CHAPTER 8 - FLUMES

9. Precomputed Design and Selection Tables for Long-Throated Flumes

Precomputed designs and selections are provided in tables 8-2 through 8-5. These tables are provided for the convenient design and selection of long-throated structures in the field or office without use of a computer. These tables provide long-throated flume selections that can be fitted into lined trape-zoidal, rectangular, circular, and earthen channels. All of the structure choices provided in the design tables consist of a simple ramp rising from the channel bottom followed by a flat horizontal crest or sill to form a broad-crested weir and ending in an abrupt drop. Tables 8-2 and 8-3 are for lined trapezoidal channels. Table 8­4 is for lined rectangular channels or earthen channels. Table 8-5 is for long-throated flumes that fit into circular conduits flowing partially full.

Long-throated V-shaped flumes which are used in natural channels are not included in this manual. Structures for natural streams are discussed in more detail in Brakensiek et al. (1979). Also, trapezoidal flumes with side contractions which are not generally selected for usual irrigation situations are not included in design tables. These flumes are usually more difficult to construct, more expensive, and increase head loss.

The calibration equations were developed from discharge tables computed with WinFlume and its predecessors (Clemmens et al. 1987 and 1993). Two equation forms are commonly used: a third-degree polynomial and a power form. The power form is selected here because it looks similar to the historical equations for weirs and flumes. It should be remembered that these equations are simply curve-fit results with no theoretical derivation. The equation coefficients, exponents, and constants are provided in tables 8-2 through 8­5. The pre-calibrated flumes in the tables have been sorted from innumerable possible choices based on practical experience and theory and reduced to a relatively few selected structures from which the designer may choose.

Besides selecting shape and size, the tables help to determine head-discharge characteristics, obtain proper measurement range, obtain sufficient sensitivity, meet the Froude number limit, and provide a final calibration.

The equation coefficients, exponents, and constants included in the tables were developed with the assumption of a known approach channel cross-sectional shape and area. However, any particular control section size and shape can be used with any approach section size and shape. But discharges must be adjusted with the approach velocity coefficient, C_v (Bos et al., 1991). The rating equations with use limits are given in design and selection tables that automatically limit the Froude number. However, if smaller approach areas are used, the designer must determine that the Froude number remains less than about 0.5.

Frequently, the site conditions may call for flumes that would have dimensions beyond the ranges provided by the ratings in this chapter. To extend beyond these limits and for further information, refer to Bos et al. (1991), Clemmens et al. (1993), Ackers et al. (1978), and Bos (1989). The designer has the option of designing a flume shape or size not presented here by using the theoretically based computer program (Clemmens et al., 1987; 1993).

(a) Long-Throated Flumes for Lined Trapezoidal Channels

Precomputed calibration tables for selected long-throated trapezoidal flumes suitable for use in some common canal sizes are included in tables 8-2 and 8-3. In selecting these standard canal sizes and slopes and their related flow rates for these design tables, consideration was given to proposals by the International Commission on Irrigation and Drainage (ICID), to the construction practices of the Bureau of Reclamation, and to design criteria for small canals used by the United States Natural Resources Conservation Service (formerly the Soil Conservation Service) (Bos et al., 1991).

Present practice dictates side slopes of 1:1 for small, monolithic, concrete-lined canals with bottom widths less than about 3 ft, and depths less than about 3 to 4 ft. Deeper and wider canals tend toward side slopes of 1.5 horizontal to 1 vertical. When the widths and depths are greater than about 10 ft, the trend is more toward 2:1 side slopes. This trend is particularly observed if canal operating procedures may allow rapid dewatering of the canal. In some soil conditions, rapid dewatering can cause hydrostatic pressures on the underside of the canal walls that lead to wall failure. Most of the lined canals used in a tertiary irrigation unit or on large farms are of the smaller size. They have 1- to 2-ft bottom widths, 1:1 side slopes, and capacities below 35 ft³/s.

