This page has been reformatted by Knovel to provide easier navigation.

22 HydraulicStructures

The late A R Thomas OBE, BSc(Eng),CEng, FICE, FASCEFormerly consultant, Binnie and Partners

Peter Ackers MSc(Eng), CEng, FICE,MIWEM, MASCEHydraulics consultant

Contents

22.1 Open channel structures 22/322.1.1 Basic concepts 22/322.1.2 Transitions 22/422.1.3 Weirs and flumes 22/522.1.4 Control weirs and barrages 22/722.1.5 Permeable foundations 22/1022.1.6 Energy dissipation 22/1022.1.7 Scour and erosion 22/14

22.2 Enclosed flow 22/1622.2.1 Head loss in large conduits and tunnels 22/1622.2.2 Unlined and lined-invert tunnels in

rock 22/1622.2.3 Transitions and bends 22/1722.2.4 Exits 22/1822.2.5 Flow routing 22/1822.2.6 Drop shafts 22/1822.2.7 Air problems in conduits 22/20

22.3 Spillways 22/2022.3.1 Purpose and types 22/2022.3.2 Channel spillways 22/2122.3.3 Weirs 22/21

22.3.4 Low-level outlets 22/2122.3.5 Bellmouth, shaft and closed-conduit

spillways 22/2222.3.6 Siphon spillways 22/2322.3.7 Chutes 22/2422.3.8 Energy dissipation 22/25

22.4 Reservoir outlet works 22/2522.4.1 Intakes 22/2522.4.2 Vortices 22/2622.4.3 Screens 22/26

22.5 Gates and valves 22/2822.5.1 Gates 22/2822.5.2 Valves 22/2922.5.3 Air demand 22/32

22.6 Cavitation 22/32

References 22/32

22.1 Open channel structures

22.1.1 Basic concepts

22.1.1.1 The Bernoulli theorem and critical flow

Two important concepts in the hydraulics of flow throughstructures are the Bernoulli and pressure-momentum theorems.The former (see page 5/8) expresses conservation of energy, andwhen applied to straight-line flow in an open channel, takingbed level as reference level, may be expressed as:

H=d+<xV2/2g (22.1)

where H is the specific energy head, d the depth of flow abovethe bed, a coefficient, V the mean velocity and g the gravita-tional constant

Where the flow is curvilinear, depth will vary across the channeland d is a mean value. Under normal conditions of flow in wideuniform channels, a = 1.02 for smooth boundaries but higherfor rough boundaries. For example, if n/d*16 = 0.0225 (where« = Manning's roughness factor) a= 1.12. In order to simplifycalculations where velocity head is relatively small, a is oftenassumed to be unity. Head loss must be allowed for in the valueof//. For channels of rectangular cross-section, Equation (22.1)can also be expressed as:

H=d+aq2/2gd2 (22.2)

where q is the discharge per unit width of channel Q/B where Qis the total discharge and B the width

To derive d from known H and q, with a = 1 Figure 22.1 may beused.

In the more general case, applicable to non-rectangularchannels of slope angle O:

critical velocity Fc= (* m^°S j ^^

For critical depth in circular and horseshoe-shaped channels seeFigure 22.19 (page 22/17).

22.1.1.2 Froude number

F= V/(gdy2 is a useful indicator of the stability of free surfaceflow. When F< 1, the flow is subcritical; when F= 1 it is criticaland when F> 1, supercritical. As Fapproaches unity from eitherdirection, the flow becomes unstable and surface waves maydevelop. Surface undulations may occur in subcritical flow whenF exceeds 0.5.

22.1.1.3 The pressure—momentum theorem

Unlike the Bernoulli theorem, this applies whether there is headloss or not. It follows from Newton's second law and can beexpressed as:

P-M1-M1-ZQ(V2-V1) (224)

where P is the resultant force on a mass of fluid over a specifiedlength, M1 and M2 represent momentum at entry and exit, w isthe specific weight of fluid, Q the constant discharge and F1 andV2 are the flow velocities at entry and exit

P usually is the resultant of fluid pressures and boundarypressures in the direction of flow.

22.1.1.4 Hydraulic jump

This is a relatively abrupt change in flow depth when the flowchanges from supercritical to subcritical as described on pages5/17 to 5/19 and illustrated in Figure 22.2. Except at the limitingcondition when both depths are critical, it involves a head loss,dissipated in extra turbulence. In Figure 22.1 it can be repre-sented by a transfer from a point on the supercritical curve to alower point on the subcritical curve. It may be stationary ormoving. Its character and movement can be determined byapplication of the pressure-momentum equation (Equation(22.4)). In a rectangular channel of width B and horizontal bed,P1 = ̂ Bd2 at entry and P2 = ̂ Bd] at exit, where d, and d2 aredepths; no other pressures have components in the direction offlow. If pressure plus momentum of the supercritical flow(/>, + M1) exceeds the pressure plus momentum of the subcriticalflow (P2 + M2), the jump will move downstream, if they are equalthe jump will be stationary and if (P2 -I- M2) exceeds (P1 + M1) thejump will move upstream.

For a stationary jump in a horizontal rectangular channel, therelationship between upstream and downstream depths is:

|=V(0.25 + 2FJ)-0.5 (225)

where d} and d2 are the conjugate depths, i.e. the depths of flowupstream and downstream of the jump, respectively, and F1 isthe Froude number upstream of the jump

A number of laboratory tests have shown close conformity tothis relationship.

The jump height, d- = (d2-*/,), on a horizontal floor may be

Figure 22.1 Specific energy of flow in open channels. Depth offlow d may be determined from specific energy head AY anddischarge per unit width q

In a channel of rectangular cross-section with horizontal bedand a = 1 (as, for example, immediately downstream of acontraction)

critical velocity Vc = (gdy12 (22.3a)

and critical depth

Jc=V2Jg = WgY13 (22.3b)

F 1 = V^,. id,/!,)*

Figure 22.2 Hydraulic jump relationships for horizontal or gentlysloping beds. (After Thomas (1958) Discussion on Bradley andPeterka (1957) op. cit. Proc. Am. Soc. Civ. Engrs, 84, HY2, Paper1616)

Equation (22.5) and Figure 22.2 give results with little error inchannels with beds sloping at 10% or less, but with steeperslopes the components of vertical pressures have significanteffect.

In channels which are not of rectangular section the jumpmay be distorted in plan, but the pressure-momentum equation(22.4) can be applied to the whole cross-section. Several meth-ods for calculating the conjugate depths in channels of variousshapes are available.2~5

22.1.2 Transitions

22.7.2.7 Subcritical flow

In channels of variable cross-section, Equation (22.1) or Figure22.1 may be used to determine depth of flow, provided changesare sufficiently gradual to avoid significant head loss. In con-verging flow, q and hence </c increase with the reduction in width.Therefore with subcritical flow and constant specific energy H, itis evident from Figure 22.1 that d reduces. As examples, achannel may be contracted at a bridge and allowed to expanddownstream, or a gated regulator may have a raised sill. In bothcases the surface is depressed in the contraction. Provided theflow remains subcritical the process is reversible in a down-stream expansion. If, however, a contraction reduces the depthto the critical value, any further contraction has the effect ofraising the upstream head, because critical depth is the mini-

Figure 22.3 Typical transitions for subcritical flow, (a)Contraction from sloping to vertical sides; (b) warped expansion;(c) expansion with vertical sides; (d) short expansion; (e) exampleof transition from stilling basin to canal in erodible material

determined from Figure 22.2, which may be extended by use ofEquations (22.1) and (22.5). The length of a jump cannot beprecisely defined but is approximately 5 to 8 x df the greaterfactor applying to lower Froude numbers.1

mum depth possible for any given specific head (see Figure22.1). The result is a rise in upstream water level, the excess headgenerates supercritical flow downstream of the throat, or sectionof maximum contraction, and is lost in a hydraulic jump wherethe flow changes back to subcritical. The throat is then acting asa 'control'. If head loss is to be avoided, the Froude numbershould not be allowed to approach close to unity.

