Hydraulic Structures. The late A R Thomas OBE, BSc(Eng), CEng, FICE, FASCE Formerly consultant, Binnie and Partners

Transcription

1 22 Hydraulic Structures The late A R Thomas OBE, BSc(Eng), CEng, FICE, FASCE Formerly consultant, Binnie and Partners Peter Ackers MSc(Eng), CEng, FICE, MIWEM, MASCE Hydraulics consultant Contents 22.1 Open channel structures 22/ Basic concepts 22/ Transitions 22/ Weirs and flumes 22/ Control weirs and barrages 22/ Permeable foundations 22/ Energy dissipation 22/ Scour and erosion 22/ Enclosed flow 22/ Head loss in large conduits and tunnels 22/ Unlined and lined-invert tunnels in rock 22/ Transitions and bends 22/ Exits 22/ Flow routing 22/ Drop shafts 22/ Air problems in conduits 22/ Spillways 22/ Purpose and types 22/ Channel spillways 22/ Weirs 22/ Low-level outlets 22/ Bellmouth, shaft and closed-conduit spillways 22/ Siphon spillways 22/ Chutes 22/ Energy dissipation 22/ Reservoir outlet works 22/ Intakes 22/ Vortices 22/ Screens 22/ Gates and valves 22/ Gates 22/ Valves 22/ Air demand 22/ Cavitation 22/32 References 22/32 This page has been reformatted by Knovel to provide easier navigation.

2 22.1 Open channel structures Basic concepts The Bernoulli theorem and critical flow Two important concepts in the hydraulics of flow through structures are the Bernoulli and pressure-momentum theorems. The former (see page 5/8) expresses conservation of energy, and when applied to straight-line flow in an open channel, taking bed level as reference level, may be expressed as: H=d+<xV 2 /2g (22.1) where H is the specific energy head, d the depth of flow above the bed, a coefficient, V the mean velocity and g the gravitational constant Where the flow is curvilinear, depth will vary across the channel and d is a mean value. Under normal conditions of flow in wide uniform channels, a = 1.02 for smooth boundaries but higher for rough boundaries. For example, if n/d* 16 = (where «= Manning's roughness factor) a= In order to simplify calculations where velocity head is relatively small, a is often assumed to be unity. Head loss must be allowed for in the value of//. For channels of rectangular cross-section, Equation (22.1) can also be expressed as: H=d+aq 2 /2gd 2 (22.2) where q is the discharge per unit width of channel Q/B where Q is the total discharge and B the width To derive d from known H and q, with a = 1 Figure 22.1 may be used. Figure 22.1 Specific energy of flow in open channels. Depth of flow d may be determined from specific energy head AY and discharge per unit width q In a channel of rectangular cross-section with horizontal bed and a = 1 (as, for example, immediately downstream of a contraction) critical velocity V c = (gdy 12 and critical depth Jc=V 2 Jg = WgY 13 (22.3a) (22.3b) In the more general case, applicable to non-rectangular channels of slope angle O: critical velocity F c = (* m^ S j ^^ For critical depth in circular and horseshoe-shaped channels see Figure (page 22/17) Froude number F= V/(gdy 2 is a useful indicator of the stability of free surface flow. When F< 1, the flow is subcritical; when F= 1 it is critical and when F> 1, supercritical. As Fapproaches unity from either direction, the flow becomes unstable and surface waves may develop. Surface undulations may occur in subcritical flow when F exceeds The pressure momentum theorem Unlike the Bernoulli theorem, this applies whether there is head loss or not. It follows from Newton's second law and can be expressed as: P-M 1 -M 1 -ZQ(V 2 -V 1 ) (224) where P is the resultant force on a mass of fluid over a specified length, M 1 and M 2 represent momentum at entry and exit, w is the specific weight of fluid, Q the constant discharge and F 1 and V 2 are the flow velocities at entry and exit P usually is the resultant of fluid pressures and boundary pressures in the direction of flow Hydraulic jump This is a relatively abrupt change in flow depth when the flow changes from supercritical to subcritical as described on pages 5/17 to 5/19 and illustrated in Figure Except at the limiting condition when both depths are critical, it involves a head loss, dissipated in extra turbulence. In Figure 22.1 it can be represented by a transfer from a point on the supercritical curve to a lower point on the subcritical curve. It may be stationary or moving. Its character and movement can be determined by application of the pressure-momentum equation (Equation (22.4)). In a rectangular channel of width B and horizontal bed, P 1 = ^Bd 2 at entry and P 2 = ^Bd] at exit, where d, and d 2 are depths; no other pressures have components in the direction of flow. If pressure plus momentum of the supercritical flow (/>, + M 1 ) exceeds the pressure plus momentum of the subcritical flow (P 2 + M 2 ), the jump will move downstream, if they are equal the jump will be stationary and if (P 2 -I- M 2 ) exceeds (P 1 + M 1 ) the jump will move upstream. For a stationary jump in a horizontal rectangular channel, the relationship between upstream and downstream depths is: =V( FJ)-0. 5 (225) where d } and d 2 are the conjugate depths, i.e. the depths of flow upstream and downstream of the jump, respectively, and F 1 is the Froude number upstream of the jump A number of laboratory tests have shown close conformity to this relationship. The jump height, d- = (d 2 -*/,), on a horizontal floor may be

3 determined from Figure 22.2, which may be extended by use of Equations (22.1) and (22.5). The length of a jump cannot be precisely defined but is approximately 5 to 8 x d f the greater factor applying to lower Froude numbers. 1 F 1 = V^,. id,/!,)* Figure 22.2 Hydraulic jump relationships for horizontal or gently sloping beds. (After Thomas (1958) Discussion on Bradley and Peterka (1957) op. cit. Proc. Am. Soc. Civ. Engrs, 84, HY2, Paper 1616) Equation (22.5) and Figure 22.2 give results with little error in channels with beds sloping at 10% or less, but with steeper slopes the components of vertical pressures have significant effect. In channels which are not of rectangular section the jump may be distorted in plan, but the pressure-momentum equation (22.4) can be applied to the whole cross-section. Several methods for calculating the conjugate depths in channels of various shapes are available. 2 ~ Transitions Subcritical flow In channels of variable cross-section, Equation (22.1) or Figure 22.1 may be used to determine depth of flow, provided changes are sufficiently gradual to avoid significant head loss. In converging flow, q and hence </ c increase with the reduction in width. Therefore with subcritical flow and constant specific energy H, it is evident from Figure 22.1 that d reduces. As examples, a channel may be contracted at a bridge and allowed to expand downstream, or a gated regulator may have a raised sill. In both cases the surface is depressed in the contraction. Provided the flow remains subcritical the process is reversible in a downstream expansion. If, however, a contraction reduces the depth to the critical value, any further contraction has the effect of raising 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) example of transition from stilling basin to canal in erodible material

