I

2. Design Considerations

, 2.1 Introduction

Before proceeding with detailed discussions of the various types of long-throated flumes, it will be worthwhile to consider some basic issues related to the functions of flow measurement and regulation structures and the demands made upon them. This discussion will facilitate the selection of the proper type of structure for a given application. We will distinguish between two basic functions of a structure- measurement of flow rate and controlled regulation of flow rate-and will consider demands upon the structure originating from four sources:

1 I

1. The hydraulic performance, 2. 3 . 4. The cost of maintenance.

The construction and/or installation cost, The ease with which the structure can be operated, and

Although we will be discussing issues of relevance to all types of flow measurement and regulation structures, we will be focusing on long-throated flumes. Design procedures for long-throated flumes are given in Chapter 5. Chapter 8 describes software that can be used to aid users with the design process, including most of the design considerations given here.

A wide variety of methods and devices are available to measure flow. To determine the specific type of structure, if any, to be used, we must first consider the frequency at which measurements are needed and the duration for which they are required. Together with information on the size and type of canal, this will lead to the use of a

Portable and reusable structure, Temporary custom-built structure, or Permanent structure.

Velocity-area method (a one-time measurement without the use of a structure),

As Figures 1.6 through 1.1 1 show, structures that only measure the flow rate do not require movable parts. The upstream sill-referenced head can be measured with a variety of instruments, which will be discussed in detail in Chapter 4. If we need to measure the total volume of flow, we can use a weir or flume and a recording device that integrates the flow rate over a period of time.

Structures that both measure and regulate the flow are needed when water is taken from a reservoir, or when an irrigation canal is to be split into two or more branches. A regulating weir has a sill that is movable in a vertical direction, while a flow division structure has a divider wall that may be movable in a horizontal direction.

29

A regulating weir can be operated to maintain a constant upstream sill-referenced head, and thus a constant flow rate. Movable weirs are discussed in detail in Chapter 3 .

2.2 Required Head Loss for Modular Flow

At the measuring site, the additional energy head needed to create critical-depth flow through a measuring flume can often be obtained from a drop in the channel bottom or from the energy head some distance upstream due to channel slope. Channel- bottom drops are often found in natural streams and can be provided in newly designed canal systems. However, if a structure has to be retrofitted to an existing channel, one must often create backwater upstream with a raised crest or narrowed throat (i.e., flow contraction) to locally increase the upstream head for use across the flume. Figure 2.1 illustrates the head loss, Hl - H2, from the upstream sill-referenced energy head, Hl, to the downstream sill-referenced energy head, H,, which can also be expressed as (Hl - H2)/H,, the fraction of the upstream head lost across the structure. This ratio can also be written as (1 - H2/H1), in which H2/H, is the submergence ratio. For low values of the submergence ratio, the tailwater level, y,, (and thereby H2) does not affect the relationship between h, and Q, and flow through the structure is called modular. For high H2/H1 ratios, flow in the throat cannot become critical, and the upstream sill-referenced head is influenced by the tailwater level, thereby affecting the relation between h, and Q; the flow is then non-modular. That submergence ratio separating modular from non-modular flow is called the modular limit, ML (see also Section 6.6.2).

If the downstream energy head, H2, is less than the critical depth, yc, at the control section, the energy available for head loss exceeds H , - yc,. In this case, there is no need to transform the kinetic energy at the control section ( i.e., velocity head, v,2/2g, see Section 6.2) into potential energy downstream from the transition. The downstream water level, h,, can be obtained even if all of the kinetic energy at the control section is lost. In other words, there is no need for a gradual transition between the throat and the downstream channel (Figure 2.2).

Figure 2.1 Terminology for flow through a long-throated flume.

30 Design Considerations

Figure 2.3 Long-throated flume with a modular limit of ML = 0.90 (Arizona).

energy loss over any combination of channel and flume. These methods are used in the software presented in Chapter 8. The following information is useful for any potential flume:

Required head loss for modular flow, H , - H2", Maximum tailwater depth for modular flow, yzmox = p2 + h2", and Modular limit ML = HZmaxlH,.

where the max subscript indicates the highest downstream energy or water level that will permit critical flow.

Analysis of the effect of the slope of the downstream transition will show that the modular limit increases with a more gradual expansion, primarily due to reduced turbulence from the expansion. However, very gradual transitions (slopes flatter than 10: l), lose so much energy due to friction in the long transition that the modular limit will not significantly increase (and may actually decrease). Because the construction cost of a very gradual and long transition is higher than that of a shorter one, we advise that the downstream transition be no flatter than 6: 1.

