7Siphon Spillways

7.1 INTRODUCTlON

The discharge over an overflow spillway is a function of the head measured over its crest. Enclosing the crest and making the resulting conduit flow full can substantially increase this effective head. The head on the spillway is then the difference in elevation between the reservoir surface and the spillway outlet. However, the flow near the crest of the spillway would then be under a negative pressure, In other words, the conduit becomes a siphon. AII necessary precautions must be taken to ensure that the vacuum is maintained and that it does not become so excessive as to cause cavitation. The maximum negative pressure at the spill-way crest IS theoretically 10m of water at sea level, Allowing for the vapor pressure of water, loss due to turbulence. Etc., the maximum net effective head is rarely more than about 7.5 m. This corresponds to a velocity of \12x 9.81 x 7.5...12ml. Which means that the initial velocity is any siphon cannot exceed about12 m/s at the inlet, Thee essence of the hydraulic design of siphon spillways, therefore, lies in ensuring maximum discharge capacity without harmful negative pressures.

7.2 TYPES OF SlPHON

Siphons can be classified in several ways (Govind Rao 1956).

l. According to the configurationA. Hood or Saddle siphon (as shown in Figure 1) B. Volute siphon (3S shown in Figure 2)11. According 10 the operating heada,

A. Low bead siphon. Operating at net head (difference between theupstream and downstream water levels) less than atmospheric pressure, i.e., about 10 0lI.B. High bead siphon exceeding the above value

129

III. According to arrangement of primingA. Water seal typeB. Tilted outletC. Baby siphonD. Tudel or stepped type, etc. IV. According to regulationA. UnregulatedB. Air-regulated

7.3 HYORAULIC ACTION

Siphons have been used as spillways for reservoirs and canals since the middle of 18th century. Their advantages over simple weirs, gated weirs and gated ori fices are: automatic control of head water level within close limits, concentration of flow within restricted space, operation without mechanical parts, independence from outside power supply. and low maintenance costs.

132 Chapter 7

Some disadvantages are: the discharge is inhibited or reduced if obstructed by debris or ice and the sudden increase of discharge on priming might cause fluctuations in head water level and flash floods downstream.In a hood or saddle siphon (Fig. 1) the crest is set at the FRL (Full Reservoir Level), It has a bell-mouth entry and exit, and a water seal to prevent air from entering from the downstream. When the water rises above FRL., i.e., above the crest. the discharge passed down through the lower limb carries away air in the throat. This action is similar to the weir overflow. With increase to the head and discharge, more and more air is dragged out resulting in fall in pressure. The difference between the atmospheric pressure 0n the outside and reduced pressure in the siphon creates more flow and a higher pressure drop until the entire throat starts flowing full, when it is said to have primed. To stop the siphonic action, there is an air inlet pipe with its mouth at FRL or a higher elevation. As soon as the water in the reservoir goes below the desired elevation, air rushes through this pipe into me siphon and breaks the vacuum, stopping the flow. The air inlet pipe is called a deprimer.

Various devices are used to induce early priming of the siphon. Thetwo most commonly used are me step or deflector (Fig, 3) and the baby siphon(Fig. 4).

Figure 4 Sipbon witb baby slphon,

In a volute siphon, (Ganesh Iyer 1950) shown in Figure 2, the lip of the funnel is kept al FRL and a number of volutes (like the blades of pumps or turbines) are placed on the funnel to induce a spiral motion of water passing along them. When the water rises above FRL. it spills, over the circumference of the lip of the funnel and flows along the volutes with a spiral motion, forming a vortex in the vertical pipe. This induces a strong suction pool creating a powerful vacuum. which sets the siphon in action. To Stop the siphonic action, air is let in through small pipes taking off from the crown of the dome with their inlet opened al FRL.

7.4 HYDRAULIC DESIGN CONSIDERATIONS

The following characteristics are relevant in the hydraulic design of siphon spillways:

Discharging capacity Priming depth Regulating flow

134 Chepter7

Stabilizing functionEffect of waves the reservoirCavitationVibration

7.5 DISCHARGING CAPACITY

The flow in the throat section of a saddle siphon can be idealized as a free vortex, so that

Subscript 1 refers to quantities at the crest and subscript 2 refers to the crown of the siphon.