Convergences for subcritical flow may be rapid but externalangles in the side walls should be avoided by the use of large-radius curves, as shown in Figure 22.3a. Diverging channels insubcritical flow are liable to result in separation of flow fromone or both side walls unless expansion is gradual. Side expan-sions of 1:10 are usually satisfactory. Sharper divergences maybe followed in some conditions;6 expansion is assisted by a risingfloor, baffle blocks or a raised sill downstream and by ahydraulic jump. The expansion ratio is also a factor - see page22/17 - where expansions in enclosed flow are discussed. Someexamples of diverging transitions are shown in Figure 22.3b to22.3e. Figure 22.3e illustrates a transition from a drop structureto the canal beyond.

Changes of direction cause head loss because of the secondaryflow which distorts the flow pattern; the flow near the bed isdeflected more sharply than the surface flow. If the bend is verysharp there may be complete separation at the inner boundary.These effects may be minimized by adopting a large radius forthe bend. In rectangular channels with depth: width ratio of 0.6to 1.2, Shukry7 found that head loss became minimal with radius3 x width. In channels with credible boundaries, unless bankprotection is provided, the minimum radius depends on thevelocity and credibility of bank material. On irrigation canals inIndia the radius is generally 20 to 30 x surface width.

22.7.2.2 Transitions - supercritical flow

The problems here are different from those discussed so far.Whereas in subcritical flow, pressure changes can be transmittedlaterally from the side walls to the whole flow, inducing changeof depth or direction, in supercritical flow the velocity oftransmission of a small disturbance or wave is less than the flowvelocity. The result is that a change in direction of a side wallcreates an oblique shock wave which is reflected from side toside downstream.

Convergences and divergences should be very gradual. Figure22.4 shows the shock waves created by a convergence. A sharpconvergence may cause high-velocity flow to ride up andovertop the wall. It is therefore preferable, if possible, to locateconvergences and other changes in wall direction where thevelocity is low, e.g. at the upstream end of a chute, and maintaina straight chute where velocity is high. It may, however, bepossible to use lateral inclination of the bed, e.g. superelevation,to assist in convergence or divergence. Where shock waves areunavoidable, they will occur in a zigzag pattern for somedistance downstream owing to reflection from side walls. Theside walls should therefore be high enough to contain them at

points of reflection. Sloping side walls, as in trapezoidal chan-nels, are particularly vulnerable. Methods are available for thecalculation of pattern and height of shock waves in simple casesand for minimizing their effects.9 Scale models may also be used.

Long-radius bends are preferable to short radius, especiallywhere overtopping is a danger. Knapp9 recommends compoundcurves for the side walls of bends, with radius 2r in the approachand exit over a length of B/tan P in each case, where r is theradius of the centreline of the main curve, B is the channel widthand sin /?= F, the Froude number. This arrangement createscounter waves which tend to neutralize the shock waves gener-ated by the main curve, so reducing disturbances downstream.

22.1.3 Weirs and flumes

22.7J.7 General

Weirs are used to control flow or water levels, or to measureflow. They range from low walls across streams to the spillwaycrests of high dams.

The basic equation for free flow over weirs is:

<7 = c(2g)*//-/2 (22.6)

where q is the discharge per unit width, c is a dischargecoefficient, g the gravitational acceleration and H the total headlevel upstream above weir crest, normally taken as H1 + FJ/2g,where /*, is the upstream depth of flow above weir crest level andK1 is the mean velocity of approach

Equation (22.6) can be derived from Equations (22.2) and (22.3)assuming critical flow and applying a coefficient c to takeaccount of departure from flow on a horizontal bed. Thecoefficient depends on the shape of the weir and, in general, itvaries with head over the weir; only in a few special cases is itconstant. There are many weir profiles, each with differentcharacteristics in relation to discharge coefficient and modular-ity. Weir flow is said to be 'modular' or 'free flow' when it isunaffected by tailwater level. The point at which a risingtailwater begins to affect the upstream head or flow is termed the'modular limit', expressed as the ratio of downstream toupstream depth above crest level. Values of the coefficients ofweirs of many different profiles have been published, e.g. byKing and Brater9 (see also section 22.5). In this section, sometypes in general use are considered as follows.

Sharp-crested weirs. These are formed of metal plates and areused for precise measurements of flow. Flow over weirs withnarrow crests having rectangular upstream corners is effectivelysharp crested, with a coefficient c approximately 0.406, providedthe nappe springs clear and is fully vented.

Triangular profile weirs. These have sensibly constant coeffi-cients throughout their modular range; no venting is requiredand the coefficient is greater than that of a sharp-crested weir.For example, the Crump weir (Figure 22.7), with 1:2 upstreamand 1:5 downstream slope, has a free-flow coefficient c of 0.442and a modular limit (within 1% of discharge) of 0.74. Weirs ofthis type are widely used for measurement of stream flows.

Trapezoidal profile weirs. Trapezoidal profile weirs have flatupstream and downstream slopes and narrow horizontal crests,formed by the gate sill, are often used in gated controls andbarrages (see, for example, Figure 22.10). They have a free-flowcoefficient which is variable but generally exceeds 0.383 andunder drowned conditions the afflux is small.

Broad-crested weirs. These have horizontal crests wide enough

Figure 22.4 Example of shock waves at convergence insupercritical flow. (After lppen etal., (1951) 'High-velocity flow inopen channels.' Trans. Am. Soc. Civ. Engrs, 116, Paper 2434)

Shock front

Negative disturbances

Figure 22.5 Discharge coefficient of free-nappe weirs at designdischarge. (Based on USBR data; US Department of the Interior(1960) Design of small dams. Denver, Colorado)

The coefficient c of the standard weir at profile discharge isshown in Figure 22.5. By adopting a profile discharge lowerthan the maximum discharge, a higher coefficient is obtained atflows exceeding profile discharge.10 Discharge in excess of theprofile discharge causes pressures on the face of the weir to fallbelow atmospheric in the vicinity of the crest where the curva-ture is sharp.11 This is usually acceptable provided that thestructure is safe against uplift, and a reasonable margin ofpressure is allowed above cavitation level to allow for fluctua-tions.

Profile coordinates have been published12 from which weirs ofstandard profile and some variations can be designed.

Sharp side contractions at the abutments of weirs reduce thedischarge capacity locally. They should be curved as in Figure25.3a. Piers have a similar effect, to avoid which spillway piersare often extended upstream, so that the contraction at the piernoses occurs in a region of lower velocity.

22.1.3.2 Submerged weirs

The effect of a tailwater level above the modular limit is to raisethe upstream water level for a given discharge. The degree towhich the upstream head or discharge is affected depends on theweir profile: moreover in certain ranges of submergence the flow

Figure 22.6 Free-nappe profile weirs. Effect of tailwater level ondischarge coefficient. (Based on USBR data; US Department of theInterior (1960) Design of small dams. Denver, Colorado)

pattern is uncertain and may change from diving nappe, whichfollows the downstream weir face, to surface nappe, whichseparates near the weir crest, a roller developing beneath.Observations of discharge related to upstream and downstreamheads or water levels therefore cannot be regarded as of generalapplication. Nevertheless, good indications can be obtained.Figure 22.6 shows the effect of submergence on standard free-nappe profile weirs12 and Figure 22.7 the effect on Crumptriangular profile weirs.13

Figure 22.7 Afflux at submerged Crump weirs. (Based on data ofWhite (1971) 'The performance of two-dimensional and flat-veetriangular profile weirs/ Proc. lnstn Civ. Engrs, Paper 735OS!)

22.1.3.3 Measuring weirs and flumes

For laboratory and other small-scale measurements, sharp-crested weirs consisting of thin plates in the form of rectangularor Vee-notch weirs are found convenient. Standard formulae ortables of discharge for these are available.9-14 For measurementof larger flows in the field, however, sharp-crested weirs havedrawbacks, particularly the need tov vent the nappe, the headdifference required to ensure modular conditions and the effectof accretion of upstream bed level following the erection of agauging weir.

Weirs of several other types have been thoroughly investi-

for parallel flow effectively to develop. Control is then at thepoint of critical depth so that c=1.70. To ensure that thiscondition applies and c is constant, the upstream edge should berounded to avoid the formation of a roller above crest level. Inpractice, the value of c is 1 to 3% lower due to friction loss. If thedownstream floor falls at a gentle slope, say 1:10, the modularlimit is between 0.7 and 0.8. Broad-crested weirs have beenextensively used for flow measurement and for proportionaldistribution of flow at dividing points in irrigation systems.