4 mum depth possible for any given specific head (see Figure 22.1). The result is a rise in upstream water level, the excess head generates supercritical flow downstream of the throat, or section of maximum contraction, and is lost in a hydraulic jump where the flow changes back to subcritical. The throat is then acting as a 'control'. If head loss is to be avoided, the Froude number should not be allowed to approach close to unity. Convergences for subcritical flow may be rapid but external angles in the side walls should be avoided by the use of largeradius curves, as shown in Figure 22.3a. Diverging channels in subcritical flow are liable to result in separation of flow from one or both side walls unless expansion is gradual. Side expansions of 1:10 are usually satisfactory. Sharper divergences may be followed in some conditions; 6 expansion is assisted by a rising floor, baffle blocks or a raised sill downstream and by a hydraulic jump. The expansion ratio is also a factor - see page 22/17 - where expansions in enclosed flow are discussed. Some examples of diverging transitions are shown in Figure 22.3b to 22.3e. Figure 22.3e illustrates a transition from a drop structure to the canal beyond. Changes of direction cause head loss because of the secondary flow which distorts the flow pattern; the flow near the bed is deflected more sharply than the surface flow. If the bend is very sharp there may be complete separation at the inner boundary. These effects may be minimized by adopting a large radius for the bend. In rectangular channels with depth: width ratio of 0.6 to 1.2, Shukry 7 found that head loss became minimal with radius 3 x width. In channels with credible boundaries, unless bank protection is provided, the minimum radius depends on the velocity and credibility of bank material. On irrigation canals in India the radius is generally 20 to 30 x surface width Transitions - supercritical flow The problems here are different from those discussed so far. Whereas in subcritical flow, pressure changes can be transmitted laterally from the side walls to the whole flow, inducing change of depth or direction, in supercritical flow the velocity of transmission of a small disturbance or wave is less than the flow velocity. The result is that a change in direction of a side wall creates an oblique shock wave which is reflected from side to side downstream. Convergences and divergences should be very gradual. Figure 22.4 shows the shock waves created by a convergence. A sharp convergence may cause high-velocity flow to ride up and overtop the wall. It is therefore preferable, if possible, to locate convergences and other changes in wall direction where the velocity is low, e.g. at the upstream end of a chute, and maintain a straight chute where velocity is high. It may, however, be possible to use lateral inclination of the bed, e.g. superelevation, to assist in convergence or divergence. Where shock waves are unavoidable, they will occur in a zigzag pattern for some distance downstream owing to reflection from side walls. The side walls should therefore be high enough to contain them at Shock front Negative disturbances Figure 22.4 Example of shock waves at convergence in supercritical flow. (After lppen etal., (1951) 'High-velocity flow in open channels.' Trans. Am. Soc. Civ. Engrs, 116, Paper 2434) points of reflection. Sloping side walls, as in trapezoidal channels, are particularly vulnerable. Methods are available for the calculation of pattern and height of shock waves in simple cases and for minimizing their effects. 9 Scale models may also be used. Long-radius bends are preferable to short radius, especially where overtopping is a danger. Knapp 9 recommends compound curves for the side walls of bends, with radius 2r in the approach and exit over a length of B/tan P in each case, where r is the radius of the centreline of the main curve, B is the channel width and sin /?= F, the Froude number. This arrangement creates counter waves which tend to neutralize the shock waves generated by the main curve, so reducing disturbances downstream Weirs and flumes 22.7J.7 General Weirs are used to control flow or water levels, or to measure flow. They range from low walls across streams to the spillway crests 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 discharge coefficient, g the gravitational acceleration and H the total head level upstream above weir crest, normally taken as H 1 + FJ/2g, where /*, is the upstream depth of flow above weir crest level and K 1 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 take account of departure from flow on a horizontal bed. The coefficient depends on the shape of the weir and, in general, it varies with head over the weir; only in a few special cases is it constant. There are many weir profiles, each with different characteristics in relation to discharge coefficient and modularity. Weir flow is said to be 'modular' or 'free flow' when it is unaffected by tailwater level. The point at which a rising tailwater begins to affect the upstream head or flow is termed the 'modular limit', expressed as the ratio of downstream to upstream depth above crest level. Values of the coefficients of weirs of many different profiles have been published, e.g. by King and Brater 9 (see also section 22.5). In this section, some types in general use are considered as follows. Sharp-crested weirs. These are formed of metal plates and are used for precise measurements of flow. Flow over weirs with narrow crests having rectangular upstream corners is effectively sharp crested, with a coefficient c approximately 0.406, provided the nappe springs clear and is fully vented. Triangular profile weirs. These have sensibly constant coefficients throughout their modular range; no venting is required and the coefficient is greater than that of a sharp-crested weir. For example, the Crump weir (Figure 22.7), with 1:2 upstream and 1:5 downstream slope, has a free-flow coefficient c of and a modular limit (within 1% of discharge) of Weirs of this type are widely used for measurement of stream flows. Trapezoidal profile weirs. Trapezoidal profile weirs have flat upstream and downstream slopes and narrow horizontal crests, formed by the gate sill, are often used in gated controls and barrages (see, for example, Figure 22.10). They have a free-flow coefficient which is variable but generally exceeds and under drowned conditions the afflux is small. Broad-crested weirs. These have horizontal crests wide enough

5 For laboratory and other small-scale measurements, sharpcrested weirs consisting of thin plates in the form of rectangular or Vee-notch weirs are found convenient. Standard formulae or tables of discharge for these are available For measurement of larger flows in the field, however, sharp-crested weirs have drawbacks, particularly the need to v vent the nappe, the head difference required to ensure modular conditions and the effect of accretion of upstream bed level following the erection of a gauging weir. Weirs of several other types have been thoroughly investifor parallel flow effectively to develop. Control is then at the point of critical depth so that c=1.70. To ensure that this condition applies and c is constant, the upstream edge should be rounded to avoid the formation of a roller above crest level. In practice, the value of c is 1 to 3% lower due to friction loss. If the downstream floor falls at a gentle slope, say 1:10, the modular limit is between 0.7 and 0.8. Broad-crested weirs have been extensively used for flow measurement and for proportional distribution of flow at dividing points in irrigation systems. Free-nappe profile weirs. Free-nappe profile weirs with profile according to the shape of an undernappe of flow over a sharpcrested weir (Figure 22.5) have been widely used for overflow spillway crests. The standard profile is one with vertical upstream face and weir height P large compared with head over crest, H. The profile varies with smaller values of PjH and sloping upstream faces. This profile has the advantages that c is comparatively high for the profile discharge (i.e. the discharge corresponding to the nappe profile used), subatmospheric pressures do not develop within the range up to profile discharge, no venting is required and the flow characteristics are well documented and predictable. Ratio of coefficients Submergence ratio C =?/A/' 5 (submerged flow) C f = 9/// f 1 ' 9 (free flow) Figure 22.6 Free-nappe profile weirs. Effect of tailwater level on discharge coefficient. (Based on USBR data; US Department of the Interior (1960) Design of small dams. Denver, Colorado) pattern is uncertain and may change from diving nappe, which follows the downstream weir face, to surface nappe, which separates near the weir crest, a roller developing beneath. Observations of discharge related to upstream and downstream heads or water levels therefore cannot be regarded as of general application. Nevertheless, good indications can be obtained. Figure 22.6 shows the effect of submergence on standard freenappe profile weirs 12 and Figure 22.7 the effect on Crump triangular profile weirs. 13 Figure 22.5 Discharge coefficient of free-nappe weirs at design discharge. (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 is shown in Figure By adopting a profile discharge lower than the maximum discharge, a higher coefficient is obtained at flows exceeding profile discharge. 10 Discharge in excess of the profile discharge causes pressures on the face of the weir to fall below atmospheric in the vicinity of the crest where the curvature is sharp. 11 This is usually acceptable provided that the structure is safe against uplift, and a reasonable margin of pressure is allowed above cavitation level to allow for fluctuations. Profile coordinates have been published 12 from which weirs of standard profile and some variations can be designed. Sharp side contractions at the abutments of weirs reduce the discharge capacity locally. They should be curved as in Figure 25.3a. Piers have a similar effect, to avoid which spillway piers are often extended upstream, so that the contraction at the pier noses occurs in a region of lower velocity Submerged weirs The effect of a tailwater level above the modular limit is to raise the upstream water level for a given discharge. The degree to which the upstream head or discharge is affected depends on the weir profile: moreover in certain ranges of submergence the flow Figure 22.7 Afflux at submerged Crump weirs. (Based on data of White (1971) 'The performance of two-dimensional and flat-vee triangular profile weirs/ Proc. lnstn Civ. Engrs, Paper 735OS!) Measuring weirs and flumes