Rather sudden expansion ratios like 1:l or 2:l are not very effective for energy conversion because the high velocity jet leaving the throat cannot suddenly change direction to follow the boundaries of the transition. In the flow separation zones that result, eddies are formed that convert kinetic energy into heat and noise. Therefore, we do not recommend the use of expansion ratios of 1 : 1, 2: 1, or 3: 1. If the length downstream from the throat is insufficient to accommodate a fully developed 6:l transition, we recommend truncating the transition to the desired length rather than using a more sudden expansion ratio (Figure 2.4). Truncating the transition to half its

32 Design Considerations

I f l o w not recommended t

I throat I I

I crecommended truncation I I I I I I I

Figure 2.4 Truncation of a gradual downstream transition.

fu l l length has a negligible effect on the modular limit. The truncation should not be rounded, since this guides the water into the channel bottom, causing additional energy losses and possible erosion.

2.2.1 Required head for desirable approach flow

To obtain an accurate flow measurement, the water level upstream from the structure must be accurately measured. This can be achieved if the approach channel Froude number is 0.5 or less. (see Section 2.1 1.1) The contraction, used to create backwater for meeting the head loss requirement discussed above, is often sufficient to meet this requirement. However, in some cases it may be necessary to provide additional contraction to adequately reduce the Froude number and slow the approach flow.

2.3 Required Freeboard

Freeboard is designed into channels to prevent overtopping of the embankment due to several reasons: wave action, changes in channel roughness over time, uncertainty about flow rates, etc. With reference to Figure 2.5, the ratio of flow rate at which the canal would overtop, Qovertopping, to the maximum design discharge is

2.1

where F , is the freeboard upstream from the structure. If, for example, the freeboard of an irrigation canal is 20% of the water depth at maximum flow, the constructed canal depth is d , = ylmax + F , = 1 .2ylmU. Equation 2.1 then reads

Chapter 2 33

(water) depth

c

I I I Aalreeboard 4 F I

I I I I discharge I i capacity -

Qmax Qovertopping

Figure 2.5 Relationship between freeboard and discharge capacity of channel.

2.2

The value of the power u depends on the shape of the channel (see Table 2.1). For wide and shallow channels, u is about 1.6, while for deep and narrow canals, u may be as large as 2.4. Hence, the extra canal capacity, AQPeeboard, provided by the 20% freeboard varies between 34 and 55 percent of Qma.

In drainage channels, the design flow rate depends on the selected return period of the discharge from the drained area. The ratio QoverroppinJQmax is determined by the designer based on the function of the channel. For example, the ratio might be set at 1 S O (50% safety margin), and the freeboard F , can be computed for the known values of ylmax and u using Equation 2. I .

When a flume or weir is placed in a channel, the requirements for freeboard upstream from the structure are greatly reduced because the relationship between flow rate and channel water depth is less variable because of the following effects:

The upstream sill-referenced head is constant for a given discharge, An increase in channel roughness immediately upstream from the structure has a reduced effect on the water level because of the backwater effect of the structure, and The future collection of data on channel flow conditions will reduce the uncertainty about the flow rate.

These effects suggest that less freeboard is required immediately upstream from flow measurement flumes. We recommend a freeboard amount of 20% of the maximum sill-referenced head. In drainage canals, we recommend that a freeboard height be determined based on providing for safe conveyance of a percentage of excess flow using Equation 2.1.

34 Design Considerations

Table 2.2 Values of u and QnlaJQmin for various control shapes.

Qmaxf Qmin Shape of the control with rating error

Crest width, b, with Basic form respect to h l at e,,,,, U 5 2 % 5 4% Rectangular ' All 1.5 35 1 O0 Triangular All 2.5 350 1970 Trapezoidal Large 1.7 55 180

Small 2.3 210 1080 Parabolic All 2.0 105 440 Complex shapes Large Variable > 100 > 200

Small Variable > 250 > 2000

2.4 Range of Discharges t o be Measured

The flow rate in an open channel tends to vary with time. The range of discharges, Qmin to Q,,, that should be measured depends strongly on the nature of the channel. Natural streams, for example, experience a considerably wider range of flows than do irrigation canals. The anticipated range of flows to be measured may be quantified with the ratio

2.3

For the weirs and flumes described in this manual, the head versus discharge relationship can be expressed in the general form

Q = C, KH," 2.4

where C, is the discharge coefficient which corrects for streamline curvature and energy loss due to friction upstream from the control section, and K is a factor that depends on the size of the structure and the units in which the discharge and head are expressed. The power u depends on the shape of the control section as follows (Clemmens and Bos 1992):

Y = Q m , f Q n i i n

2.5

where B, is the top-width of the water surface at the control section, y, is the critical depth at the control section, H, is the energy head at the control section, and A , is the wetted area at the control section. For a rectangular control section u = 1.5, while for a triangular control section, u = 2.5. For all other shapes, u ranges between these values. (see Table 2.2)

The mathematical model presented in Section 6.5 produces a head-discharge rating with an error of less than 2% in the computed flow if the energy head to crest length ratio is in the range

Chapter 2 35

0.070 2 H,IL 20.70 2.6

where L is the length of the flume throat. Over this range of heads, the discharge coefficient changes by about 10% (e.g., Bos (1985) shows that for H,IL = 0.070, C, averages 0.917; and for H,IL = 0.70, C, averages 1.002). Applying Equation 2.4 at Q,, and Q,,, with K fixed, it follows that the corresponding range of flows that can be measured by a certain shape of the control section is

2.7

Equation 2.5 shows that the value of u depends on the shape and relative width of the control section. Ranges of u are shown in Table 2.2 together with rounded-off values of Q i n J Q m i n .