Standard sizes and precalibrations are given in tables 8-2 and 8-3 so that the designer may select one of these structures to be built into an existing lined channel as shown on figure 8-5. The designer need only select a weir width with its corresponding sill height. Standard bottom ramp-flat crest combination flumes in typical slip-formed canals were selected for precalibrations.

Table 8-2 gives precomputed flume selections for trapezoidal canals with bottom widths of 1, 2, and 3 ft. Canal sizes with bottom widths in excess of 3 ft are omitted in the precomputed design tables on the assumption that larger sizes deserve special design consideration and should be computer designed and calibrated using accessible programs such as those provided in Clemmens et al. (1993).

Table 8-2 provides a number of precomputed flumes that may be used for the various combinations of bottom widths and sidewall

slopes as given in the first two columns. The third column lists recommended values of maximum canal depth, d, for each side-slope and bottom-width combination.

The offering of many precomputed sizes will aid in retrofitting older canal systems and yet not prevent the adoption of standard sized canals as proposed by other agencies and international bodies, such as the Natural Resources Conservation Service, U.S. Department of Agriculture (USDA), and the ICID.

For each combination of bottom and side slope, several standard crest sill heights can be used (column 8 in table 8-2). Columns 4 and 5 give the limits on discharge for each canal-flume combination. These limits on canal capacity originate from three sources:

(1) The Froude number, equation 2-25, in the approach channel, is limited to less than 0.5 to assure water surface stability.

(2) The canal freeboard, F_b, upstream from the structure, should be greater than 20 percent of the upstream sill-referenced head, h₁. In terms of canal depth, this limit is d>(p₁ + 1.2h_1max).

(3) The sensitivity of the flume at maximum flow should be such that a 3/8-in change in the value of the sill-referenced head, h₁, causes less than a 10-percent change in discharge.

Also indicated in the last column of table 8-2 is a minimum head loss, H, that the structure must provide. Excessive downstream water levels may prevent this minimum head loss, which means that the structure exceeds its modular limit or submergence limit and no longer functions as an accurate measuring device.

When flumes are placed in irrigation canals, the downstream channel is similar to the upstream channel, and the modular limit range for a flume with no expansion section of 72 to 93 percent for low flow to high flow is appropriate. The tables presented herein for long-throated flumes and broad-crested weirs are based on this assumption, except that the upper limit is conservatively reduced to 90 percent.

Thus, the design head loss is either 0.1 h₁ or the listed value for H, whichever is greater. For these tables, it was assumed that the weir was placed in a continuous channel with a constant cross section. Technically, this limit of submergence is based on the total energy drop through the structure, but the velocity head component is usually of the same order of magnitude upstream and downstream so that h may be satisfactorily substituted for H.

Table 8-2 is primarily intended for the selection among these structures. It is also useful for the selection of canal sizes. The Froude number in the canal is automatically limited to 0.5. Selecting the smallest canal for a given capacity will give a reasonably efficient section. For instance, if the design capacity of the canal is to be 35 ft³/s, the smallest canal that can be incorporated with a measuring flume has b₁ = 2 ft, z₁ = 1.0, and d = 3 ft.

Each standard flume can be used for a range of bottom widths because the change in flow area upstream from the structure causes only a small change in velocity of approach and a corresponding small change in energy head. The width ranges have been selected so that the error in discharge caused by the change in flow area is less than 1 percent. This is a systematic error for any particular approach channel size, and the extent of this error varies with discharge. However, the width of the crest must match the table dimension value.

A flume suitable for several of the listed canal bottom widths is also suitable for any intermediate width. For example, in table 8-2, structure E_e can be used in canals with bottom widths between 1 and 2 ft; for example, b₁ = 1.25 ft. The user will need to determine the sill height to match b_c, head loss, and maximum design discharge for these intermediate sizes.

The rating equation coefficients and constants for the flumes are given in table 8-3 and will reproduce the values presented in the original calibration tables produced by computer modeling (Bos et al., 1991) to within about +1 percent. The original tables were computed using the following criteria and the symbols on figure 8-5:

(1) Each flume has a constant bottom width, b_c, and a sill height, p₁, that varies with the canal dimensions.