6 gated and are subjects of national and international standards. A comprehensive account of the performance and use of the main types of weir and flumes is given by Ackers et a/. 14 Bos 15 has reviewed a wide range of devices capable of use for flow measurement. Those most useful in a civil engineering context depend on the creation of critical flow. This can be induced by providing a sill or weir, or by contracting the width, or by a combination. The critical flow formula in a rectangular cross-section channel, Equation (22.6), is the most basic formula for flow measurement by weirs and flumes, and applies to free flow, i.e. when the critical flow at the crest of a weir or in the throat of a flume is not drowned by the tailwater level exceeding the modular limit (see para ). The cross-section of flow may also be made nonrectangular - V-shape, U-shape or trapezoidal - for particular applications, but then adjustment has to be made to the flow formula of Equation (22.6). For precise measurement with weirs and flumes, allowance for boundary layer development and other secondary effects has to be made. 14 Unless there is already a local drop in level, the introduction of a measuring device will result in a rise in upstream level, though this may be quite small if a device with high modular limit is chosen, or a Crump weir with crest tapping which can be used when drowned by high tailwater level. 13 Where the range of discharge is large and it is desired to obtain an accurate measurement of low flows, a stepped weir may be used, consisting of a short weir at low level for the low flows flanked by longer weirs at a higher level. Alternatively, a flat Vee-weir may be used with crest tapping for submerged conditions. 13 In the UK, broad-crested weirs with a round nose and Crump weirs have been accepted as standard. 16 In the US, Parshall measuring flumes have been widely used. 17 These were designed with plane surfaces so that they might be easily constructed of wood or concrete, c is not constant but calibration formulae and tables are available. Where the stream to be gauged carries appreciable bed load, a critical-depth flume with a flat or nearly flat bed at the channel bed level is desirable. The bed load can then pass through without excessive accretion upstream, though there may be some at the sides. A measuring flume of this type is shown in Figure The degree of contraction sufficient to ensure modular flow can be checked by comparing calculated upstream water levels (using c=1.66) with existing tailwater levels. The broad-crested weir coefficient is applicable, adjusted for head loss upstream of the location of critical depth. 14 Longitudinal section Figure 22.8 Measuring flume with flat floor for debris-laden flow Structures of many other types are used for flow measurement, mostly depending on the critical depth principle or on orifice control as, for example, devices on irrigation canal outlets Control weirs and barrages Gated weirs Weirs are used to control the water levels of a river or canal, for such purposes as diversion of flow into canals, extraction of water by pumping, creating head for hydro-electric power or maintaining a required depth of water for navigation. A fixed weir also raises flood levels, which may not be acceptable. A gated weir, or barrage, however, does not have this drawback if the gate sill is level with the river bed, or on a low weir crest. The gates are kept closed during low flows, maintaining the required upstream water level, but opened as may be necessary to pass floods. The range of water level is thus much less than with a simple weir, and the gates can be operated to maintain constant water level over a wide range of flow. Types of gates are described on pages 22/11 to 22/28. The choice of crest profile depends on the circumstances. For example, a weir with a free-nappe profile is suitable where the crest is to be above the upstream channel bed and there is considerable head difference from upstream to downstream. On the other hand, a low crest with flat triangular profile is better suited where, at high rates of flow, the afflux or rise of upstream water level due to the weir must be kept to a minimum Control structures in alluvial rivers Whereas structures in rivers with rocky beds and banks can often be of simple design, with an upstream cutoff wall into the rock and a basin or bucket energy dissipator downstream, the design of control structures in alluvial rivers requires consideration of many other factors. Firstly, the site and orientation of the structure in relation to the river channel pattern is most important and generally should take priority over other considerations. Alluvial rivers without constraint by structures, training works or outcrops of rock or clay, may change course over a period of years, forming new patterns of river channels. The history of a river course is a good guide to such tendencies. The site for a control structure should be a stable one in the long term, i.e. it should remain operative despite changes in the channel pattern over a number of years, maintained if necessary with the aid of training works. Where a weir or barrage is used for diversion or abstraction of water it is usually desirable to ensure that the quantity of sediment in the water abstracted is a minimum. The best location for the offtake with this in view is generally on the outside of a bend, and the training works should be located to maintain the approach channel accordingly. This consideration applies even where special arrangements are made for sediment exclusion. A typical barrage forming the headworks of an irrigation canal system on a large river in Pakistan is shown in Figure A weir or barrage may occupy only a small part of the width of river channel and floodplain. For example, in India and Pakistan it is general practice to make the width of waterways between abutments equal to or rather greater than the width of Lacey regime channel 4.8 1/2 where Q is the maximum design discharge in cubic metres per second. 19 Flanking bunds or embankments are then required extending from the abutments to high ground on either side. Where flood levels are being raised by the control, marginal bunds or flood embankments are often provided extending upstream on each bank. To prevent oblique approach, protect the bunds and avoid outflanking; guide banks are required extending upstream from the abutments (see Figure 22.9). In stable rivers these may be quite short, but where there may be wide swings in the river course they are generally approximately equal in length to the width of waterway between them. In addition, in rivers of this type, spurs or groynes may be provided upstream, but these may cause further

7 Left bank of river Temporary cofferdam around working area Lower Jhelum feeder canal Radial gates Pond level Flow Roadway Right guide bank Barrage Left guide bank Left bank of river Rasul Qadirabad link canal Right bank of river Spur Piers at 20.4 m cc Impact Deflector blocks blocks Stone apron Reinforced concrete Concrete block apron Reinforced concrete Mass concrete Steel sheet pile cut-offs Concrete block apron Stone apron Figure 22.9 Rasul barrage on the river Jhelum, Pakistan. General layout (top), longitudinal section (above). Note the flow from right in layout (top) and from left in section. (Consulting Engineers: Coode and Partners) trouble unless correctly located. Model tests are desirable before construction. Similar measures are used to train alluvial rivers at bridges. The guide banks and spur heads are protected against scour, by rip-rap or concrete slabs (see pages 22/15). Low-level sluices provided in the weir or barrage, generally adjoining the canal regulator, have three functions: (1) they discharge river flow during construction at a low level; (2) during operation of the works they enable the approach to the regulator to be sluiced at intervals to remove deposit of sediment deposit; and (3) if kept open during a flood they draw the main stream towards the canal regulator, thus maintaining a deep channel for water to gain access to the intake during the dry season. To fulfil these functions the sill should be well below the canal regulator sill level and the sluices should have sufficient capacity to influence flood flow distribution. A divide wall is often provided normal to the weir between undersluices and weir to enable the canal to draw supplies from a pocket of lowvelocity water, the undersluices being kept closed. A divide wall also facilitates the sluicing operation. If the canal must operate continuously, control of coarse sediment can be provided by tunnels beneath the level of the canal regulator sill, which draw off the bed load and discharge it downstream. 20 Downstream of the weir and undersluices, a floor is provided to protect the foundations against scour (Figure 22.9). The drop in water level across the weir or undersluices is accompanied by the formation of a hydraulic jump, except possibly at high flood flows 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 per unit width of floor should exceed the mean by an allowance depending on the approach conditions. In India and Pakistan a factor of 20% has generally been added for alluvial rivers but in extreme conditions it should be higher, e.g. where curvature of approach could cause a high concentration Irrigation canal structures Canal head regulators are usually located immediately upstream of a weir or barrage (see Figure 22.9). On alluvial rivers the intake should be well above the sill of the undersluices. A stilling basin of sufficient depth, to ensure that the hydraulic jump is retained 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 a canal, falls or drop structures are required at intervals to dissipate the excess head and lower the canal to conform to the ground level. Falls are designed in a similar way to weirs, with ungated crest and stilling basin. To reduce cost, the width of waterway is often made less than the width of canal. The upstream contraction presents little difficulty, but the downstream expansion must be gentle to avoid asymmetrical flow downstream (see page 22/4).