V = V, ~ (2)RReferring to Figure 1. Discharge through an elemental area dA formed by a stripdR and throat width b is

Q. = V, R, dA = V, ~bdR (2a)

R Rand hence

R ? dR {R_].. R .. R R.Since, the maximum value of V, is 12 m/s.Q_ = 12R, {lO ~]

and the average,velocity will be

(4)

V.= Q 12R,b[ln.&]A (R: - R,)b Ro

12RI [In.&.](R.-R,) R,

(5)

This velocity should be the same at all sections a1ong the siphon barrel unless there is expansion or contraction or the section. However, when the siphon is running full, the velocity is given by the total head H (from reservoir level up to the tail water level or crown of the outlet section. as the case may be),V .. p.V2iH (6)

Copynghted m a

Mu= siphon-coefficient accounting for various losses such as inlet, friction, bend,Etc.135Slphon Spillways

If the siphon barrel is of constant cross section without constriction or expansion,

I I- - --r.7'==:====:====:="7-Tt-

J(I+k,+k,+k.+ ...)

Where k, etc. are toss coefficients for inlet, friction, bend and outlet.

(7)It may be necessary to limit the head in some manner to prevent V from exceeding the value specified in Equation 5. This can be done either by increasing the outlet loss by constricting the outlet section or by decreasing the total head by raising the elevation of the outlet.When the outlet section is constricted, the exit velocity V is given by

Where V. is obtained from Equation The required outlet area A can then be calculated from V-. The above procedure can also be represented by a single relationshipJI" = -Q = .A:..:V....a. = ""'I'!'''''!'!''_ ...A... _VD Yo 2gH-. -(k,+J:, + ....+. ...)V.

(9)The discharge in the volute siphon can also be calculated in the same way by assuming that the flow entering the funnel al the lip (Fig. 5) takes a circular path (Govind Rao 1956).

V,R

,.

.

lf the area at the outlet section is A. and H is the operating bead available,

CD. may be assumed to be 0.70. However, model observations have shown this to be as high as 0.85.Ackers (1975) have summarized the discharge characteristics in a nondimensional form as shown in Figure 6, applicable for all air-regulated siphons. Initially, the discharge rises slowly as relative to upstream head. When priming occurs, the curve flattens, representing a wide range of discharge for a small difference in head.This is the range within which the siphon will operate f1owiog full of air water mixture, until the upstream level falls below the depriming head. To avoid hunting it is desirable for the curve in the operating range to gently rise with increase in the discharge. If the upstream level rises beyond this operating range, the siphon will run to black water (a term used to define flow without air), when the discharge will increase in proportion to only VH. Generally, the siphon should be designed such that the black water condition is not reached.Beto. (l989) have reported experiments with air regulation through two pipes, which dip into the surface of the headwater. One of these dip pipes admits air to the crown of the siphon passage and the other admits air at the crest. This form of air admission produces good dispersion of air into the f1ow. This results in a head-discharge characteristic that is considerably flat, showing large change in discharge for very little change in headwater level as shown in Figure 7.

Illustrative Examples

1. A reservoir requires a spillway to surplus a maximum discharge of 450 cumec with its FRL 20 to above the tail water elevation.

a.If an overflow spillway with a WES crest profile is used with crest elevation 5 m below the FRL, what should be the length of such a spi1lway?b. lf a siphon spillway is used, with a constant cross section 5 m in depth and formed by radii of 5 m and 10 m, what should be the width of such a siphon?c. If the total head loss through the siphon (excluding velocity head at outlet) is 10 m, how far above or below the tail water level should the siphon discharge in order to avoid cavitation?

a. For overflow spillway. the coefficient of discharge may be taken as2.20.138138Chapter 7

138Slphon SpUlways

(lla)

b. With R = 5 m and R2 = lOm, average velocity allowed through the siphon is given by Equation 5.v. = Q = 12R,b [In R.]= 12R, [10 R,] (1Ib)A (I?, - R,)b R, (R, - R,) R,

and hence the required crest width is

teri

Thus, using a siphon spillway affects a reduction of width by about40%.