Free-nappe profile weirs. Free-nappe profile weirs with profileaccording to the shape of an undernappe of flow over a sharp-crested weir (Figure 22.5) have been widely used for overflowspillway crests. The standard profile is one with verticalupstream face and weir height P large compared with head overcrest, H. The profile varies with smaller values of PjH andsloping upstream faces. This profile has the advantages that c iscomparatively high for the profile discharge (i.e. the dischargecorresponding to the nappe profile used), subatmospheric pres-sures do not develop within the range up to profile discharge, noventing is required and the flow characteristics are well docu-mented and predictable.

Submergence ratio

Ratio

of co

efficie

nts

C = ?/A/'5 (submerged f low)Cf = 9///f

1'9 (free flow)

gated and are subjects of national and international standards.A comprehensive account of the performance and use of themain types of weir and flumes is given by Ackers et a/.14 Bos15

has reviewed a wide range of devices capable of use for flowmeasurement. Those most useful in a civil engineering contextdepend on the creation of critical flow. This can be induced byproviding a sill or weir, or by contracting the width, or by acombination.

The critical flow formula in a rectangular cross-section chan-nel, Equation (22.6), is the most basic formula for flow measure-ment by weirs and flumes, and applies to free flow, i.e. when thecritical flow at the crest of a weir or in the throat of a flume is notdrowned by the tailwater level exceeding the modular limit (seepara 22.1.3.1). The cross-section of flow may also be made non-rectangular - V-shape, U-shape or trapezoidal - for particularapplications, but then adjustment has to be made to the flowformula of Equation (22.6). For precise measurement with weirsand flumes, allowance for boundary layer development andother secondary effects has to be made.14

Unless there is already a local drop in level, the introductionof a measuring device will result in a rise in upstream level,though this may be quite small if a device with high modularlimit is chosen, or a Crump weir with crest tapping which can beused when drowned by high tailwater level.13 Where the range ofdischarge is large and it is desired to obtain an accuratemeasurement of low flows, a stepped weir may be used, consist-ing of a short weir at low level for the low flows flanked bylonger weirs at a higher level. Alternatively, a flat Vee-weir maybe used with crest tapping for submerged conditions.13

In the UK, broad-crested weirs with a round nose and Crumpweirs have been accepted as standard.16 In the US, Parshallmeasuring flumes have been widely used.17 These were designedwith plane surfaces so that they might be easily constructed ofwood or concrete, c is not constant but calibration formulae andtables are available. Where the stream to be gauged carriesappreciable bed load, a critical-depth flume with a flat or nearlyflat bed at the channel bed level is desirable. The bed load canthen pass through without excessive accretion upstream, thoughthere may be some at the sides. A measuring flume of this type isshown in Figure 22.8. The degree of contraction sufficient toensure modular flow can be checked by comparing calculatedupstream water levels (using c=1.66) with existing tailwaterlevels. The broad-crested weir coefficient is applicable, adjustedfor head loss upstream of the location of critical depth.14

22.1.4 Control weirs and barrages

22.1.4.1 Gated weirs

Weirs are used to control the water levels of a river or canal, forsuch purposes as diversion of flow into canals, extraction ofwater by pumping, creating head for hydro-electric power ormaintaining a required depth of water for navigation. A fixedweir also raises flood levels, which may not be acceptable. Agated weir, or barrage, however, does not have this drawback ifthe gate sill is level with the river bed, or on a low weir crest. Thegates are kept closed during low flows, maintaining the requiredupstream water level, but opened as may be necessary to passfloods. The range of water level is thus much less than with asimple weir, and the gates can be operated to maintain constantwater level over a wide range of flow. Types of gates aredescribed on pages 22/11 to 22/28.

The choice of crest profile depends on the circumstances. Forexample, a weir with a free-nappe profile is suitable where thecrest is to be above the upstream channel bed and there isconsiderable head difference from upstream to downstream. Onthe other hand, a low crest with flat triangular profile is bettersuited where, at high rates of flow, the afflux or rise of upstreamwater level due to the weir must be kept to a minimum.

22.1.4.2 Control structures in alluvial rivers

Whereas structures in rivers with rocky beds and banks canoften be of simple design, with an upstream cutoff wall into therock and a basin or bucket energy dissipator downstream, thedesign of control structures in alluvial rivers requires consider-ation of many other factors.

Firstly, the site and orientation of the structure in relation tothe river channel pattern is most important and generally shouldtake priority over other considerations. Alluvial rivers withoutconstraint by structures, training works or outcrops of rock orclay, may change course over a period of years, forming newpatterns of river channels. The history of a river course is a goodguide to such tendencies. The site for a control structure shouldbe a stable one in the long term, i.e. it should remain operativedespite changes in the channel pattern over a number of years,maintained if necessary with the aid of training works. Where aweir or barrage is used for diversion or abstraction of water it isusually desirable to ensure that the quantity of sediment in thewater abstracted is a minimum. The best location for the offtakewith this in view is generally on the outside of a bend, and thetraining works should be located to maintain the approachchannel accordingly. This consideration applies even wherespecial arrangements are made for sediment exclusion.

A typical barrage forming the headworks of an irrigationcanal system on a large river in Pakistan is shown in Figure 22.9.A weir or barrage may occupy only a small part of the width ofriver channel and floodplain. For example, in India and Paki-stan it is general practice to make the width of waterwaysbetween abutments equal to or rather greater than the width ofLacey regime channel 4.8£1/2 where Q is the maximum designdischarge in cubic metres per second.19 Flanking bunds orembankments are then required extending from the abutmentsto high ground on either side. Where flood levels are beingraised by the control, marginal bunds or flood embankments areoften provided extending upstream on each bank. To preventoblique approach, protect the bunds and avoid outflanking;guide banks are required extending upstream from the abut-ments (see Figure 22.9). In stable rivers these may be quite short,but where there may be wide swings in the river course they aregenerally approximately equal in length to the width of water-way between them. In addition, in rivers of this type, spurs orgroynes may be provided upstream, but these may cause further

Figure 22.8 Measuring flume with flat floor for debris-laden flow

Structures of many other types are used for flow measure-ment, mostly depending on the critical depth principle or onorifice control as, for example, devices on irrigation canaloutlets.18

Longitudinal section

Figure 22.9 Rasul barrage on the river Jhelum, Pakistan. Generallayout (top), longitudinal section (above). Note the flow from rightin layout (top) and from left in section. (Consulting Engineers:Coode and Partners)

trouble unless correctly located. Model tests are desirable beforeconstruction. Similar measures are used to train alluvial rivers atbridges. The guide banks and spur heads are protected againstscour, by rip-rap or concrete slabs (see pages 22/15).

Low-level sluices provided in the weir or barrage, generallyadjoining the canal regulator, have three functions: (1) theydischarge river flow during construction at a low level; (2)during operation of the works they enable the approach to theregulator to be sluiced at intervals to remove deposit of sedi-ment deposit; and (3) if kept open during a flood they draw themain stream towards the canal regulator, thus maintaining adeep channel for water to gain access to the intake during thedry season. To fulfil these functions the sill should be well belowthe canal regulator sill level and the sluices should have suffi-cient capacity to influence flood flow distribution. A divide wallis often provided normal to the weir between undersluices andweir to enable the canal to draw supplies from a pocket of low-velocity water, the undersluices being kept closed. A divide wallalso facilitates the sluicing operation. If the canal must operatecontinuously, control of coarse sediment can be provided bytunnels beneath the level of the canal regulator sill, which drawoff the bed load and discharge it downstream.20

Downstream of the weir and undersluices, a floor is providedto protect the foundations against scour (Figure 22.9). The dropin water level across the weir or undersluices is accompanied bythe formation of a hydraulic jump, except possibly at high floodflows when it may be drowned. A flexible apron of loose stone

or concrete blocks is beneficial as an extension to the floor.For design of floor and apron see page 22/15. To allow for

nonuniform discharge distribution, the design discharge perunit width of floor should exceed the mean by an allowancedepending on the approach conditions. In India and Pakistan afactor of 20% has generally been added for alluvial rivers but inextreme conditions it should be higher, e.g. where curvature ofapproach could cause a high concentration.