In irrigation canals, the ratio QmJQmin rarely exceeds 35, so that all control shapes can be used. In natural drains, however, the range of flows to be measured usually will determine the shape of the control. In natural streams with a small catchment area, the range of discharges to be measured may exceed QmaJQnlin = 350. However, depending on the characteristics of the catchment area, flows in the range of enli, or Q,,,, may not contribute significantly to the total discharged volume of water. If a somewhat larger error (up to 4%) can be tolerated in the rating at the extreme flows, the range of flows that can be measured increases considerably to the values shown in the last column of Table 2.2 (based on 0.05 I H,/L I 1 .O). These values are computed from

2.8

2.5 Influence of Downstream Channel Conditions

As discussed in Section 2.2, for a structure to produce a unique relationship between the sill-referenced head in the approach channel, h , , and the discharge, Q, the upstream water level must be sufficiently higher than the tailwater level, y2. Hence, to design a structure, the tailwater levels must be known over the range of discharges to be measured. Usually, the tailwater levels need only be checked at e,;,, and Q,,, since if flow is modular at those two flows it should also be modular at intermediate flows.

There are two situations of interest with regard to the downstream channel. First, the tailwater level downstream from the flume may be influenced only by downstream channel friction. When this occurs, the flow is said to be uniform (not varying with location along the channel) and the water depth is at normal depth. The Manning equation is often used to describe flow at normal depth:

36 Design Considerations

Table 2.3 Conservative values of Manning’s roughness coefficient to estimate water levels downstream from a flume.

Type of channel and description Concrete-lined

Float finished Float finished, with gravel on bottom Gunite With algae growth

Masonry Cemented rubble Dry rubble, open joints

Earthen channels Straight and uniform, few weeds Winding, cobble bottom, clean sides Non-uniform, light vegetation on banks Not maintained, weeds and brush uncut

Conservative n-value

0.018 0.020 0.025 0.030

0.030 0.035

0.035 0.050 0.060 O. 150

where Q is the discharge, n is the Manning roughness coefficient, A is the cross- sectional area of the channel, R is the hydraulic radius (area divided by wetted perimeter), S’ is the friction slope, and Cu is a constant that has a value of 1.0 when using units of meters and mVs, or 1.486 when using units of ft and ft3/s. When the flow in the downstream channel is at normal depth, the friction slope and bed slope of the channel are equal. Because channel roughness changes over time, tailwater levels should be determined for the seasonal maximum downstream channel roughness. The n-values given in Table 2.3 may be used for a tentative estimate. For broad-crested weirs in channels with a uniform cross section and with tailwater at normal depth, the submergence need only be checked at maximum flow. This is because the tailwater level will generally decline faster than the upstream depth if the flow rate is reduced. Often, there are structures in the channel downstream from the flume or weir to be designed. When this occurs, the tailwater level downstream from the flume is not governed by normal depth, but by backwater (or drawdown) from the downstream structure (or obstruction, overfall, etc.). In such cases, the tailwater level depends greatly on the properties and settings of the downstream structure. From a practical standpoint, the easiest way to determine the resulting tailwater level is to measure it during the worst-case conditions. Even with a broad-crested weir, tailwater needs to be checked at both minimum and maximum flow in these situations, since backwater can cause high tailwater depths even at low flows.

2.6 Sediment Transport Capability

Besides transporting water, almost all open channels will transport sediments. To obtain reliable long-term performance of a flow measurement or regulation structure, sediment transported by the channel should be passed through the structure to the extent possible.

Chapter 2 3 1

1 wash-load 1

o r i g i n of suspended- t ransported load sediments

bed m a t e r i a l - > load

bed-load

Figure 2.6 Terminology used to discuss sediment transport.

This ensures that approach flow conditions and performance characteristics will not change over time because of sediment accumulation. Sediments of varying sizes are present in most channels, and they originate from different sources and are transported by different mechanisms, as illustrated in Figure 2.6. Some basic discussion of the different terminology and possible transport mechanisms is valuable before we address the design of a sediment-discharging structure.