(2) The ramp length can be chosen such that it is between 2 and 3 times the sill height. The 3:1 ramp slope is preferable.

(3) The gage is located a distance equal to at least maximum total head, H_1max, upstream from the toe of the ramp. In addition, the gage should be located a distance of roughly 2 to 3 times H_1max from the entrance to the throat.

(4) The throat length should be at least 1.5 times the maximum expected sill referenced measured head, h_1max, but should be within the limits indicated in table 8-2.

(5) The canal depth must be greater than the sum of (p₁ + h_1max + F_b), where F_b is the freeboard requirement, which is roughly 0.2 times the sill referenced maximum measured head, h_1max.

Occasionally, a flume cannot be found from these design tables that will work satisfactorily. The user must then judge and select between several options; for example:

(1) Find a new site for the structure with more vertical space.

(2) Add to the canal wall height upstream from the site so that more backwater effect can be created.

(3) Try one of the other shapes.

(4) Use the design tables to interpolate and get a rating for an intermediate width, probably with some sacrifice in accuracy.

(5) Produce a special design using the computer model.

(b) Long-Throated Flumes for Unlined Channels

Measurement flumes for earthen (unlined) channels require a structure that contains the following basic parts: entrance to approach channel, approach channel, converging transition, throat, diverging transition, stilling basin, and riprap protection. As illustrated on figure 8-6, the discharge measurement structure for an earthen channel is longer, and thus more expensive, than a structure in a concrete-lined canal (figure 8-5). In the latter, the approach channel and sides of the control section already exist, and the riprap is not needed.

For earthen canals, the designer selects both structure flow width and a sill height and must be more aware of the other design considerations. For lined channel design, only the sill height must be selected.

If the upstream sill­referenced head is not measured in a rectangular approach canal of this same width, but instead is measured in the upstream earthen section, then these tables require correction to the discharge, Q, for the change in the approach velocity. The tables and equations can also be used to determine the rating for side-contracted rectangular flumes. Procedures needed to handle and correct for change of velocity of approach are given in Bos (1989), Bos et al. (1991), and Clemmens et al. (1993). Throat lengths for side contractions appear to work best if they exceed about 2 times the throat width.

The full-length structure of figure 8-6 can be simplified by deleting the diverging transition (downstream ramp) or the entire extended rectangular tailwater channel.  These changes will increase the head loss across the structure and force energy dissipation to take place within the earthen canal section.  The extended tailwater section of the structure may be deleted only if adequate riprap is provided and if the Froude number in the tailwater channel is less than 1.7 at maximum flow (Bos et al. 1991).

The approach canal of figure 8-6 provides a known flow area and velocity of approach. The coefficients and constants for rating equations for the rectangular flumes given in table 8-4 assume that the approach section is rectangular and has the same width as the throat.

The rectangular measurement flume discharges nearly equal quantities of water over equal widths. The major differences are associated with the friction along the walls. Thus, the flow is nearly two-dimensional along the crest, so rating tables can provide the unit flow rate, q, in cubic feet per second per foot width of crest for each value of h₁. This allows a wide variety of sizes for rectangular long-throated structures. For each width, b_c, of the structure, an accurate rating table can be developed by multiplying the design table discharges by b_c:

The equation, coefficients, and exponents for a series of rectangular flat-crested, long-throated flumes given in table 8-4 were developed from computer modeled tables given in Bos et al. (1991). The equation will reproduce those computer-derived table values to within +1.5 percent. The equation coefficients and exponents are given for sets of p₁ or crest heights. However, interpolation between crest heights gives reasonable results. Small groupings of structure widths were averaged to keep sidewall effect error to within 1 percent. Overall accuracy of rectangular long-throated flumes can be between 2 and +5 percent, depending on how accurately water levels are measured. Overall accuracy of +2 percent is possible but requires calibration by the computer program of Clemmens et al. (1993) and sensitive stilling well water level measurements.