22.1.4.3 Irrigation canal structures

Canal head regulators are usually located immediately upstreamof a weir or barrage (see Figure 22.9). On alluvial rivers theintake should be well above the sill of the undersluices. A stillingbasin of sufficient depth, to ensure that the hydraulic jump isretained within it, is essential where the canal bed is credible,and is also generally provided where the canal is lined.

Where the general ground slope exceeds the design slope of acanal, falls or drop structures are required at intervals todissipate the excess head and lower the canal to conform to theground level. Falls are designed in a similar way to weirs, withungated crest and stilling basin. To reduce cost, the width ofwaterway is often made less than the width of canal. Theupstream contraction presents little difficulty, but the down-stream expansion must be gentle to avoid asymmetrical flowdownstream (see page 22/4).

Left bankof river — Right

guide bank

Spur

Right bankof river

BarrageLeftguide bank

Left bankof river

Rasul Qadirabadlink canal

Lower Jhelumfeeder canal

Temporarycofferdamaroundworkingarea

Radial gatesRoadway Piers at 20.4 m cc

Impactblocks

Deflectorblocks

Pond levelFlow

Stoneapron

Concreteblock apron

Reinforcedconcrete Reinforced

concreteMassconcrete

Steel sheetpile cut-offs

Concreteblock apron

Stone apron

NORTH ELEVATION(LOOKING DOWNCREEK)

Figure 22.10 Tidal barrier, Barking Creek. (Consulting Engineers: Binnie and Partners)

Control Room

Generator Building

West TowerGate

<t Navigation Channel

East Tower

+6.9 Defence Level+3.63M.H.W.S.T.

Transformer House

22.1.4.4 Tidal barriers

The risk of serious flooding from tidal surges penetrating inlandvia estuaries and tidal inlets has led to several major schemes fortide-excluding barriers. These are in the form of gates, perhapssingle gates for schemes of modest size but multiple gates formajor estuaries. Navigation is often the controlling featuredetermining the necessary span, the elevation of the sill and theclearance under any structure spanning over the waterway.

Very large vertical lift gates have been used as tidal barriersand one example, at Barking Creek in the Thames Estuary,21 isillustrated in Figure 22.10. The gate normally rests at the top ofits support towers, thus providing clearance for navigation bymedium-sized ships.

Rising sector gates do not require a high supporting structurebecause they normally rest below the bed of the navigationchannel. The main gates of the Thames Barrier are of this typeand their operating mechanism is such that they can be rotatedthrough 180° from their normal position in their sills on theestuary bed to raise them above water level for maintenance.They turn through 90° to close the barrier against the tide(Figure 22.11). The rising sector gates in the four main spans ofthe Thames Barrier have a span of 61 m and effectively theyform box-girders between their end wheels. There are sixsubsidiary gates with spans of 31.5 m.22

22.1.5 Permeable foundations

Special consideration is required if a hydraulic gradient willexist across a structure founded on permeable materials. Ex-amples include weirs, regulators across canals, barrages andtidal barriers. Two important requirements are that every partof the structure must be safe against uplift pressures beneathand that underflow or seepage through the permeable materialsshould be controlled so that there is no failure by 'piping'.Where a continuous impermeable stratum is within reach,underflow can be prevented by a line of sheet piles or a curtainwall intersecting it, or possibly by grouting, but the sealing mustbe perfect. If, however, the permeable materials are too deep forthis treatment, the floor must be safe against uplift pressuresexceeding the tailwater level acting on the underside of thestructure throughout.

Uplift depends on the hydraulic gradient of flow through thematerial beneath the work, reducing from the upstream waterlevel to the downstream water level. Its distribution may beaffected considerably by the nonuniformity of the materials so aprior investigation of the character of the material, its uniform-ity and the existence of strata of different permeability isnecessary. The floor upstream of a weir or gates is safe againstuplift because of the water load above but the downstream flooris particularly vulnerable at times of high upstream and lowdownstream water levels. Measures to reduce uplift pressures onthe downstream floor include the lengthening of the upstreamfloor and provision of transverse lines of sheet piling upstreamor beneath the weir, both serving to lengthen the effectiveseepage path, and provision of relief drains. Typical protectivemeasures beneath a gated structure are shown in Figure 22.9.'Piping' consists of the removal of foundation material by theflow of seepage water. It can occur at the tail end of a structurewhere the underflow emerges and is a potential cause ofundermining and ultimate failure of the structure. It is caused byexcessive exit gradient. Information on flow nets to determineuplift pressures and exit gradient is given in Chapter 9.

It is usual to protect against piping, where the foundationmaterial is granular, by providing coarser filter material tointercept the seepage over its exit area. This is generally coveredby loose stone or other protection against scour, but in case this

should fail, other measures are needed to reduce the exitgradient. Such measures include the lengthening of the structureand the provision of transverse lines of sheet piling to reduce theoverall hydraulic gradient, provision of relief drains and theprovision of a curtain wall or line of sheet piling at the tail end ofthe floor. The last is most important to avoid a locally steepgradient and protect the floor from undermining by scour, but itshould not be too deep because it increases uplift beneath thefloor. The upstream or central sheet piling should extendlaterally into the flanking embankments, and lines of piling arecarried around as may be necessary to intersect seepage pathsand box in the foundations. For general design procedures,reference may be made to Haigh,20 Leliavsky23 and Foy andGreen.24

22.1.6 Energy dissipation

22.1.6.1 Stilling basins

At weirs, barrages, sluices, spillways, tunnel outfalls, canal fallsand in general where a sharp fall occurs in total energy level, astilling basin is needed to contain the flow in the region ofenergy dissipation. This is especially important where the chan-nel bed is credible. The surplus energy may be dissipated bywater spilling into a pool, which may be in bed rock, or linedwith rip-rap or concrete.

In most cases the energy head to be dissipated is sufficient tocreate supercritical flow, defined on page 22/3. A hydraulic jumpis then generally the most effective and economical way ofdissipating the surplus energy. The object is to provide a stillingbasin lined with nonerodible material, usually concrete, deepenough to retain the jump over the whole range of flowconditions and long enough for the eddies generated in the jumpto be reduced to an acceptable intensity before reaching thechannel downstream. The minimum depth is thus related to thecharacteristics of the jump while the minimum length is relatedalso to the degree of stilling required. Where the channel bed iscredible, a greater length of basin is generally required thanwhere it is in rock or is concrete-lined. In the basin, chuteblocks, baffle blocks or piers are often provided to help tostabilize the jump and reduce the length of basin required.

As shown earlier, the stability of a hydraulic jump isexpressed by the pressure-momentum equation (Equation (22.5))representing the condition at which the jump is at its limit ofstability, i.e. any increase in discharge or upstream head wouldcause 'sweep-out' or movement of the jump downstream andpossibly out of the basin. In the design of stilling basins,however, the quantities which are known are usually the dis-charge, head drop and tailwater level and it is required todetermine the basin floor level. Equation (22.5) therefore cannotbe applied directly, but the maximum acceptable floor level canbe easily found with the aid of Figure 22.2. The procedure is tocompute upstream and downstream total energy levels (waterlevel + velocity head), compute H1=H1-H2 (see Figure 22.2),compute critical depth dc by Equation (22.3a), compute HJdc,read off H2/dc directly beneath HJdc, i.e. for same F1, andcompute H2. This gives the minimum depth of basin floorbeneath tailwater total energy level. It applies to a plain floorand may be reduced by 10 to 20% if chute blocks and/or baffleblocks and end sill are provided. However, it is often thepractice to provide the full depth and consider the blocks toprovide a safety margin in addition. It is usually necessary todetermine minimum basin depth for several discharges through-out the range, because the most severe case is not always withthe maximum discharge. When determining q in cases of non-uniform distribution across the basin it may be necessary to usea value rather higher than mean q = Q/B, where Q is the total

Figure 22.11 Thames Barrier, 61 m span rising sector gate.(Consulting Engineers: Rendel, Palmer and Tritton)

Gate loweringSilt

Gate in maintenance position

High water level

Gate risingGate in open position Flood control position

Water Funder G

Sillunit

Bed

Waterflow

Flapvalves

Gatearm

SECTION ON $.OF GATE LOOKING DOWNRIVER

Surge LV

Fixed end Gate span Hinged end

Trunnion assembly

Gate arm

Levels relateto ordnancedatum Newlyn

Section through rising sector gateDownriverUpriver

discharge and B the width. Tailwater level is clearly of criticalimportance for the stability of the jump and it is necessary tohave a reliable stage discharge curve, with allowance for futurechanges as, for example, due to channel bed degradationdownstream. The lowest probable levels should be used. In thecase of basins for gated spillway releases, where discharge maybe increased rapidly over a short period, allowance should bemade for low tailwater levels due to time lag.