8 East Tower Gate West Tower <t Navigation Channel Transformer House +6.9 Defence Level +3.63M.H.W.S.T. Control Room Generator Building Figure NORTH ELEVATION (LOOKING DOWNCREEK) Tidal barrier, Barking Creek. (Consulting Engineers: Binnie and Partners)

9 Tidal barriers The risk of serious flooding from tidal surges penetrating inland via estuaries and tidal inlets has led to several major schemes for tide-excluding barriers. These are in the form of gates, perhaps single gates for schemes of modest size but multiple gates for major estuaries. Navigation is often the controlling feature determining the necessary span, the elevation of the sill and the clearance under any structure spanning over the waterway. Very large vertical lift gates have been used as tidal barriers and one example, at Barking Creek in the Thames Estuary, 21 is illustrated in Figure The gate normally rests at the top of its support towers, thus providing clearance for navigation by medium-sized ships. Rising sector gates do not require a high supporting structure because they normally rest below the bed of the navigation channel. The main gates of the Thames Barrier are of this type and their operating mechanism is such that they can be rotated through 180 from their normal position in their sills on the estuary 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 of the Thames Barrier have a span of 61 m and effectively they form box-girders between their end wheels. There are six subsidiary gates with spans of 31.5 m Permeable foundations Special consideration is required if a hydraulic gradient will exist across a structure founded on permeable materials. Examples include weirs, regulators across canals, barrages and tidal barriers. Two important requirements are that every part of the structure must be safe against uplift pressures beneath and that underflow or seepage through the permeable materials should 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 curtain wall intersecting it, or possibly by grouting, but the sealing must be perfect. If, however, the permeable materials are too deep for this treatment, the floor must be safe against uplift pressures exceeding the tailwater level acting on the underside of the structure throughout. Uplift depends on the hydraulic gradient of flow through the material beneath the work, reducing from the upstream water level to the downstream water level. Its distribution may be affected considerably by the nonuniformity of the materials so a prior investigation of the character of the material, its uniformity and the existence of strata of different permeability is necessary. The floor upstream of a weir or gates is safe against uplift because of the water load above but the downstream floor is particularly vulnerable at times of high upstream and low downstream water levels. Measures to reduce uplift pressures on the downstream floor include the lengthening of the upstream floor and provision of transverse lines of sheet piling upstream or beneath the weir, both serving to lengthen the effective seepage path, and provision of relief drains. Typical protective measures beneath a gated structure are shown in Figure 'Piping' consists of the removal of foundation material by the flow of seepage water. It can occur at the tail end of a structure where the underflow emerges and is a potential cause of undermining and ultimate failure of the structure. It is caused by excessive exit gradient. Information on flow nets to determine uplift pressures and exit gradient is given in Chapter 9. It is usual to protect against piping, where the foundation material is granular, by providing coarser filter material to intercept the seepage over its exit area. This is generally covered by loose stone or other protection against scour, but in case this should fail, other measures are needed to reduce the exit gradient. Such measures include the lengthening of the structure and the provision of transverse lines of sheet piling to reduce the overall hydraulic gradient, provision of relief drains and the provision of a curtain wall or line of sheet piling at the tail end of the floor. The last is most important to avoid a locally steep gradient and protect the floor from undermining by scour, but it should not be too deep because it increases uplift beneath the floor. The upstream or central sheet piling should extend laterally into the flanking embankments, and lines of piling are carried around as may be necessary to intersect seepage paths and box in the foundations. For general design procedures, reference may be made to Haigh, 20 Leliavsky 23 and Foy and Green Energy dissipation Stilling basins At weirs, barrages, sluices, spillways, tunnel outfalls, canal falls and in general where a sharp fall occurs in total energy level, a stilling basin is needed to contain the flow in the region of energy dissipation. This is especially important where the channel bed is credible. The surplus energy may be dissipated by water spilling into a pool, which may be in bed rock, or lined with rip-rap or concrete. In most cases the energy head to be dissipated is sufficient to create supercritical flow, defined on page 22/3. A hydraulic jump is then generally the most effective and economical way of dissipating the surplus energy. The object is to provide a stilling basin lined with nonerodible material, usually concrete, deep enough to retain the jump over the whole range of flow conditions and long enough for the eddies generated in the jump to be reduced to an acceptable intensity before reaching the channel downstream. The minimum depth is thus related to the characteristics of the jump while the minimum length is related also to the degree of stilling required. Where the channel bed is credible, a greater length of basin is generally required than where it is in rock or is concrete-lined. In the basin, chute blocks, baffle blocks or piers are often provided to help to stabilize the jump and reduce the length of basin required. As shown earlier, the stability of a hydraulic jump is expressed by the pressure-momentum equation (Equation (22.5)) representing the condition at which the jump is at its limit of stability, i.e. any increase in discharge or upstream head would cause 'sweep-out' or movement of the jump downstream and possibly out of the basin. In the design of stilling basins, however, the quantities which are known are usually the discharge, head drop and tailwater level and it is required to determine the basin floor level. Equation (22.5) therefore cannot be applied directly, but the maximum acceptable floor level can be easily found with the aid of Figure The procedure is to compute upstream and downstream total energy levels (water level + velocity head), compute H 1 =H 1 -H 2 (see Figure 22.2), compute critical depth d c by Equation (22.3a), compute HJd c, read off H 2 /d c directly beneath HJd c, i.e. for same F 1, and compute H 2. This gives the minimum depth of basin floor beneath tailwater total energy level. It applies to a plain floor and may be reduced by 10 to 20% if chute blocks and/or baffle blocks and end sill are provided. However, it is often the practice to provide the full depth and consider the blocks to provide a safety margin in addition. It is usually necessary to determine minimum basin depth for several discharges throughout the range, because the most severe case is not always with the maximum discharge. When determining q in cases of nonuniform distribution across the basin it may be necessary to use a value rather higher than mean q = Q/B, where Q is the total

10 Upriver Section through rising sector gate Downriver Levels relate to ordnance datum Newlyn Gate arm Trunnion assembly Fixed end Gate span Hinged end SECTION ON $.OF GATE LOOKING DOWNRIVER Gate in open position Gate arm Flap valves Gate rising Water flow Sill unit Bed Surge LV Water F under G Flood control position High water level Silt Gate lowering Gate in maintenance position Figure Thames Barrier, 61 m span rising sector gate. (Consulting Engineers: Rendel, Palmer and Tritton)