140140Chapter 7

Slpnon Splllw.y.139

c. Applying energy equation from the reservoir surface to the siphon outlet end, the operating head H will be

H = V2

+ HL => H= 832'

10= I 353m. (1le)........

-'-+2g 19.62

The siphon outlet should be placed (20- 13.53) = 6.47 m above the tail water elevation.

2. A siphon spillway of constant rectangular cross section 4 m wide X 2.5 m high has configuration as shown in Figure 8. The total length of the siphon is 80 m. Various loss coefficients are:

inlet 0.12 outlet 1.0gama (bend loss coefficient) 0.75Friction factor 0.018

Determine (a) the maximum discharge. (b) Whether cavitation would occur for that discharge, and if so, the safe discharge for avoiding cavitation, and (e) The required constriction of lth outlet section 10 restrict that discharge.

(l. The gross operating head = El 111.25 - El 81.25 = 30 m.

Max discharge equals 10 X 15.87= 158.7 cumec

b. The average velocity should not exceed that given by Equation 5.

V. = 12R.

Since the velocity in (a) of 15.87 m/s is considerably larger than 9.19 m/s, there would be danger or cavitation. The discharge should, there fore, not exceed 9.19 x 10 = 91.9 cumec.

c. Required outlet area to restrict the discharge to 91.9 cumec is givenBy Equation9.

If the width of the outlet section is retained the same, then the depth of the section should be reduced from 2.5 m 10 (4.28/4) - 1.07 m.

7.6 PRIMING OEPTH

The priming action of a siphon depends on the power of its air evacuation,On the inlet side, this is easily done by keeping the lip of the hood below the reservoir level. To prevent the entry of air from downstream and ensure smooth priming, it is necessary to provide a water seal in the downstream leg as shown in Figure l. In a saddle siphon, other factors that facilitate low priming are a narrow throat, a large radius at the crest, and a critical depth of submergence at the outlet exit, Enrique (1975) express the entrainment of air by a falling nappe within the siphon barrel in terms of depth of free fall H., water velocity V, jet geometry (b), (p), (1), and water discharge Qw.9.."'.21!X!!J.)a"'(l-~) (12)\..1'

Q. I Vwhere

.Q. - Air dischargeQ. - Water discharget ~ Thickness of the rectangular jet b ; Width of the rectangular jetH, = Depth of fall of the rectangular jetp e Perimeter of the jet exposed to atmosphereV ... = Minimum velocity to entrain air

Equation 12 indicates the relative influence of various parameters on the rate of air entrainment within the siphon barrel and thus, on the rapidity of the priming.Bollrich (1994) states that priming depth is approximately 0.16 to 0.20 limes the vertical dimension of the waterway al the crest, i.e .. Hp "-O.16-{).20 d.ln a volute siphon, priming depth decreases with the increase in the numberand height of volutes, 8 decrease in the angle of their lake-off from the lip, a decrease in the rise of the dome and in the slope of the funnel, and an increase in the height of the funnel.However, it is observed that most of the factors that favor a low primingdepth adversely affect the coefficient of discharge.

7.7 FLOW REGULATION

One of the prime disadvantages of the siphon spillway is the sudden release of discharge on priming and the sudden stoppage of this discharge on depriming leaving any effort of flow regulation.Air regulated siphons (similar 10 those proposed by Prellyjohns el al.) offer a relatively flatter discharge curve to ensure a wide range of discharge for smallrise in upstream water level. However, discharge and water level in the downstream increase rapidly.ln the case of spillways with battery of siphons, at least partial regulation of flow in the downstream is possible (i.e., adding or stopping discharge in steps) by manually closing or opening of air inlet valves of some siphons.However, this must be done with due regard to inflow in the reservoir. Another method is to install siphons at different crest levels such that their priming/depriming occurs in stages, with increasing/decreasing upstream water levels, as described by Bollrieh (1994) in the case of the Burgkhnmmcr dam, Germany, having three pairs; of siphons with their crest levels differing by 10 cm. Each siphon with inlet dimension of 3m wide X 1.8 m deep, has been designed to pass a safe discharge of 42 cumec, with a priming depth in the range of 30-47 cm. Depriming is expected at a water level 5 cm above the relevant entrance lip (al the same level as the crest). Figure 9 shows the operating cycle of the siphon spillway.Partial control of discharge through a siphon may also be possible by manipulating a valve-controlled air vent installed on the crown of the siphon. The necessary cross section of the air vent must be ('Bollrich.I994).

wbere

::E(. = sum of hydraulic loss coefficients in the air ventPo = pressure at me summit of the siphonP..., = Airbrent pressure

This is, however, seldom resorted to in actual practice because of apprehension about serious operational problems.