The length of basin required cannot be defined so precisely.On a plain floor the length of a jump may be 4 or 5 times thedepth d2 in the basin. If residual eddies can be tolerateddownstream because the bed is not credible or is protected by aflexible apron, as in Figure 22.12, a length of 4d2 may suffice.Where chute blocks and baffle blocks are provided in such cases,a length of 2.Sd2 is sometimes considered adequate (but seebelow).

Many standard designs of hydraulic jump stilling basins havebeen developed from model tests, one of the most comprehen-sive being that of Bradley and Peterka.2526 Four types of jumpwere defined according to the Froude number F1, each withsomewhat different characteristics, namely:

F1 from 1.7 to 2.5 Pre-jump, low energy lossF1 from 2.5 to 4.5 Transition, rough pulsating water sur-

faceF1 from 4.5 to 9.0 Range of good jumps least affected by

tailwater variationsF1 exceeding 9.0 Effective but rough

IfF1 is in the range 2.5 to 4.5 the pulsations are likely to producesurface waves which are propagated downstream. The Froudenumber is generally determined by other factors, but if there isany choice it is clearly desirable for it to be within the range 4.5to 9.0. Bradley and Peterka's basin III for F1 between 4.5 and 9is shown in Figure 22.12. The dimensions of the chute blocks aremade equal to the depth d} and those of the baffle blocks rangefrom 1.3</, for F1 = 4 to 3d, for F1 = 14. The height of end sillranges from 1.2</, for F1 =4 to 2d} for F1 = 14.

liable to be damaged by cavitation. They can be omitted orprotected by steel cladding, as at Mangla Spillway.28

Erosion of bed and banks immediately downstream of thestilling basin can be a serious problem, whether the head dropthrough the structure is great or small - see remarks ontransitions, page 22/4.

A normal cause of erosion is the residual turbulence from thehydraulic jump. This may scour the bed beneath the level of thebasin floor, so a flexible protection such as rip-rap is neededwhich will adjust its level to the scoured bed downstream of it(see page 22/8). When the banks are formed of credible materialthey need slope protection to guard against local velocities andwave wash. In the case of weirs and barrages on alluvial riversthe banks are carried downstream a short distance - perhapsequal to a quarter of the width of river channel (see Figure 22.9).A loose stone apron is provided at the toe. In the case of canalswhere the banks are erodible, the slope protection is continuedfor a distance in which the surface waves will be reduced andvelocity distribution will become normal.

A layout of stilling basin and canal banks which has beenfound satisfactory is shown in Figure 22.3e. The gently diverg-ing side walls are free-standing at their downstream ends, wherethey consequently do not have to serve as high earth-retainingwalls; the channel downstream is widened to accommodate theside rollers which will develop and the banks are protected byrip-rap.

In the case of small flows, shorter and simpler structures havebeen used, e.g. the straight-drop spillway basin of the USDepartment of Agriculture.29

For large flows and high heads, experience has shown thathydraulic jump basins are generally satisfactory. Damage whichhas occurred has been due mainly to the basin being ofinadequate depth, to cavitation where baffle blocks have beenexposed to high velocity flow and to abrasion due to loosematerials in the basin.3031 In some cases these materials mayhave remained from river diversion operations but in other casesbed material and even rip-rap has been carried into the basins bybackwash. There have also been instances of vibration andshock due to flow instability. In large-scale basins it is especiallynecessary to guard against flow separation at the side walls,which can be a cause of both these last effects and of backwash.

22.1.6.2 Bucket energy dissipators

The hydraulic jump stilling basins described above are effectivebut costly, especially for high-discharge concentrations. Wherethe foundations of the structure are in rock, even an erodiblerock, a much higher degree of residual turbulence may beacceptable.

A submerged roller bucket (see Figure 22.13) is suitable over awide range of Froude numbers. The bucket is placed well belowthe tailwater level so that a submerged roller forms in the bucketand exit velocities are not excessive. Compared with a hydraulicjump basin, it is deeper but shorter and generally less costly; but

Figure 22.13 Submerged roller bucket-Angostura-type slottedbucket. (After Beichley and Peterka (1959) The hydraulic design ofslotted spillway buckets.' Proc. Am. Soc. Civ. Engrs, 85, HY10)

Figure 22.12 US Bureau of Reclamation stilling basin, type III.(After Beichley (1978) 'Hydraulic design of stilling basin for pipe orchannel outlets/ USBR Water Resources Research Report No. 24)

Where F1 is between 2.5 and 4.5 (basin IV) the chute blockheight is 2d\ and the baffle blocks are omitted or, according toBhowmik,27 a special arrangement of blocks and deflector maybe provided to give improved jump stability. Where F1 exceeds 9(basin H) the baffle blocks are omitted and a dentated end sill isrecommended. Basins II and IV, having no baffle blocks, arerequired to be longer than basin HI, with floor lengths ofapproximately Ad2. In the case of high head structures, if thevelocity much exceeds 15 m/s, chute blocks and baffle blocks are

Bucket roller

Standing waveGround roller

the range of tailwater level for satisfactory operation is limited,which precludes its use in some cases. Rules for design have beengiven by McPherson and Karr32 and by Bleichley and Peterka33

who found that slotted buckets were superior to plain buckets.

22.1.6.3 Terminal structures for pipes and valves

High-velocity jets from pipes and terminal valves have consider-able erosive power, even on hard rock. Means of protection

include the use of valves which disperse the jet in the air, e.g. thecone valve, or valves which project the jet some distance, wherea plunge pool can be provided, or structures devised to containthe jet and allow most of the energy to be dissipated beforedischarge into an credible channel.

Figure 22.14 shows an impact stilling basin developed by theUS Bureau of Reclamation (USBR)5 for pipe and open-channeloutlets with discharges up to 10 m3/s and velocities up to 9 m/s.It may also be considered for terminal valves within the limits

Figure 22.14 US Bureau of Reclamation impact-type energydissipator- basin Vl. (After Beichley (1978) 'Hydraulic design ofstilling basin for pipe or channel outlets.' USBR Water ResourcesResearch Report No. 24)

W = inside width of basinD = square root of area of flow entering basinV = velocity of flow entering basinTail water depth uncontrolled

Froude number V//gD

Unsatisfactoryhydraulicperformance

Satisfactoryhydraulicperformance

H = 3W/4L = 4W/3a = W/2b = 3W/8

SECTION Bedding SECTION

Rip-rap stone size diameter = W/20

PLANP L AtM

SECTIONA-A

FilletFl

at fi

llet

I Pipe

dia.

Flow

suggested minimum

ALTERNATEENDSILLANDWINGWALL

Qfi/b3 (metric)

Figure 22.15 Vertical stilling well with sleeve valve (USBRdesign). Well is of square section in plan with corner fillets asshown. Q is discharge, H is head above pedestal. (After Beichley(1978) 'Hydraulic design for pipe or channel outlets.' USBR WaterResources Research Report No. 24)

Regulation is provided by the sleeve valve at the pipe outlet,operated from above (see page 22/31).

22.1.7 Scour and erosion

22.1.7.1 Depth of scour at structures

Apart from scour downstream of stilling basins, structures suchas bridges, jetties, groynes and constrictions forming obstruc-tions to flow in rivers and channels with credible beds can giverise to scour due to disturbance of the normal flow pattern.Scour can also be caused by oblique flow at the upstream ofcontrol structures such as barrages and-regulators. It is gener-ally required to estimate the depth of scour so that adequateprotection can be provided or so that the foundations can belocated at sufficient depth to avoid the possibility of undermin-ing.

Local scour results from the deflection and, hence, concentra-tion of flow caused by an obstruction. The depth of scourdepends on the shape of the obstruction, its orientation to theflow, the channel cross-section and discharge, the character ofthe credible bed material, the sediment in transport and the timehistory of the flow. With so many variables it is not surprisingthat there is no single formula available for calculation of scour.In the case of important works it is usual to carry out modeltests.