11 discharge and B the width. Tailwater level is clearly of critical importance for the stability of the jump and it is necessary to have a reliable stage discharge curve, with allowance for future changes as, for example, due to channel bed degradation downstream. The lowest probable levels should be used. In the case of basins for gated spillway releases, where discharge may be increased rapidly over a short period, allowance should be made 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 the depth d 2 in the basin. If residual eddies can be tolerated downstream because the bed is not credible or is protected by a flexible apron, as in Figure 22.12, a length of 4d 2 may suffice. Where chute blocks and baffle blocks are provided in such cases, a length of 2.Sd 2 is sometimes considered adequate (but see below). Many standard designs of hydraulic jump stilling basins have been developed from model tests, one of the most comprehensive being that of Bradley and Peterka Four types of jump were defined according to the Froude number F 1, each with somewhat different characteristics, namely: F 1 from 1.7 to 2.5 Pre-jump, low energy loss F 1 from 2.5 to 4.5 Transition, rough pulsating water surface F 1 from 4.5 to 9.0 Range of good jumps least affected by tailwater variations F 1 exceeding 9.0 Effective but rough IfF 1 is in the range 2.5 to 4.5 the pulsations are likely to produce surface waves which are propagated downstream. The Froude number is generally determined by other factors, but if there is any choice it is clearly desirable for it to be within the range 4.5 to 9.0. Bradley and Peterka's basin III for F 1 between 4.5 and 9 is shown in Figure The dimensions of the chute blocks are made equal to the depth d } and those of the baffle blocks range from 1.3</, for F 1 = 4 to 3d, for F 1 = 14. The height of end sill ranges from 1.2</, for F 1 =4 to 2d } for F 1 = 14. Figure US Bureau of Reclamation stilling basin, type III. (After Beichley (1978) 'Hydraulic design of stilling basin for pipe or channel outlets/ USBR Water Resources Research Report No. 24) Where F 1 is between 2.5 and 4.5 (basin IV) the chute block height is 2d\ and the baffle blocks are omitted or, according to Bhowmik, 27 a special arrangement of blocks and deflector may be provided to give improved jump stability. Where F 1 exceeds 9 (basin H) the baffle blocks are omitted and a dentated end sill is recommended. Basins II and IV, having no baffle blocks, are required to be longer than basin HI, with floor lengths of approximately Ad 2. In the case of high head structures, if the velocity much exceeds 15 m/s, chute blocks and baffle blocks are liable to be damaged by cavitation. They can be omitted or protected by steel cladding, as at Mangla Spillway. 28 Erosion of bed and banks immediately downstream of the stilling basin can be a serious problem, whether the head drop through the structure is great or small - see remarks on transitions, page 22/4. A normal cause of erosion is the residual turbulence from the hydraulic jump. This may scour the bed beneath the level of the basin floor, so a flexible protection such as rip-rap is needed which will adjust its level to the scoured bed downstream of it (see page 22/8). When the banks are formed of credible material they need slope protection to guard against local velocities and wave wash. In the case of weirs and barrages on alluvial rivers the banks are carried downstream a short distance - perhaps equal 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 canals where the banks are erodible, the slope protection is continued for a distance in which the surface waves will be reduced and velocity distribution will become normal. A layout of stilling basin and canal banks which has been found satisfactory is shown in Figure 22.3e. The gently diverging side walls are free-standing at their downstream ends, where they consequently do not have to serve as high earth-retaining walls; the channel downstream is widened to accommodate the side rollers which will develop and the banks are protected by rip-rap. In the case of small flows, shorter and simpler structures have been used, e.g. the straight-drop spillway basin of the US Department of Agriculture. 29 For large flows and high heads, experience has shown that hydraulic jump basins are generally satisfactory. Damage which has occurred has been due mainly to the basin being of inadequate depth, to cavitation where baffle blocks have been exposed to high velocity flow and to abrasion due to loose materials in the basin In some cases these materials may have remained from river diversion operations but in other cases bed material and even rip-rap has been carried into the basins by backwash. There have also been instances of vibration and shock due to flow instability. In large-scale basins it is especially necessary to guard against flow separation at the side walls, which can be a cause of both these last effects and of backwash Bucket energy dissipators The hydraulic jump stilling basins described above are effective but costly, especially for high-discharge concentrations. Where the foundations of the structure are in rock, even an erodible rock, a much higher degree of residual turbulence may be acceptable. A submerged roller bucket (see Figure 22.13) is suitable over a wide range of Froude numbers. The bucket is placed well below the tailwater level so that a submerged roller forms in the bucket and exit velocities are not excessive. Compared with a hydraulic jump basin, it is deeper but shorter and generally less costly; but Bucket roller Standing wave Ground roller Figure Submerged roller bucket-angostura-type slotted bucket. (After Beichley and Peterka (1959) The hydraulic design of slotted spillway buckets.' Proc. Am. Soc. Civ. Engrs, 85, HY10)

12 the range of tailwater level for satisfactory operation is limited, which precludes its use in some cases. Rules for design have been given by McPherson and Karr 32 and by Bleichley and Peterka 33 who found that slotted buckets were superior to plain buckets Terminal structures for pipes and valves High-velocity jets from pipes and terminal valves have considerable erosive power, even on hard rock. Means of protection include the use of valves which disperse the jet in the air, e.g. the cone valve, or valves which project the jet some distance, where a plunge pool can be provided, or structures devised to contain the jet and allow most of the energy to be dissipated before discharge into an credible channel. Figure shows an impact stilling basin developed by the US Bureau of Reclamation (USBR) 5 for pipe and open-channel outlets with discharges up to 10 m 3 /s and velocities up to 9 m/s. It may also be considered for terminal valves within the limits I Pipe dia. SECTIONA-A Flat fillet Flow P L AtM Fillet PLAN SECTION Bedding SECTION H = 3W/4 L = 4W/3 a = W/2 b = 3W/8 suggested minimum Rip-rap stone size diameter = W/20 ALTERNATE ENDSILLAND WINGWALL Satisfactory hydraulic performance Unsatisfactory hydraulic performance Froude number V//gD W = inside width of basin D = square root of area of flow entering basin V = velocity of flow entering basin Tail water depth uncontrolled Figure US Bureau of Reclamation impact-type energy dissipator- basin Vl. (After Beichley (1978) 'Hydraulic design of stilling basin for pipe or channel outlets.' USBR Water Resources Research Report No. 24)