If the approach area, A₁, is larger than that used to develop these rating design tables, either because of a higher sill or a wider approach channel, the ratings must be adjusted for C_v. To simplify this process, the discharge over the structure for a C_v value of 1.0 is given in the far right column of each grouping. This column is labeled p₁ = infinity because that would cause the approach velocity of zero, and C_v would be 1.0. This scenario approximates a structure at the outlet of a reservoir or lake. The complete correction procedure is given in Bos (1989), Bos et al. (1991), and Clemmens et al. (1993).

The design procedure for lined rectangular canals is relatively straightforward. It consists of selecting a table crest height, p₁, that causes modular flow throughout the discharge range and provides sufficient freeboard at the maximum discharge. An appropriate width must be chosen for unlined canals. Several widths will usually work. Extremely wide, shallow flows are subject to measurement errors because of low head detection sensitivity. Extremely narrow, deep flows require long structures and large head losses.

Because of the wide variety of shapes that can be encountered in earthen channels and in the range of discharges to be measured, determining the interrelated values of h_1max, p₁, and b_c of the structure is complicated. Although this difficulty complicates the design process, it allows the designer greater flexibility and expands the applicability of the flumes. The following criteria should be considered by the designer:

(1) The discharges to be measured (per foot of width) must be within the range of discharges shown in the table for the selected structure if the dimensions in the tables are to be used.

(2) The needed or selected allowable combined measurement error should be checked and not exceeded. The allowable error may vary for different flow ranges (Bos et al., 1991; Clemmens et al., 1993).

(3) Sufficient head loss should be available across the structure at all flow rates.  If there is an abrupt expansion (no downstream ramp) into a rectangular channel the same width as the crest, the head loss should be the greater of 0.1H₁ or the value shown in table 8-4.  If the downstream channel is wider than the crest, the head loss should be at least 0.4H₁.


(4) Placing a structure in the canal should not cause overtopping upstream.

(5) A uniform, straight, and unobstructed approach channel section of 10 times the channel width should precede the structure.

(6) The Froude number, as defined in chapter 3, should not exceed 0.5 for a distance of at least 30 times h₁ upstream from the structure.

Following these criteria will allow the designer to select a satisfactory structure that will operate as intended.

For a rectangular long-throated flume in an earthen canal, the rectangular section need not extend 10 times its width upstream from the structure if a gradual taper is used to guide the flow into the rectangular section. For the structures given here, it is recommended that the rectangular section extend upstream from the head measurement location (gaging station) as shown on figure 8-6. It is also recommended that well-designed protective riprap be placed downstream from the structure for a distance of four times the maximum downstream channel flow depth, y_2max (figure 8-6). A step should be provided at the downstream end of the structure just before the riprap section to avoid local erosion from floor jets. Sizing of riprap and filters is discussed by Bos (1989) and Bos et al. (1991).

A freeboard criteria of 0.2 h_1max has been used satisfactorily for lined channels. For unlined channels, it may be more appropriate to specify a maximum approach flow water depth, y_1max. The downstream water depth, y₂, needs to be checked and must not exceed the submergence or modular limit for both the minimum and maximum expected discharge.

If the channel is rectangular or the length of the rectangular-throated flume downstream from the crest end is as on figure 8­6, then 0.1 H₁ or the H value given at the bottom of table 8-4 can be used as the lower value of minimum required total head loss, H. If a shorter length in an earthen channel is used and the tailwater channel is significantly larger than the stilling basin would be, then considerably more head loss will probably be required. The designer should use the head loss value for the discharge into a lake or pool, H=0.4H₁. This value may represent a drastic difference in the value of head loss. The designer may decide to use the shortened structure and calculate the actual modular limit by use of the computer model (Bos et al., 1991). Another alternative is to build a prototype in the field and set the crest to the appropriate level by trial and error.

(c) Measuring Flow in Circular Conduits Partly Full

As previously mentioned, long-throated flumes for circular conduits are convenient for use as portable and permanent measurement structures. Bottom ramps followed by flat crests or sills can be used in circular conduits. These flumes (figure 8-7) are usually placed in the conduit at a crest height from 0.2 to 0.5 times the pipe diameter in height. The open channel depth limit in the conduit is about 0.9 times the approach conduit diameter.

