CHAPTER 8  FLUMES
Although Parshall flumes are in extensive use in many western irrigation projects, they are no longer generally recommended because of the advantages of longthroated flumes previously cited and the disadvantages of Parshall flumes to be subsequently discussed. Some states specify the use of Parshall flumes by law for certain situations.
In the past, it was common to size and set flumes for 95percent submergence to reduce approach flow depths 4 to 6 in. The 1976 second edition of this manual gives detailed examples of selecting size and setting crest elevation for free flow and intended submergence. Although correction methods for determining submerged discharge exist, designing flumes for submerged flow measurement is no longer considered good design practice because it compromises accuracy. For example, imprecision of head measurement increases discharge error by 4 to 20 percent over the primary freeflow accuracy of 3 to 5 percent. In addition, a recent study (Peck, 1988) found a 12percent discontinuity in the submergence correction function for a 1ft flume depending upon whether downstream measuring head results from a falling or rising water surface.
Designing and setting Parshall flumes for submerged flow measurement is not usually recommended because less expensive, longthroated flumes can be designed that approach or exceed 90 percent submergence limits with a single upstream head measurement. Moreover, the absolute required drop in water surface is usually less for the longthroated flumes, particularly the modified broadcrested weir styles.
Because so many Parshall flumes are currently in use, the remaining part of this section is concerned mainly with structural dimensions for checking existing flumes, equations for computing discharges, freeflow discharge tables for each size flume, plots for submerged discharge measurement corrections, and head loss curves for assessing upstream depth changes caused by downstream delivery depth changes.
Care must be taken to construct Parshall flumes according to the structural dimensions given on figure 89. This factor becomes more important as size gets smaller. The portion of the flume downstream from the end of the converging section need not be constructed if the flume has been set for free flow where it is not expected to operate above submergence limit. This truncated version of the Parshall flume is sometimes referred to as the Montana flume. Submergence corrections or discharge cannot be determined for Montana flumes or other modified Parshall flumes because they do not include the part of the full Parshall flume where the submergence head, h_{b}, was measured during calibration.Different size Parshall flumes are not geometrically proportional. For example, a dimension in the 12ft flume cannot be assumed to be three times the corresponding dimension in the 4ft flume. Each of the flumes on figure 89 is a standard device and has been calibrated for the range of discharges shown in the table. The flumes can reliably measure freeflow discharge to within "3 to "5 percent, plus head detection error, if standard dimensions are attained during construction, the flume is correctly set, and the flume is operated and maintained according to the recommended procedures.


Parshall flume sizes are designated by the throat width, W, and dimensions are available for flumes from the 1in size for free flow of 0.03 ft^{3}/s at 0.2 ft of measuring head up to the 50ft size with 3,000 ft^{3}/s at a head of 5.7 ft. The freeflow discharge range and dimensions for Parshall flumes are given on figure 89. The minimum flows in this table up to the 1ftsize flume are for a head of 0.2 ft because measuring at smaller heads results in imprecision of head measurement and surface tension effects. The remaining discharge limits are based on the range of the calibration data and practical size considerations.
(a) FreeFlow Discharge Tables and Equations
Parshall flumes were calibrated empirically to generate the freeflow head versus discharge rating for the 1in to 50ft flumes. Some of the larger sizes were not directly calibrated but were scale modeled. The freeflow discharge equations for the standard Parshall flume sizes are of the form:
(83)
where:
h_{a} = measuring head (ft)
Q = discharge (ft^{3}/s)
C and n for each size are given in table 86
Head versus discharge is given in tables A87 through A821 for all sizes (see appendix).
Table 86
Coefficients (C) and exponents (n) for Parshall flumes for equation 83
Throat width 
Coefficient (C) 
Exponent (n) 
1 in 
0.338 
1.55 
2 in 
0.676 
1.55 
3 in 
0.992 
1.55 
6 in 
2.06 
1.58 
9 in 
3.07 
1.53 
1 ft 
3.95 
1.55 
2 ft 
8.00 
1.55 
3 ft 
12.00 
1.57 
4 ft 
16.00 
1.58 
5 ft 
20.00 
1.59 
6 ft 
24.00 
1.59 
7 ft 
28.00 
1.60 
8 ft 
32.00 
1.61 
10 ft 
39.38 
1.60 
12 ft 
46.75 
1.60 
15 ft 
57.81 
1.60 
20 ft 
76.25 
1.60 
25 ft 
94.69 
1.60 
30 ft 
113.13 
1.60 
40 ft 
150.00 
1.60 
50 ft 
186.88 
1.60 
(b) Submerged Flow Determination
Calibration tests show that the discharge at a given upstream measuring head is not reduced until the submergence ratio, h_{b}/h_{a} (submergence head to measuring head) expressed in percent, exceeds the following values:
50 percent for flumes 1, 2, and 3 in wide
60 percent for flumes 6 and 9 in wide
70 percent for flumes 1 to 8 ft wide
80 percent for flumes 8 to 50 ft wide
These submergence limits are based on two measuring head locations shown in figure 89 within the structure and do not measure all the head loss caused by the flume. Thus, these limits do not represent the total required head loss needed to measure flow with one head measurement. The method of determining submerged flow discharge varies with different flume size groups. Examples are provided later.
(1) Submerged Flow in 1 Through 3Inch Flumes
Submergence begins to reduce the discharge through the 1, 2, and 3in flumes when it exceeds 50 percent. To determine discharges for submerged flows, the heads h_{a} and h_{b} are used with figures 810, 811, and 812. Users found they had difficulties in obtaining field readings of h_{b} because of wave interference. To solve this problem, figure 813 was developed to relate h_{b} to h_{c}, which is located at the downstream end of the flume divergence where the water surface is smoother.