7.8 STABILITY OF FUNCTIONING

An examination of Figure 6 and Figure 7 will show that once the siphon primes.the increase in the discharge is substantial as compared to the increase in !he upstream water level, A stage may be reached when the outflow through the siphon exceeds the inflow, at which time the upstream water level may start depleting leading to depriming. This results in reduction of discharge and increase in the upstream water level and priming again. This is called hunting or instability of siphonic action and is undesirable. Ackc el al (1975), however, noted that the indications of model test on the control of upstream level by an air-regulated siphon could be misleading because in the full-scale situation the head pool area and the capacity are proportionately much greater,The phenomenon of hunting of the siphon has been extensively studied on hydraulic models by Benfratello (1955), Boreli (1955). and Crump el al. (1961). The hunting of the siphon is influenced by the elevation of the lip of the siphon entry hood from the crest Hh. with reference to the priming depth Hp For H. :S Hp violent hunting was evident. It has been recommended by Crump el al.(1961) that

(14)

7.9 EFFECTOF WAVES

Perkins el al. (1975) have described model tests in which the performance of a siphon was effected by waves with amplitude up 10 1.83 m and period varying from 3.5 10 7 seconds. Although, siphon did not deprime, the mean water levels were up to 0.46 m higher than they had been previously and the air was seen entering the siphon in bursts. In addition, the action of waves was cyclic. The arrangement suggested by them includes provision of 3. stilling box to suppressthe effect of waves as shown in Figure 10.

7.10 CAVITATION

Siphons opemling al high bcad muy cnviuue. This was evideol from the experi ments on !he model of a saddle siphon as well as 00 a fuU-!Cale. 14 cumec siphon. haviog 1.5 m higb barrel al !he throar and operating under a bead of 7.3 m. Thepressures on !he erest weee about - 7.5 m of water. However, by puning n flured oullel uf 1:5 in the modcl. Ibe negativo pressure inercascd 10 -8.2 III and the discharge showed 8.11 increase or 31 percent. In the full-scale, lhe dischnrgc in creased by only 3% because of cavitauon and separauon, lt was confirmed lhal Ibe limiring oegarive pressure in a well-designed sipboo corresponds lO about8.2 m of water.Protorype investigations in regard 10 functiooing of the Hirebhasgar volute siphons, such as ooe in India. brougbt OUI the limitations of vollile siphons operar ing al heads in exeess of 20 m. Cavitarion damages were ooticed 00 the vertical barrel just below the throat and on the bends.

Predlctlon of Cavltatlon

An approximate veleeity in excess of about 12 mis is a condilion for Ihe onsei of cavitatlon. Bollrich (1994) has SIISscsled a more precise method based 00 the vcrtex-core thcory. According to lhis lheory. the tenson PI< inside rhe core 01' a single vonex rocaling with a velocity VI equal to the fiow velocy can be ex pressed as

p. V,'

where

-=-/"",--'2gr

(15)b... = vacuum pressure bcad, i.e., thc difference between the annosphericpressure (correspanding to lhe elevation of lhe structure with respect 100151). and !he vapour pressure P.(p)" _[.!'e.._ p.] (ISa) r y

The critical values of the pressure and Ihe velocity are al the inner side (crest) of lhe siphon. Referring 10 Figure I and the general expression for discharge through sipbon,

Q:bR,I{I+ ~~2g(Hp-"'-h.",) (16)

Where hl e head 105Sdue 10 entrance, bend. (rietion etc. from thc entrance up10 Ibe cresr, Because of!he proper bell-mouth entranee and tbe relatively shorterIcnglh involved, ibis loss of head is suggested lo be only

", = 0.08 V,' "0.08..:L...