13 stated. The required dimensions may be obtained from Figure 22.14, A special basin has been developed by the USBR for hollow jet valves Basins have also been used for cone valves. A very effective energy dissipator for pipe outlets is a vertical well in which the pipe outlet is deeply submerged at a short distance above the bottom. Figure shows a USBR type of well. 35 Local scour results from the deflection and, hence, concentration of flow caused by an obstruction. The depth of scour depends on the shape of the obstruction, its orientation to the flow, the channel cross-section and discharge, the character of the credible bed material, the sediment in transport and the time history of the flow. With so many variables it is not surprising that there is no single formula available for calculation of scour. In the case of important works it is usual to carry out model tests. It is also possible to determine the order of magnitude and probably the upper limit of scour depth by comparison with depths observed in actual cases, providing a useful check on model results or a fair indication in other cases. Local experience is a guide but may not embrace the highest discharges. To apply historical data from elsewhere it is necessary to adjust for scale. In the cases of rivers in alluvial bed materials, the Lacey regime formulae 19 ' 36 can be used, the depth of scour being related to the normal depth of channel of the same discharge. The relevant formulae in the present context are: B = / 2 (22.7) Sleeve valve 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 constant discharge. / L may be taken as unity for fine sand Qfi/b 3 (metric) Figure Vertical stilling well with sleeve valve (USBR design). Well is of square section in plan with corner fillets as shown. Q is discharge, H is head above pedestal. (After Beichley (1978) 'Hydraulic design for pipe or channel outlets.' USBR Water Resources Research Report No. 24) Regulation is provided by the sleeve valve at the pipe outlet, operated from above (see page 22/31) Scour and erosion Depth of scour at structures Apart from scour downstream of stilling basins, structures such as bridges, jetties, groynes and constrictions forming obstructions to flow in rivers and channels with credible beds can give rise to scour due to disturbance of the normal flow pattern. Scour can also be caused by oblique flow at the upstream of control structures such as barrages and-regulators. It is generally required to estimate the depth of scour so that adequate protection can be provided or so that the foundations can be located at sufficient depth to avoid the possibility of undermining. Width calculated by Equation (22.7) with Q = design discharge is a useful indicator of the maximum bridge length required for an alluvial river with floodplain, but if the banks are of cohesive materials, the river channel width may be less; Nixon 37 found the average widths of British rivers to be approximately 3g 1/2, where Q is bank-full discharge. Lacey proposed that the maximum depths of scour at sharp bends in alluvial rivers could be taken as approximately 2d, where d is calculated from Equation (22.8). Inglis 38 collated data of deep scour observed at structures and training works in alluvial rivers at thirty different locations in India and Pakistan, compared them with the normal depths indicated by Equation (22.8) and reached the following conclusions 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 that large flood flows cannot be measured but are estimated, while maximum depths of scour are transient and may, in fact, have been greater than observed. The scour depths are related to the total rather than the local flow on the grounds that the scour results from the concentration of the whole flow. In the case of braided rivers, allowance could be made for the division of total flow into several channels. Scour depth in rivers in gravel and boulders would be less than indicated but the difference may be small. Scour depths in cohesive materials could be less because of the time required to reach maximum scour.

14 For the purpose of design of aprons upstream and downstream of barrages in northern India, maximum depth of scour below water level was taken as 1.5d at the upstream end of the hard floor and 2d at the downstream end of the basin. Here d was calculated from Equation (22.9) using mean q. Scour at bridge piers has been studied in some detail in models, scour depth being related to discharge per unit width and sometimes expressed as depth below upstream bed level. 39 " 41 To apply such relationships, the discharge concentration, which can in the worst case greatly exceed the average, has to be estimated, and the upstream depth has then to be calculated for the corresponding flood condition. The latter can be done using Equation (22.9) which is likely to give a conservative value because of time lag and sediment load. The calculation should be checked by use of the appropriate Inglis factor above Protection against scour This generally consists of one of the following materials. Boulders. Boulders from the river bed which are generally rounded and therefore less stable than quarried stone of similar weight. Rip-Rap. Rip-rap, or pitching of quarried stone, is widely used. In some cases it is hand-packed, especially on side slopes which are expected to remain as placed without settlement, but with increasing use of mechanical equipment it is more often placed in a random manner. This is also preferable in locations where it is expected to settle or move down due to scour. On side slopes the thickness of rip-rap should be sufficient to accommodate the biggest stones without large gaps - at least 1.5 x median stone diameter - and an underlayer or filter of smaller stone is generally provided to prevent the base material from being washed 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 the channel bed may scour beneath the apron level, the volume of rip-rap should be sufficient to protect a slope at the angle of repose of the rip-rap on the bed material (for a sand bed generally 1:2) extending from the apron level to the level of anticipated deepest scour. For this purpose the rip-rap may be laid on a prepared slope or it may be laid in a horizontal apron which it is assumed will settle to a slope when scour occurs. A margin should be allowed for uneven settlement. The size of rip-rap which will remain stable may be estimated from Figure Sixty per cent by weight of the material should be equal to or larger than the size shown. In the case of rigid structures it may be dangerous to rely on loose stone protection; it is generally best to provide foundations at low levels beneath possible scour. If stone or concrete blocks are used to protect existing structures they should be placed as low as possible beneath normal bed level. Derrick stone. Derrick stone is stone in blocks too heavy to be placed by bulk handling and which therefore requires individual placing. It is usually placed on an underlayer of graded rip-rap. Concrete blocks, slabs or units of various shapes. As the density of concrete is less than that of stone, larger and heavier blocks are required than the corresponding stone sizes. Concrete blocks are used in locations where stone of suitable quality and weight is not available or is too costly. Concrete blocks or slabs on edge, e.g. 2m wide x 0.5m longx Im deep, have been used successfully for flexible aprons downstream of barrages in rivers with sand beds. Concrete slabs are used in slope protection but require good compaction of fill beneath to avoid uneven settlement. Concrete units of special shapes have been developed Stone weight (kg) Maximum Velocity (m/s) Figure Stability of loose rock in flowing water. Graph relates to rock of specific gravity For other specific gravity rock weight = weight shown * 1.7s/(s-1 ) 3 where s= specific gravity. Use minimum weight graph in normal flow and maximum weight graph for very turbulent flow. (After US Army Corps of Engineers ( ) Hydraulic design criteria. US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi) which require less concrete than do concrete cubes for the same duty; some of these are extensively used in coastal protection and can also be used in river channel works. Gabions. Gabions, consisting of wire crates containing boulders or broken stone, generally wired together to form an apron, form an economical temporary protection against erosion and have been used in permanent works, though the wire crates may be subject to corrosion. The standard metric size is 2 x 1 x ] m but thinner mattresses are available. They offer great resistance to removal by flow and a gabion apron has considerable flexibility in adjusting to scour, though less than an apron of rip-rap. Asphalt. Asphalt provides a smooth impervious cover but does not have much flexibility. Sheets of polypropylene. These, and other synthetic materials, woven to a fine mesh provide an effective filter layer over sand and have been used to form thin mattresses, with pockets filled with cement grout, for side slope protection. Brushwood fascine mattresses. These form a traditional protection consisting generally of willow twigs bound in bundles and formed into longitudinal and lateral layers bound together before it is launched by weighting with stone and sinking into place, which is still used and has a considerable life under water. Vegetation. Vegetation, in particular certain grasses and shrubs, when established above normal water level, can protect a bank against occasional high level wave wash or even shallow overtopping. For protection of formed banks in cut or fill, any of the above materials would be suitable (see also Chapter 18) subject to adequate protection against scour of the toe of the bank or the channel bed near it. This may be provided by a line of sheet piling at the toe or by a flexible apron laid horizontally which will subside and protect the underwater slope when scour occurs. Quarried stone rip-rap is usually used for the apron where available.