It is also possible to determine the order of magnitude andprobably the upper limit of scour depth by comparison withdepths observed in actual cases, providing a useful check onmodel results or a fair indication in other cases. Local ex-perience is a guide but may not embrace the highest discharges.To apply historical data from elsewhere it is necessary to adjustfor scale. In the cases of rivers in alluvial bed materials, theLacey regime formulae19'36 can be used, the depth of scour beingrelated to the normal depth of channel of the same discharge.The relevant formulae in the present context are:

B = 4.801/2 (22.7)

and

rf=0.47«2//L)1/3 (22.8)

from which can be derived

rf=1.34?V/l/3 (22.9)

where B is the surface width, d the mean depth, Q the discharge,q the discharge per metre width Q/B, and/L is a sediment factor,all in metric units relating to stable channels of constantdischarge. /L may be taken as unity for fine sand

Width calculated by Equation (22.7) with Q = design dischargeis a useful indicator of the maximum bridge length required foran alluvial river with floodplain, but if the banks are of cohesivematerials, the river channel width may be less; Nixon37 found theaverage widths of British rivers to be approximately 3g1/2, whereQ is bank-full discharge. Lacey proposed that the maximumdepths of scour at sharp bends in alluvial rivers could be takenas approximately 2d, where d is calculated from Equation (22.8).Inglis38 collated data of deep scour observed at structures andtraining works in alluvial rivers at thirty different locations inIndia and Pakistan, compared them with the normal depthsindicated by Equation (22.8) and reached the following conclu-sions for maximum depth of scour below water level:

(1) At bridge piers, 2d.(2) At large radius guide banks, 2.15d.(3) At spurs along river banks, l.ld to 3.8d, depending on

length of spur projection, sharpness of curvature of flow,position and orientation.

Here d is Lacey's normal mean depth calculated from Equation(22.8) using estimated peak discharge. It will be appreciated thatlarge flood flows cannot be measured but are estimated, whilemaximum depths of scour are transient and may, in fact, havebeen greater than observed. The scour depths are related to thetotal rather than the local flow on the grounds that the scourresults from the concentration of the whole flow. In the case ofbraided rivers, allowance could be made for the division of totalflow into several channels. Scour depth in rivers in gravel andboulders would be less than indicated but the difference may besmall. Scour depths in cohesive materials could be less becauseof the time required to reach maximum scour.

stated. The required dimensions may be obtained from Figure22.14,

A special basin has been developed by the USBR for hollowjet valves.5-34 Basins have also been used for cone valves. A veryeffective energy dissipator for pipe outlets is a vertical well inwhich the pipe outlet is deeply submerged at a short distanceabove the bottom. Figure 22.15 shows a USBR type of well.35

Sleevevalve

For the purpose of design of aprons upstream and down-stream of barrages in northern India, maximum depth of scourbelow water level was taken as 1.5d at the upstream end of thehard floor and 2d at the downstream end of the basin. Here dwas calculated from Equation (22.9) using mean q.

Scour at bridge piers has been studied in some detail inmodels, scour depth being related to discharge per unit widthand sometimes expressed as depth below upstream bed level.39"41

To apply such relationships, the discharge concentration, whichcan in the worst case greatly exceed the average, has to beestimated, and the upstream depth has then to be calculated forthe corresponding flood condition. The latter can be done usingEquation (22.9) which is likely to give a conservative valuebecause of time lag and sediment load. The calculation shouldbe checked by use of the appropriate Inglis factor above.

22.1.7.2 Protection against scour

This generally consists of one of the following materials.

Boulders. Boulders from the river bed which are generallyrounded and therefore less stable than quarried stone of similarweight.

Rip-Rap. Rip-rap, or pitching of quarried stone, is widelyused. In some cases it is hand-packed, especially on side slopeswhich are expected to remain as placed without settlement, butwith increasing use of mechanical equipment it is more oftenplaced in a random manner. This is also preferable in locationswhere it is expected to settle or move down due to scour. On sideslopes the thickness of rip-rap should be sufficient to accommo-date the biggest stones without large gaps - at least 1.5 x medianstone diameter - and an underlayer or filter of smaller stone isgenerally provided to prevent the base material from beingwashed out by wave action. In the case of bed protection,surfaces not subject to scour may be treated in the same way,but at transitions from stilling basins and in general where thechannel bed may scour beneath the apron level, the volume ofrip-rap should be sufficient to protect a slope at the angle ofrepose of the rip-rap on the bed material (for a sand bedgenerally 1:2) extending from the apron level to the level ofanticipated deepest scour. For this purpose the rip-rap may belaid on a prepared slope or it may be laid in a horizontal apronwhich it is assumed will settle to a slope when scour occurs. Amargin should be allowed for uneven settlement.

The size of rip-rap which will remain stable may be estimatedfrom Figure 22.16. Sixty per cent by weight of the materialshould be equal to or larger than the size shown. In the case ofrigid structures it may be dangerous to rely on loose stoneprotection; it is generally best to provide foundations at lowlevels beneath possible scour. If stone or concrete blocks areused to protect existing structures they should be placed as lowas possible beneath normal bed level.

Derrick stone. Derrick stone is stone in blocks too heavy to beplaced by bulk handling and which therefore requires individualplacing. It is usually placed on an underlayer of graded rip-rap.

Concrete blocks, slabs or units of various shapes. As the densityof concrete is less than that of stone, larger and heavier blocksare required than the corresponding stone sizes. Concrete blocksare used in locations where stone of suitable quality and weightis not available or is too costly. Concrete blocks or slabs onedge, e.g. 2m wide x 0.5m longx I m deep, have been usedsuccessfully for flexible aprons downstream of barrages in riverswith sand beds. Concrete slabs are used in slope protection butrequire good compaction of fill beneath to avoid uneven settle-ment. Concrete units of special shapes have been developed

Velocity (m/s)

Figure 22.16 Stability of loose rock in flowing water. Graphrelates to rock of specific gravity 2.65. For other specific gravityrock weight = weight shown * 1.7s/(s-1 )3 where s= specificgravity. Use minimum weight graph in normal flow and maximumweight graph for very turbulent flow. (After US Army Corps ofEngineers (1952-70) Hydraulic design criteria. US Army EngineerWaterways Experiment Station, Vicksburg, Mississippi)

which require less concrete than do concrete cubes for the sameduty; some of these are extensively used in coastal protectionand can also be used in river channel works.

Gabions. Gabions, consisting of wire crates containingboulders or broken stone, generally wired together to form anapron, form an economical temporary protection against ero-sion and have been used in permanent works, though the wirecrates may be subject to corrosion. The standard metric size is2 x 1 x ] m but thinner mattresses are available. They offer greatresistance to removal by flow and a gabion apron has consider-able flexibility in adjusting to scour, though less than an apronof rip-rap.

Asphalt. Asphalt provides a smooth impervious cover butdoes not have much flexibility.

Sheets of polypropylene. These, and other synthetic materials,woven to a fine mesh provide an effective filter layer over sandand have been used to form thin mattresses, with pockets filledwith cement grout, for side slope protection.

Brushwood fascine mattresses. These form a traditional protec-tion consisting generally of willow twigs bound in bundles andformed into longitudinal and lateral layers bound togetherbefore it is launched by weighting with stone and sinking intoplace, which is still used and has a considerable life under water.

Vegetation. Vegetation, in particular certain grasses andshrubs, when established above normal water level, can protecta bank against occasional high level wave wash or even shallowovertopping.

For protection of formed banks in cut or fill, any of the abovematerials would be suitable (see also Chapter 18) subject toadequate protection against scour of the toe of the bank or thechannel bed near it. This may be provided by a line of sheetpiling at the toe or by a flexible apron laid horizontally whichwill subside and protect the underwater slope when scouroccurs. Quarried stone rip-rap is usually used for the apronwhere available.

