. The closed-conduit emergency spillways were opened for the first time and were soon at capacity. Temporary 10-ft extensions were added to the top of the 716-ft high dam. The crisis was averted as the flow into the reservoir decreased. When the spillway tunnels where inspected, the 3-ft thick concrete lining had been breached, and cavities as large as 50 ft deep had formed due to cavitation. The tunnels were repaired and the design changed to prevent future cavitation damage.

AERATION SLOTS HAVE SINCE BEEN USED TO MITIGATE THE EFFECTS OF CAVITATION AT THESE STRUCTURES.
ONE OF THE REQUIREMENTS IN DESIGNING FOR CAVITATION IS TO MAKE AN ESTIMATE OF THE σ VALUE THAT WILL PREVENT EXCESSIVE DAMAGE.
DAMAGE IS NOT JUST A FUNCTION OF σ BUT ALSO OF THE TIME OF OPERATION.
SEE FIG 7-42 FOR USBR EXPERIENCE.
SEE THAT AS σ DECREASES (GOING UP IN GRAPH) AND TIME OF EXPOSURE INCREASES, DAMAGE INCREASES.

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