In a 3in flume, assume h_{a} of 0.20 ft and the downstream head measured at the h_{c} gage is 0.19 ft. To determine the discharge, turn to the curve on figure 813, which shows the relationship of h_{c} to h_{b}. For a value of h_{c} equal to 0.19, h_{b} is found to be 0.17. The submergence, h_{b}/h_{a} = 0.17/0.20 = 0.85 or 85 percent.
Enter figure 812 with the value of the upstream head, h_{a}, of 0.20 and move horizontally to the right to the vertical line for h_{b}/h_{a} of 85 percent. This intersection point lies about seventenths of the distance from the curved discharge line for 0.06 ft^{3}/s, toward the 0.07ft^{3}/s line. The interpolated discharge value is 0.067 ft^{3}/s. This rate of flow for submerged conditions is considerably less than the freeflow discharge value of 0.082 ft^{3}/s for h_{a} of 0.20 ft. As mentioned previously in section 7 of this chapter, correcting for submergences greater than 90 percent does not provide reliable accuracy.
(2) Submerged Flow Determination With 6 and 9Inch Flumes
When 6 and 9in flumes are operating with submergences greater than 60 percent, the discharge is directly determined using figures 814 and 815, respectively. For example, determine the discharge through a 6in flume when h_{a} is 1.32 ft and h_{b} is 1.20 ft. The submergence ratio, 1.20 divided by 1.32, is 0.91, or 91 percent. On figure 814, find 91 percent along the lefthand vertical scale and follow the 91percent line horizontally to intersect the curved line for h_{a}, which is 1.32 (onefifth the distance between the 1.3 and 1.4 lines). Then move vertically downward from this point to the scale at the base of the diagram and find that the submerged rate of flow is 2.02 ft^{3}/s. As mentioned previously in section 7 of this chapter, correcting for submergences greater than 90 percent does not provide reliable accuracy.


(3) Submergence Correction for 1 to 8Foot Flumes
The submergence corrections that must be subtracted from the freeflow values in table A812 to obtain submerged flow values in a 1ft flume are shown on figure 816. For example, in a 1ft flume with h_{a} of 1.00 ft, the discharge from table A812 is 4.00 ft^{3}/s. If h_{b} is measured to be 0.8, the submergence, h_{b}/h_{a}, is equal to 80 percent. If figure 812 for h_{a} is 1.00 and submergence is 80 percent, the correction is 0.35 ft^{3}/s. Therefore, submergence would result in a reduction in discharge of 0.35 ft^{3}/s or an actual discharge of 3.65 ft^{3}/s, compared to a freeflow discharge of 4.00 ft^{3}/s.