Maximum

Stone

weig

ht (kg

)

22.2 Enclosed flow

22.2.1 Head loss in large conduits and tunnels

Head loss in pipes is dealt with on pages 5/8 to 5/11. Head loss inlarge conduits and tunnels may similarly be estimated by theDarcy formula:

i = /I V1JIgD = /I K2/8gm (22.10)

where / is the hydraulic gradient, A the friction factor, V themean velocity, D the diameter of circular conduit flowing full, orm the hydraulic radius to be used for part full and noncircularconduits. A and Manning's n are related by:

n = Ji112D116IlO.* = VW6/13.6 (22.11)

In nearly all actual cases of large conduits the boundary cannotbe classed as smooth or rough but falls within the transitionregion. A therefore depends on the effective roughness and onthe Reynolds number VD/v or 4 Vm/v, where v is the kinematicviscosity (for values of v see pages 5/8 to 5/10). Although manytypes of roughness are composite, e.g. smooth concrete withprojections due to formwork joints, and therefore the equivalentsand roughness concept is not completely representative, it doesprovide a method of predicting the friction factor, based onrecorded experience. In the case of new works this depends onthe type of forms used, quality of workmanship and degree towhich projections are ground down. Deterioration occurs withage and use. A steel lining may corrode and be roughened bytuberculation, as for pipes. Concrete inverts may be roughenedby abrasion during river diversion. There may be deposits due toleaching through joints and cracks in a concrete lining, evenvegetation and animal growths, while the deposit of slime byuntreated water is commonplace.

Typical values of equivalent sand roughness k for newsurfaces, based mainly on Ackers42 and USBR experience,43 aregiven in Table 22.1.

It is more difficult to predict the friction factor in a tunnelafter many years of use; the best guide is often obtained fromactual measurements in similar tunnels under similar con-ditions. Observations in many tunnels have been published.43^*5

The effect of slime has been studied by Colebrook.45

Table 22.1

Surface k range (mm)

Asbestos 0.012 to 0.015Spun bitumen lined 0.0 to 0.030Spun concrete lined pipes 0.0 to 0.030Uncoated steel 0.015 to 0.060Coated steel 0.03 to 0.15Rivetted steel 0.3 to 6.000Wood stave, planed planks 0.2 to 1.5Concrete:

against oiled steel forms with no surfaceirregularities 0.04 to 0.25

against steel forms, wet mix or spunprecast pipes 0.3 to 1.5

against rough forms, rough precast pipesor cement gun 0.6 to 2.0

smooth trowelled surface 0.3 to 1.5Glazed brickwork 0.6 to 3.0Brick in cement mortar 1.5 to 6.0Ashlar and well laid brickwork 1.5Rough brickwork 3.0

When a suitable k value has been determined, the relativeroughness k/D or k/4m can be calculated and a value of Adetermined from Figure 22.17 which is based on the Karman-Nikuradse-Prandtl formulae with Colebrook-White transitionsdescribed on page 5/9). Some examples of large-conduit obser-vations are shown in Figure 22.1 T.43-44 Figures 22.18 and 22.19show characteristics of circular and horseshoe conduits flowingpart full.

The surface of conduits for high-velocity flows should be to avery high standard of finish to avoid damage by cavitation - seepage 22/7.

22.2.2 Unlined and lined-invert tunnels in rock

Excavated rock surfaces are very rough and the hydraulics arecomplicated by 'overbreak', i.e. excavation beyond the mini-mum required by the specification. Rahm found a relationbetween the variation in cross-sectional area and the friction

Reynolds number, RFigure 22.17 Head loss in uniform conduits. Open symbols,computed; solid symbols, observed. (After US Army Corps ofEngineers (1952-70) HydraOlic design criteria. US Army EngineerWaterways Experiment Station, Vicksburg, Mississippi)

Computed-open symbolObserved-solid symbol

Rough flow limit

Smooth pipes

DenisonFt. Randall, vinylFt. Randall, coal tarEnidOahePine Flat, 52Pine Flat, 56-58

Maximum smooth pipe sectionMinimum smooth pipe section

Relati

ve ro

ughn

ess,

Resis

tance

coeff

icient,

A

Figure 22.19 Critical depth in circular and horseshoe conduits

factor. The subject was further developed by Colebrook45 andagain by Wright,46 who showed that the resistance of unlinedtunnels can be reduced considerably by providing a concreteinvert.

22.2.3 Transitions and bends

Transitions may be from circular to noncircular sections or viceversa, or from one circular section to another of differentdiameter. In conduits for high-velocity flows, transitions aregenerally gradual to avoid flow separation and possibly cavi-tation. It is also necessary to adopt moderate rates of expansionif head is to be conserved and instability of flow downstreamavoided. Circular sections can be merged into rectangular orhorseshoe sections without double curvature and avoidingsharp local divergences. Figure 22.20 shows head loss in dif-fusers of circular section; curves of similar pattern but slightlydiffering values apply to diffusers of rectangular section.47 It willbe seen that for expansion ratios of 2 or more the head loss maybe considerable unless the angle of divergence is small. Whererapid expansion is required, divide walls may be used so that the

Figure 22.20 Head loss coefficient Kd of conical diffusers withtailpipe. (After Miller (1971) Internal flow. A guide to losses in pipeand duct systems. British Hydro-mechanics Research Association,Cranfield)

Figure 22.18 Area and hydraulic radius of conduits, part full. Forkey, see Figure 22.19

flow is carried in a number of ducts, each of which is areasonably efficient diffuser while the overall angle of expansionmay be as much as 90°. For head loss in a sudden enlargement,see Chapter 5, pages 5/10 and 5/11; expansions of this type aresometimes used for energy dissipation in closed conduits. Con-tractions may be more rapid than diffusers, but to avoid headloss due to the formation of a vena contracta in the downstreamconduit, it is desirable to provide a rounded external anglebetween the transition and conduit at a radius of at least one-sixth diameter. In high-velocity flow this is an area of potentialcavitation and the radius should be greater.

Head losses at bends in large conduits are similar to those inpipe bends (see pages 5/11). A compromise then has often to bereached between the greater head loss of a short-radius bendand the greater cost of long-radius bend; bend radii of between1.5 and 3 diameters are often adopted. The flow instabilityinduced by a bend persists for a distance of many diametersdownstream and may affect the performance' of turbines orpumps.

Bifurcations and manifolds, dividing the flow, for example,for two or more machines, are generally designed with great careto achieve a smooth change of velocity, absence of swirl andminimum head loss. Model tests with air are useful to indicateflow pattern and pressure drop in closed conduit transitions;relatively low pressures are used to avoid compressibility effects.

Transitions leading from subcritical flow in open channels toclosed conduit flow may, where the approach velocity is low, bedesigned on the same principles as apply to intakes fromreservoirs (see page 22/25). Sharp corners lead to separation andthe formation of a vena contracta with head loss; this may beavoided by providing a rounded or bellmouth entry. Withhigher approach velocity the transition should be more gradual,with curves of larger radius. To avoid the formation of ahydraulic jump with resulting air entrainment the design shouldbe such that the contact between free surface and roof occurswhere the flow is subcritical, preferably with Froude numberwell below unity.

22.2.4 ExitsIf the exit of a conduit is fully or partially submerged, head losscan be reduced by providing a gradual expansion, which canoften be extended in the tail channel. If the conduit exit is notsubmerged, a free surface may develop some distance upstreamof the exit portal, even when the conduit is flowing underpressure. The depth of the exit depends on downstream condi-tions but where tailwater level is low the flow becomes supercri-tical and the conduit exit acts as a control. The end depth stilldepends to some extent on the tail channel, particularly whetherthe flow is supported at the sides and bed, but the end depth maybe estimated from Figure 22.21. If the emerging flow is supercri-tical and downstream flow subcritical, a hydraulic jump willoccur and a stilling basin may be needed.

22.2.5 Flow routingFlow through conduits can be routed and energy gradientplotted by use of the Bernoulli equation (see page 5/8). Allow-ance should be made for head loss due to friction, bends,transitions and hydraulic jumps. Subcritical flow is routed in anupstream direction starting from the tail channel or a control,and supercritical flow in a downstream direction, using stepmethods if necessary. Computer programs exist which ease theburden of calculation. To locate a hydraulic jump the pressure-momentum theorem can be used, taking account of the slope ofthe conduit and the pressure against the conduit roof if sub-merged downstream. The method is described by Kalinske andRobertson.48 Critical depths in circular and horseshoe conduits

Figure 22.21 Exit depth in circular conduits. V is the meanvelocity in the conduit flowing full (based on USWES data). (AfterUS Army Corps of Engineers (1952-70) Hydraulic design criteria.US Army Engineer Waterways Experiment Station, Vicksburg,Mississippi)

may be determined from Figure 22.19, and diagrams facilitatingcomputation of jumps in conduits of circular and other cross-sections have been published.2^* In cases where hydraulic jumpsmight occur in closed conduits with undesirable results, due toadditional head loss or air (see below), it is recommended thatthe routing be repeated for several discharges using both highand low values of head loss coefficients and upper and lowerlimits of tailwater rating curve, to obtain a complete account ofthe flow.