15 22.2 Enclosed flow Head loss in large conduits and tunnels Head loss in pipes is dealt with on pages 5/8 to 5/11. Head loss in large conduits and tunnels may similarly be estimated by the Darcy formula: i = /I V 1 JIgD = /I K 2 /8gm (22.10) where / is the hydraulic gradient, A the friction factor, V the mean velocity, D the diameter of circular conduit flowing full, or m the hydraulic radius to be used for part full and noncircular conduits. A and Manning's n are related by: n = Ji 112 D 116 IlO.* = VW 6 /13.6 (22.11) In nearly all actual cases of large conduits the boundary cannot be classed as smooth or rough but falls within the transition region. A therefore depends on the effective roughness and on the Reynolds number VD/v or 4 Vm/v, where v is the kinematic viscosity (for values of v see pages 5/8 to 5/10). Although many types of roughness are composite, e.g. smooth concrete with projections due to formwork joints, and therefore the equivalent sand roughness concept is not completely representative, it does provide a method of predicting the friction factor, based on recorded experience. In the case of new works this depends on the type of forms used, quality of workmanship and degree to which projections are ground down. Deterioration occurs with age and use. A steel lining may corrode and be roughened by tuberculation, as for pipes. Concrete inverts may be roughened by abrasion during river diversion. There may be deposits due to leaching through joints and cracks in a concrete lining, even vegetation and animal growths, while the deposit of slime by untreated water is commonplace. Typical values of equivalent sand roughness k for new surfaces, based mainly on Ackers 42 and USBR experience, 43 are given in Table It is more difficult to predict the friction factor in a tunnel after many years of use; the best guide is often obtained from actual measurements in similar tunnels under similar conditions. 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 to Spun bitumen lined 0.0 to Spun concrete lined pipes 0.0 to Uncoated steel to Coated steel 0.03 to 0.15 Rivetted steel 0.3 to Wood stave, planed planks 0.2 to 1.5 Concrete: against oiled steel forms with no surface irregularities 0.04 to 0.25 against steel forms, wet mix or spun precast pipes 0.3 to 1.5 against rough forms, rough precast pipes or cement gun 0.6 to 2.0 smooth trowelled surface 0.3 to 1.5 Glazed brickwork 0.6 to 3.0 Brick in cement mortar 1.5 to 6.0 Ashlar and well laid brickwork 1.5 Rough brickwork 3.0 When a suitable k value has been determined, the relative roughness k/d or k/4m can be calculated and a value of A determined from Figure which is based on the Karman- Nikuradse-Prandtl formulae with Colebrook-White transitions described on page 5/9). Some examples of large-conduit observations are shown in Figure 22.1 T Figures and show characteristics of circular and horseshoe conduits flowing part full. The surface of conduits for high-velocity flows should be to a very high standard of finish to avoid damage by cavitation - see page 22/ Unlined and lined-invert tunnels in rock Excavated rock surfaces are very rough and the hydraulics are complicated by 'overbreak', i.e. excavation beyond the minimum required by the specification. Rahm found a relation between the variation in cross-sectional area and the friction Rough flow limit Computed-open symbol Observed-solid symbol Resistance coefficient, A Smooth pipes Denison Ft. Randall, vinyl Ft. Randall, coal tar Enid Oahe Pine Flat, 52 Pine Flat, Maximum smooth pipe section Minimum smooth pipe section Relative roughness, Reynolds number, R Figure Head loss in uniform conduits. Open symbols, computed; solid symbols, observed. (After US Army Corps of Engineers ( ) HydraOlic design criteria. US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi)

16 Figure Area and hydraulic radius of conduits, part full. For key, see Figure Transitions and bends Transitions may be from circular to noncircular sections or vice versa, or from one circular section to another of different diameter. In conduits for high-velocity flows, transitions are generally gradual to avoid flow separation and possibly cavitation. It is also necessary to adopt moderate rates of expansion if head is to be conserved and instability of flow downstream avoided. Circular sections can be merged into rectangular or horseshoe sections without double curvature and avoiding sharp local divergences. Figure shows head loss in diffusers of circular section; curves of similar pattern but slightly differing values apply to diffusers of rectangular section. 47 It will be seen that for expansion ratios of 2 or more the head loss may be considerable unless the angle of divergence is small. Where rapid expansion is required, divide walls may be used so that the Figure Critical depth in circular and horseshoe conduits factor. The subject was further developed by Colebrook 45 and again by Wright, 46 who showed that the resistance of unlined tunnels can be reduced considerably by providing a concrete invert. Figure Head loss coefficient K d of conical diffusers with tailpipe. (After Miller (1971) Internal flow. A guide to losses in pipe and duct systems. British Hydro-mechanics Research Association, Cranfield)

17 flow is carried in a number of ducts, each of which is a reasonably efficient diffuser while the overall angle of expansion may 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 are sometimes used for energy dissipation in closed conduits. Contractions may be more rapid than diffusers, but to avoid head loss due to the formation of a vena contracta in the downstream conduit, it is desirable to provide a rounded external angle between the transition and conduit at a radius of at least onesixth diameter. In high-velocity flow this is an area of potential cavitation and the radius should be greater. Head losses at bends in large conduits are similar to those in pipe bends (see pages 5/11). A compromise then has often to be reached between the greater head loss of a short-radius bend and the greater cost of long-radius bend; bend radii of between 1.5 and 3 diameters are often adopted. The flow instability induced by a bend persists for a distance of many diameters downstream and may affect the performance' of turbines or pumps. Bifurcations and manifolds, dividing the flow, for example, for two or more machines, are generally designed with great care to achieve a smooth change of velocity, absence of swirl and minimum head loss. Model tests with air are useful to indicate flow 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 to closed conduit flow may, where the approach velocity is low, be designed on the same principles as apply to intakes from reservoirs (see page 22/25). Sharp corners lead to separation and the formation of a vena contracta with head loss; this may be avoided by providing a rounded or bellmouth entry. With higher approach velocity the transition should be more gradual, with curves of larger radius. To avoid the formation of a hydraulic jump with resulting air entrainment the design should be such that the contact between free surface and roof occurs where the flow is subcritical, preferably with Froude number well below unity Exits If the exit of a conduit is fully or partially submerged, head loss can be reduced by providing a gradual expansion, which can often be extended in the tail channel. If the conduit exit is not submerged, a free surface may develop some distance upstream of the exit portal, even when the conduit is flowing under pressure. The depth of the exit depends on downstream conditions but where tailwater level is low the flow becomes supercritical and the conduit exit acts as a control. The end depth still depends to some extent on the tail channel, particularly whether the flow is supported at the sides and bed, but the end depth may be estimated from Figure If the emerging flow is supercritical and downstream flow subcritical, a hydraulic jump will occur and a stilling basin may be needed Flow routing Flow through conduits can be routed and energy gradient plotted by use of the Bernoulli equation (see page 5/8). Allowance should be made for head loss due to friction, bends, transitions and hydraulic jumps. Subcritical flow is routed in an upstream direction starting from the tail channel or a control, and supercritical flow in a downstream direction, using step methods if necessary. Computer programs exist which ease the burden of calculation. To locate a hydraulic jump the pressuremomentum theorem can be used, taking account of the slope of the conduit and the pressure against the conduit roof if submerged downstream. The method is described by Kalinske and Robertson. 48 Critical depths in circular and horseshoe conduits Figure Exit depth in circular conduits. V is the mean velocity in the conduit flowing full (based on USWES data). (After US Army Corps of Engineers ( ) Hydraulic design criteria. US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi) may be determined from Figure 22.19, and diagrams facilitating computation of jumps in conduits of circular and other crosssections have been published. 2^* In cases where hydraulic jumps might occur in closed conduits with undesirable results, due to additional head loss or air (see below), it is recommended that the routing be repeated for several discharges using both high and low values of head loss coefficients and upper and lower limits of tailwater rating curve, to obtain a complete account of the flow Drop shafts Sometimes flow has to be dropped from a high-level system to a low-level system, e.g. from shallow sewers to deep interceptors, from river intakes in mountains to a water-transfer tunnel, from the drainage of an open-pit mine to an adit from an adjacent valley. An economic solution is to use a shaft, but there are problems associated with air entrainment and release in any shaft system, especially if the base of the shaft is submerged by the hydraulic conditions in the low-level system. These problems can be minimized by generating a vortex at the top of the shaft, either by a scroll-shaped inlet chamber (Figure 22.22a) or by a tangential vertical slot (Figure 22.22b). The vortex action ensures that the flow down the shaft will cling to the walls. This has the advantage of minimizing air entrainment and encouraging the return of air back up the centre to the head of the shaft, and at the same time maximizes head dissipation in the shaft by wall friction. The vortex motion is persistent: it will continue for the full length of fairly deep shafts provided the entry is well designed. The theory of the scroll inlet is given by Ackers and Crump, 49 and the slot inlet has been investigated by Eppema, Jain and Kennedy. 47 If the bottom of the shaft is submerged, as in Figure 22.22c, it will be necessary to provide an air-release chamber. If the fullbore shaft velocity exceeds about 0.5 m/s, bubbles will be carried down with theflow.problems - perhaps serious ones - could arise if this entrained air was allowed to travel along the tunnel system (due to potentially explosive blowout further downstream) and hence a stilling chamber should be provided to allow the entrained air to separate and rise to the crown of the chamber where the bubbles will coalesce to return via the vent pipe. For unsubmerged conditions, Figure 22.22a illustrates a type of collecting chamber at the base of the shaft found suitable for