Submergence correction values for 1 to 8ft flumes are obtained from figure 816, but the procedures contained in the note in the figure must be followed. These procedures state that values read from the curve are multiplied by the M values listed in the table on figure 816 for each size to obtain the product or correction to subtract from the free discharge values.
For example, assume that submerged flow occurs in a 3ft flume where h_{a} is 2.10 ft and h_{b} is 1.89 ft. The submergence ratio, 1.89 divided by 2.10, is 0.90, or 90percent submergence. The freeflow discharge for a 3ft flume with h_{a} of 2.10 is found from table A812 to be 38.4 ft^{3}/s. On figure 816, h_{a} is 2.10 and submergence is 90 percent: a correction of 3.5 ft^{3}/s. However, this correction is only for a 1ft flume. For a 3ft flume, the correction must be multiplied by 2.4 (from tabulation on figure 816) to get the total correction of 8.4 ft^{3}/s. The corrected submerged discharge is, therefore, 38.4 minus 8.4, or 30.0 ft^{3}/s. As mentioned previously in section 7 of this chapter, correcting for submergences greater than 90 percent does not provide reliable accuracy.
(4) Submergence Correction for 10 to 50Foot Flumes
The submergence ratio, h_{b}/h_{a}, expressed in percent, and the h_{a} value are used on figure 817 to obtain the correction to be subtracted from the freeflow discharge determined from tables A812 through A820.

The correction values, indicated along the base of the diagram on figure 817, give the number of cubic feet per second to be subtracted for each 10 ft of crest width, W. To aid in determining the multi plying factor, a tabulation has been incorporated on figure 817.
Thus, to determine the discharge for submerged flow through a 20ft flume when h_{a} is 3.25 ft and h_{b} is 3.06 ft, first determine the submergence ratio:
Enter at the left side of the diagram of figure 817, and at h_{a} equals 3.25, project a horizontal line to intersect the 94percent line, then continue on to onetenth of the distance between the 94 and 95percent lines. Vertically below this point on the horizontal scale is the correction value, 56 ft^{3}/s. For a 20ft flume, the multiplying factor is 2.0 (from tabulation on figure 817), and the total correction is:
2.0 x 56 = 112 ft^{3}/s
The free discharge value from table A816 for h_{a} of 3.25 is about 503 ft^{3}/s. Therefore, the submerged flow is 503 minus 112, or 391 ft^{3}/s. As mentioned previously in section 7 of this chapter, correcting for submergences greater than 90 percent does not provide reliable accuracy.
(c) Head Loss Determination
Flumes are obstructions that produce backwater that extends upstream from the flume and raises the water surface in the approach channel. This difference in elevation of the flow upstream from the structure with and without the flume in place is the head loss caused by the flume. The difference in measuring heads is not the head loss of Parshall flumes.
Downstream channel depthdischarge relationships often change with changes of downstream flow resistance, which frequently varies with sediment deposits, debris, canal checking operations, and aging. Downstream changes in flow resistance plus head loss can cause overtopping of upstream approach channel banks. Thus, irrigation system managers that have Parshall flumes need to determine head losses.
(1) Head Loss for 10 to 50Foot Throats
The increase in depth upstream from the structure or the head loss for the 10 to 50ft flume is determined using figure 818. For example, assume a 20ft flume is set 1.4 ft above the bottom of the channel, is discharging 950 ft^{3}/s, and is at 90percent submergence. The head loss from figure 818 is obtained by following the vertical 90percent submergence line up to the curved discharge line for 950 ft^{3}/s, projecting a horizontal line to the sloping 20ft throat line, and coming vertically down to the head loss scale reading of 0.9 ft.

(2) Head Loss for 1 to 8Foot Throats
The head loss values for flumes 1 to 8 ft wide can be determined from figure 819. For example, assume a 4ft flume which has a 70percent submergence with 20 ft^{3}/s, and determine the head loss. Using figure 819, find the intersection of the vertical 70percent line with the slanting 20ft^{3}/s discharge line in the left side of the figure. Then, from this intersection, project a horizontal line to the intersection with the slanting line for the 4ft throat width in the right side of the figure. From this point, project vertically down to read head loss on the bottom scale, which reads 0.43 ft.

(3) Head Loss for 9Inch Throats and Smaller
Losses for 9in flumes and smaller are usually less critical, and the elevation of the upstream water surface is determined in the manner used for the
1, 2, and 3in flumes. The difference between h_{a} and h_{b} is considered an adequate estimate of head loss.