General methods of computing calibrations for long-throated flumes in circular conduits and selected construction configurations were developed using the computer model described in Clemmens et al. (1993).

The precalibrated selections given in table 8-5 are for average roughnesses of construction materials and are based on curve-fitted equations of computed discharge tables in English units for dimensions proportioned in terms of pipe diameter. Calibration equations for other pipe diameters can be approximated using Froude modeling relationships, which produce the following equation:

where:

Q = discharge, ft³/s
D = diameter of pipe, ft
K₁ = constant from table 8-5
K₂ = constant from table 8-5
h₁ = head measured from sill top (bottom of contracted section), ft
U = Exponent

Precalibrated flumes represented in table 8-5 are subject to Froude scaling. These and all the long-throated flume shapes can be similarly scaled without using the computer model as long as all dimensions remain proportional. Small differences from direct computer results are to be expected because roughness of construction materials is not usually scaled. Smooth concrete roughness was used to develop the values in table 8­5. The calibration equations, coefficients, constants, and exponents for the equation from table 8-5 will usually produce calibrations within +3 percent of discharge, not counting the error of head measurement, for scaling ratios between 1:5 and 5:1. Scaling expansion by 10 tends to overemphasize roughness and will underpredict discharge by 5 to 10 percent. Accuracy within +2 percent requires individual computation of the constructed device using the constructed dimensions in the computer model of Clemmens et al. (1993).

As with the other broad-crested weirs and long-throated flumes, the width of the flat crest or sill surface, b_c, is one of the two most important dimensions in the flume. The other is the zero elevation of the head measuring device.

For portable measurements, it is recommended to translocate the water surface to a small stilling well overhanging the crest at the head reference location. Thus, the translocated head in the stilling well is conveniently referenced to the crest without the necessity of surveyor leveling of the structure (Bos et al., 1991). The measuring head and crest elevation can both be measured by the same point gage. The upstream gage should be used only if it is accurately leveled or is part of a permanently installed flume.

For example:

A circular concrete culvert 4 ft in diameter and 20 ft long is to be converted into a measuring structure. The outlet ends in an overfall so that a minimum sill height of 0.2D is useable. Develop the calibration equation using table 8-5, and sketch the installation dimensions.

Using equation 8-2 and table 8-5 gives:

The modular or submergence limits should be checked and should not exceed 0.8h₁ if a vertical drop exists at the end of the downstream crest and should not exceed 0.9h₁ if a 1:6 horizontal sloping ramp downstream is added such as shown on figure 8-6. These modular limits are equivalent to minimum required head loss to measure flow of 0.2h₁. All flow rates to be measured should be checked for exceeding the modular limit.

A stilling well can be placed in the channel if it does not significantly obstruct flow or divert flow to a far bank and cause erosion. Placing the stilling well in the upstream channel often causes detrimental flow patterns that can affect the function of the flow measuring device, unless it is dug deep into the bank or placed a substantial distance upstream.

Represented on figure 8-8 is a static pressure tube consisting of several 1/8-in-diameter holes drilled into 1-in polyvinylchloride pipe used as a head measurement pickup. These holes are located about 2 ft from the end of the capped pipe so that flow separation around the end of the pipe is neutralized by the time the flow passes the pressure sensing holes. The water level sensed here is transmitted to the stilling well where the depth can be observed by any of the several methods discussed in section 7 of this chapter.

Note that the sensing holes are well above the floor of the channel, which should reduce sediment plugging. Also, note that the sensing pipe is clamped tightly to the wall of the culvert so that debris trapping is minimized. The area obstruction of the pipe crossing the sill control area is small and can be ignored.

(d) Constructing Portable Long-Throated Flumes for Circular and Semicircular Conduits

A 0.2D sill height is commonly selected for semicircular conduits. For either semicircular or complete pipes, the sloping ramp can be fabricated from sheet materials such as galvanized steel, stainless steel, aluminum, or marine plywood. A suggested method for layout of the necessary portion of an ellipse is illustrated on figure 8-8.