22.2.6 Drop shaftsSometimes flow has to be dropped from a high-level system to alow-level system, e.g. from shallow sewers to deep interceptors,from river intakes in mountains to a water-transfer tunnel, fromthe drainage of an open-pit mine to an adit from an adjacentvalley. An economic solution is to use a shaft, but there areproblems associated with air entrainment and release in anyshaft system, especially if the base of the shaft is submerged bythe hydraulic conditions in the low-level system. These problemscan be minimized by generating a vortex at the top of the shaft,either by a scroll-shaped inlet chamber (Figure 22.22a) or by atangential vertical slot (Figure 22.22b).

The vortex action ensures that the flow down the shaft willcling to the walls. This has the advantage of minimizing airentrainment and encouraging the return of air back up thecentre to the head of the shaft, and at the same time maximizeshead dissipation in the shaft by wall friction. The vortex motionis persistent: it will continue for the full length of fairly deepshafts provided the entry is well designed. The theory of thescroll inlet is given by Ackers and Crump,49 and the slot inlet hasbeen investigated by Eppema, Jain and Kennedy.47

If the bottom of the shaft is submerged, as in Figure 22.22c, itwill be necessary to provide an air-release chamber. If the full-bore shaft velocity exceeds about 0.5 m/s, bubbles will be carrieddown with the flow. Problems - perhaps serious ones - couldarise if this entrained air was allowed to travel along the tunnelsystem (due to potentially explosive blowout further down-stream) and hence a stilling chamber should be provided toallow the entrained air to separate and rise to the crown of thechamber where the bubbles will coalesce to return via the ventpipe.

For unsubmerged conditions, Figure 22.22a illustrates a typeof collecting chamber at the base of the shaft found suitable for

a) Normal sewage structure with vortex chamber inlet

Figure 22.22 Vortex drop. Alternative forms: (a) normal sewagestructure; (b) alternative deep slot inlet; (c) outlet chamber forsubmerged discharge with air-release provision

c) Outlet chamber for submerged discharge with air-release provision

Outlet chamberfor freedischarge

Outlettunnel

SECTION

Crenellateddish

Air bubbles

Vent pipeShaft flows fullof air/watermixture

Annulusof flow

Level ofsubmergence

Annulus of flow

Air entrainment

Vent pipe

Shaft

Throat

Minimum air core

b) Alternative deep slot inletSECTION

PLAN

Vortex chamberSpiral flow

Inlet

Lip of bell mouth

PLAN

Slot

TaperInlet

Slot

sewerage systems. With deep shafts, the annulus of flow mayreach terminal conditions where the gravitational component isequalled by the friction at the shaft walls, and so there is a limitto the amount of energy to be dissipated at the base of the shaft.

22.2.7 Air problems in conduits

Air entrained at high velocity releases through gates and valvesinto conduits, e.g. at outlets from reservoirs, air entering fromdrop shafts or junctions and air entrained at hydraulic jumps,can lead to dangerous air and cavitation problems unless theconduits are adequately vented. Air can also collect and restrictthe flow of water. Air release valves, often combined withvacuum relief to admit air if pressure falls below atmospheric,are therefore provided at high points. Vents are often providedin horizontal tunnels downstream of junctions where entrainedair may enter. Air which has collected beneath the soffit tends tobe carried forward by the flow, even against a small gradient,but with a variable flow may move upstream and downstream atdifferent times. At vertical shafts in pressure conduits and atdeeply submerged exits the intermittent escape of air producesshock waves due to slap on the soffit as water replaces the air.This effect can be minimized by vents for controlled air release.

Hydraulic jumps entrain air and when a jump in a conduit isin contact with the soffit much of the air is released downstream.Following model tests in a conduit with various slopes byKalinske and Robertson48 and others, and several observationsat full scale, the US Army Corps of Engineers11 use the formula:

^=0.03(F,-1)16 (22.12)

which gives higher values than found in the model tests to allowfor scale effect. Here P is the air:water ratio QJQw F1=VJV(&4)> V\ is tne upstream velocity and de the effective upstreamdepth ( = water area:surface width). A particular application ofthese formulae is the estimation of air demand downstream ofgates or valves located in closed conduits, where high-velocityflow at part openings is transformed to full-conduit flowthrough a jump (see Figure 22.23). Full-scale observations inthree different cases showed that with rectangular gate openingspeak demand occurred at 60 to 85% opening, with a secondarypeak at about 5%. Further analysis has been provided bySharma.50

Sailer51 compared these curves with conditions in a number offull-scale inverted siphons and found verification in that fivecases where blowback had occurred were represented by highervalues of (F1-I) than shown by the curves, while others givingno trouble were on or below the curves. With large flows,blowback through the jump is, like 'blowout' at the exit,explosive and potentially dangerous.

22.3 Spillways

22.3.1 Purpose and types

A spillway is provided to remove surplus water from a reservoirand thus protect the dam and flanking embankments againstdamage by overtopping.

The best type and location of a spillway depends very muchon the topography and geology of the dam site and adjoiningarea, and on the type of dam. Where the dam is of concrete ormasonry founded on hard rock, the spillway may be within thedam, consisting either of a high-level overflow or of submergedorifices, discharging into the river bed beneath. In the case of anearth or rockfill dam, it is usual to site the spillway away fromthe deepest part of the dam; high flanking ground or a saddleaway from the dam site can be suitable locations where aspillway channel may be excavated and control structure pro-vided (see, for example, Figure 22.24). Where the dam is built ina narrow gorge and there is no suitable separate site for thespillway, a side-channel spillway is often adopted (Figure22.25).

If control is by a fixed ungated weir, the maximum retentionlevel of the reservoir is the weir crest level; at times of spill thereservoir level rises and sufficient freeboard has to be allowedabove maximum water level, which is the level at which thedesign maximum flood discharge is released. In the case of gate-regulated spillways, on the other hand, flood flows can bedischarged with reservoir at retention level, which need never beexceeded. For a given dam height, retention storage can thus begreater but, because there is less flood storage, the spillwaycapacity also may have to be greater. The gates, however, enablethe reservoir to be drawn down in advance of a flood peak, givenadequate forecasting. Low-level orifices, having greater capacitythan required for purposes of normal supply, have greatercapability than has a gated crest overflow in drawing down areservoir in the event of damage to the dam, an important aspectin areas where earthquake risk is present. But crest overflowweirs have a greater rate of increase of capacity as a reservoirlevel rises above normal, thus providing additional safety mar-gin.

Cost is a major consideration in the choice between a regu-lated and an unregulated spillway, but spillways without gateshave advantages in respect of reliability, absence of mechanicalmaintenance problems and no power requirements. They aretherefore often adopted at remote sites and for small damswhere the cost of gates would not be justified.

Siphon spillways carry some of the advantages of both gatedand ungated spillways. They can be designed to prime andoperate to maximum discharge within a small range of reservoirlevel and they are automatic, with no moving parts.

Another type of spillway, particularly suited for use withearth or rockfill dams is the bellmouth or 'morning glory'spillway, which can be built quite independently from the dam,and which is described further in section 22.3.5. If the reservoiris for water supply, the bellmouth and shaft are often combinedin the same structure as a drawoff tower and the low-level tunnelcan be used for river diversion during construction, as discussedand illustrated in section 22.4.1.

In many cases it is advantageous to provide more than onespillway. Instead of relying on a single spillway to control all

Figure 22.23 Stability of entrained air downstream of hydraulicjumps in circular conduits. (After Kalinske and Robertson (1943)'Closed conduit flow. Symposium on entrainments of air in flowingwater.' Trans. Am. Soc. Civ. Engrs, 108, Paper 2205, 1435)

The air pumped by the jump may be carried downstream bythe full-bore flow but, if the velocity is insufficient for this, airwill collect immediately downstream of the jump and when aquantity of air has accumulated it will 'blow back' through thejump. Figure 22.23 shows the limiting conditions for the air justcarried by the flow, as found by Kalinske and Robertson.48