Q' I (17)1

282gb d

Copynghted m a

148148148Slphon Splllway.

Chapter7148

H. is laken equal to zero as o worst case.11Ius. Equauon 15 can be writlen asa=bR,ln(I+'!") 28(-0.08 Q: 1-"-)R, 2gb d

(17a)

(18)

wbere

a=bR,ln(l+ ;.)

From whicb h... can be evaluated in terms of Q.Also. v, = Q/a and hence

(ISa).v;.L'

=_Q'

(19)2g 2ga1110$P'y = -"_ - V1l2g can be expressed as a function of Ql.

P. = {JQ'r

(20)Assigning various values 10 P/r gives correspooding values of discbarge Q.GeDeraJly.P,y = - 10m corresponds to the beginning of local cavitation,1be entine procedure is explaned next with neference 10 !he sipbon spillway of Illustrative Example 2.

lIIustraUve Example8

3. Determine lhe discharge through the siphon spillway of Example 2 ceerespondng 10 !he condinon of begnning of local cavitaton.v.' Q'/1, = 0.08-'- = 0.08 2 'd'28 gb= 0.08 a' = 0.0000408Q'2...9.81...100

(20a)

~~ =2g(-O.0000408Q'-It .)attd a:bR,ln(l+ ~)=7.66 (2Ob)

~ s (7.66)2 .t2x9.811-0.0000408 (2 - h...,)= 1151.931- 0.000048 Q2 - 11."",]::0 e = -0.047 e - 11.51.93 h~::o I,_ = - 0.000909 Q2

v. = Q ~-

\(,.:.t... =

Q', 0.000868 Q'

(2Oc)a 28 19.62.t7.66

Po \('...!.=-It"" --' =-O.OOO909Q' -O.OOO868Q' =-O.00178Q'r 28Q = ./--::P'-.'fr~-0.00178

(2Od) (20e)

For the limring valu of P,jy = - 10m. Q = 74.9Scllmec from Equaton (20e).Thus, llle maxlmum discharge should be resrricted 10nbout 7S cumec, Wilh this, !.he veloeity V, at the eres! would be Q/a '" 7Sn.66 '" 9.8 mis nnd tbe average velocity V. = 75/10 .. 7.5 mis.

7.11 VIBRATlON

There may be a porerual danger of vibration when a siphon operares with a large quantiry of air that ls gulped intermittenlly and !hen carried through the struc:ture in discrete lorge pockets. Ackers el al. (1975) siate thal lhe intermiuem odmis.,ion of air and lurbulent Ilow lllrougb tbc siphon mean tIlu!'Ihe structure oC !he hood must be capable of willlstanding Iluctuating suction pressures, There could be a dynamic interaction between the suucture and the two-phase flow of air and water, However, any instance o severe vibrations 00 !be saddle siphons has no! come 10 the Ight, 00 !be other hand, volute sipbons bave been subjeeted 10severe vibrations (CBIP 1979). The tests cooducted 00 volute sipbons of Hirebhasgar dam revealed vibrations with !be geeeral level from 0.059 g to 0.15 g, 1I was also found lhal when the oullel of a siphon was tapered, though tbc discharge apparenlly droppcd, the siphon ran smoothly.

Notatlona

A = Arca of flow section Po., '" Are u of ouuer seeoe A", .. Area of the air venta .. Are. of annular space in volute siphon b = Widlh of sipbon throat seetionCd =- Coefficient of discharged ~ Dcpth or height of lhroal sectionf - Friction factor

H : TOIal operaiing headH~ : Total head 1055 throegh !he siphonH. = Priming deplhH, = Depth of free fnll of tbe jeth, - Head IOS5 in the siphon fmm entrnnce up to crest b"", - VQCUUtll pressure headk '" Loss coefficients for inleL friction, beod, outler etc.L '" Widlh of the siphonP; = Criiical value of pressure al CJ'eS1Po = Pressure al crownp : Perimerer of rectangular jet exposed 10 atmospherep_ = Ambienr pressureP.... a Atmospheric pressurep. = vapour pressure of waterQ '" Discharge tbrough siphon