18 Lip of bell mouth Inlet Taper Slot Inlet Spiral flow Vortex chamber PLAN PLAN Slot Throat Minimum air core SECTION b) Alternative deep slot inlet Shaft Vent pipe Annulus of flow Level of submergence Shaft flows full of air/water mixture Annulus of flow Air entrainment Vent pipe Crenellated dish SECTION Air bubbles Outlet chamber for free discharge Outlet tunnel c) Outlet chamber for submerged discharge with air-release provision a) Normal sewage structure with vortex chamber inlet Figure Vortex drop. Alternative forms: (a) normal sewage structure; (b) alternative deep slot inlet; (c) outlet chamber for submerged discharge with air-release provision

19 sewerage systems. With deep shafts, the annulus of flow may reach terminal conditions where the gravitational component is equalled by the friction at the shaft walls, and so there is a limit to the amount of energy to be dissipated at the base of the shaft Air problems in conduits Air entrained at high velocity releases through gates and valves into conduits, e.g. at outlets from reservoirs, air entering from drop shafts or junctions and air entrained at hydraulic jumps, can lead to dangerous air and cavitation problems unless the conduits are adequately vented. Air can also collect and restrict the flow of water. Air release valves, often combined with vacuum relief to admit air if pressure falls below atmospheric, are therefore provided at high points. Vents are often provided in horizontal tunnels downstream of junctions where entrained air may enter. Air which has collected beneath the soffit tends to be carried forward by the flow, even against a small gradient, but with a variable flow may move upstream and downstream at different times. At vertical shafts in pressure conduits and at deeply submerged exits the intermittent escape of air produces shock 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 is in contact with the soffit much of the air is released downstream. Following model tests in a conduit with various slopes by Kalinske and Robertson 48 and others, and several observations at full scale, the US Army Corps of Engineers 11 use the formula: ^=0.03(F,-1) 16 (22.12) which gives higher values than found in the model tests to allow for scale effect. Here P is the air:water ratio QJQw F 1 =VJ V(&4)> V\ i s tne upstream velocity and d e the effective upstream depth ( = water area:surface width). A particular application of these formulae is the estimation of air demand downstream of gates or valves located in closed conduits, where high-velocity flow at part openings is transformed to full-conduit flow through a jump (see Figure 22.23). Full-scale observations in three different cases showed that with rectangular gate openings peak demand occurred at 60 to 85% opening, with a secondary peak at about 5%. Further analysis has been provided by Sharma. 50 Figure Stability of entrained air downstream of hydraulic jumps in circular conduits. (After Kalinske and Robertson (1943) 'Closed conduit flow. Symposium on entrainments of air in flowing water.' Trans. Am. Soc. Civ. Engrs, 108, Paper 2205, 1435) The air pumped by the jump may be carried downstream by the full-bore flow but, if the velocity is insufficient for this, air will collect immediately downstream of the jump and when a quantity of air has accumulated it will 'blow back' through the jump. Figure shows the limiting conditions for the air just carried by the flow, as found by Kalinske and Robertson. 48 Sailer 51 compared these curves with conditions in a number of full-scale inverted siphons and found verification in that five cases where blowback had occurred were represented by higher values of (F 1 -I) than shown by the curves, while others giving no trouble were on or below the curves. With large flows, blowback through the jump is, like 'blowout' at the exit, explosive and potentially dangerous Spillways Purpose and types A spillway is provided to remove surplus water from a reservoir and thus protect the dam and flanking embankments against damage by overtopping. The best type and location of a spillway depends very much on the topography and geology of the dam site and adjoining area, and on the type of dam. Where the dam is of concrete or masonry founded on hard rock, the spillway may be within the dam, consisting either of a high-level overflow or of submerged orifices, discharging into the river bed beneath. In the case of an earth or rockfill dam, it is usual to site the spillway away from the deepest part of the dam; high flanking ground or a saddle away from the dam site can be suitable locations where a spillway channel may be excavated and control structure provided (see, for example, Figure 22.24). Where the dam is built in a narrow gorge and there is no suitable separate site for the spillway, a side-channel spillway is often adopted (Figure 22.25). If control is by a fixed ungated weir, the maximum retention level of the reservoir is the weir crest level; at times of spill the reservoir level rises and sufficient freeboard has to be allowed above maximum water level, which is the level at which the design maximum flood discharge is released. In the case of gateregulated spillways, on the other hand, flood flows can be discharged with reservoir at retention level, which need never be exceeded. For a given dam height, retention storage can thus be greater but, because there is less flood storage, the spillway capacity also may have to be greater. The gates, however, enable the reservoir to be drawn down in advance of a flood peak, given adequate forecasting. Low-level orifices, having greater capacity than required for purposes of normal supply, have greater capability than has a gated crest overflow in drawing down a reservoir in the event of damage to the dam, an important aspect in areas where earthquake risk is present. But crest overflow weirs have a greater rate of increase of capacity as a reservoir level rises above normal, thus providing additional safety margin. Cost is a major consideration in the choice between a regulated and an unregulated spillway, but spillways without gates have advantages in respect of reliability, absence of mechanical maintenance problems and no power requirements. They are therefore often adopted at remote sites and for small dams where the cost of gates would not be justified. Siphon spillways carry some of the advantages of both gated and ungated spillways. They can be designed to prime and operate to maximum discharge within a small range of reservoir level and they are automatic, with no moving parts. Another type of spillway, particularly suited for use with earth 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 If the reservoir is for water supply, the bellmouth and shaft are often combined in the same structure as a drawoff tower and the low-level tunnel can be used for river diversion during construction, as discussed and illustrated in section In many cases it is advantageous to provide more than one spillway. Instead of relying on a single spillway to control all