2.6.1 Bed load and suspended load

Bed load consists of sediment particles sliding, rolling, or bouncing (saltating) along or near the channel bed, often in the form of moving bed forms such as dunes and ripples (Figure 2.7). Suspended load refers to bed particles in transport for which the gravity force is counterbalanced by upward forces due to turbulence of the flowing water, so that the particles remain suspended above the bed for appreciable distances and are primarily transported while suspended. These definitions are necessarily imprecise, and clearly distinguishing between the two forms of transport is generally difficult in practice.

2.6.2 Bed material load and wash load

Total sediment load can be subdivided based on the size of the transported particles. Bed material load is the portion of the load consisting of particle sizes found in appreciable quantities in the shifting upper portions of the bed; transport occurs both as bed load and suspended load. Wash load is made up of particles smaller than the bulk of the bed material; these particles are always in suspension and color the water. The total sediment load is the sum of the bed material load and the wash load. However, wash load particles are usually so small (< 50") and have such low fall velocities that they do not contribute significantly to local scour and siltation problems, except in reservoirs, ponded canals, and fields. Passing the bed material load is the primary concern for flow measurement structures.

Bed material load can be estimated using a variety of equations, most of which compute the sediment transport capacity, T, expressed as a volume per unit width of

38 Design Considerations

ripples. This is called bed-load transport, and it can be calculated with the equation of Meyer-Peter and Müller (1 948), which reads

X = A , ( Y - 0.047)1.5 2.1 1

where A , is a factor with an average value of 8 and X is the transport parameter (dimensionless), which is

2.12

with

g T

= acceleration of gravity (9.81 m/s2), and = sediment transport in solid volume per unit width of channel (m3/s per meter

width).

For a particular channel, the values of y, p,., and D, are fixed. The flow parameter and the sediment transport capacity per unit width change if the water depth and/or hydraulic gradient change.

2.6.3 Avoiding sediment deposition

The most appropriate method of avoiding sediment deposition in the channel reach upstream from the flume or weir is to avoid a decrease in the flow parameter, Y. This requires the product of the depth,y, and the hydraulic gradient, S' to remain constant. To achieve this, the structure should be designed in such a way that it creates a minimal backwater effect. With respect to the approach channel bottom, this-means that the curve of Q versus h, f p , for the control should coincide to the extent possible with the curve of Q versus y , for the upstream channel (Figure 2.8). This near coincidence should occur for those flows that are expected to transport bed-load material (i.e., Y > 0.047 in Equation 2.10).

To obtain a reasonable match of the two curves, when the contraction is from the sides only (p, = O), the U-value of the control section (i.e., the exponent in the approximate head-discharge rating equation Q = K,h,") should equal the U-value of the upstream channel. However, if a raised sill is used, the U-value of the control should be less than that of the channel. The U-value of most trapezoidal channels varies between 2.3 for narrow-bottomed channels and 1.7 for wide channels; the shape of an appropriate control section can be selected using the information in Table 2.2.

To obtain a perfect match of the two curves, the structure should create essentially no backwater in the channel section upstream. To achieve this, a drop in the channel bottom is required that is sufficient to provide the needed flume head loss and thus guarantee modular flow. In natural channels, the structure can be located at a site where the channel bottom has a natural drop. When designing flow measurement

40 Descgn Considerations

Figure 2.8 O I

Matching of Q vs. y , and Q vs. h , curves for a sediment-discharging structure.

structures for new canal systems, we recommend including the necessary bottom drop as a part of the system design. When adding flow measurement structures to an existing canal system, it will not be possible to completely satisfy this requirement unless measurement devices can be located at existing drops in the system.

Laboratory tests have shown that both long-throated flumes and broad-crested weirs can pass all sediment that the upstream channel can transport (Bos 1985; Bos and Wijbenga 1997). Figure 2.9 shows a flat-bottomed long-throated flume that has performed satisfactorily since 1970.

If no bottom drop is available to provide for head loss over the structure, the head versus discharge curve of the structure will always be above the stage versus discharge curve of the upstream channel. Even if the structure is designed to operate with the minimum possible head loss, sedimentation will occur in the upstream channel. To avoid sedimentation at the gaging station, the approach channel should be smaller than the upstream channel. It is recommended to contract the channel so the Froude number at the gaging station equals 0.5 at maximum flow and remains as high as possible at lower flows (i.e., minimal bottom contraction). In this way sediment that reaches the structure will pass through the approach channel and the control section, and the structure thus can measure flow accurately. As mentioned before, however, sedimentation will occur in the upstream channel. This trapped sediment needs to be removed at regular intervals.

Chapter 2 41

2. Design considerations2.1 Introduction2.2 Required head loss for modular flow2.2.1 Required head for desirable approach flow2.3 Required freeboard2.4 Range of discharges to be measured2.5 Influence of downstream channel conditions2.6 Sediment transport capability2.6.1 Bed load and suspended load2.6.2 Bed material load and wash load2.6.3 Avoiding sediment deposition