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1、TECHNICAL REPORT IS0 TR 11656 First edition 1993-06-01 Measurement of liquid flow in open channels - Mixing length of a tracer Mew-e de d - type 2, when the subject is still under technical development or where for any other reason there is the future but not immediate possibility of an agreement on
2、 an International Standard; - type 3, when a technical committee has collected data of a different kind from that which is normally published as an International Stan- dard (“state of the art”, for example). Technical Reports of types 1 and 2 are subject to review within three years of publication,
3、to decide whether they can be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be reviewed until the data they provide are considered to be no longer valid or useful. ISO/TR 11656, which is a Technical Report of type 3, was prepared by Technical Commit
4、tee ISO/TC 113, Measurement of liquid flow in open channels, Sub-Committee SC 4, Dilution methods. Annexes A, B and C of this Technical Report are for information only. . . . III Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Rock Island Arse
5、nal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction or networking permitted without license from IHS -,-,- ISOlTR 11656:1993(E) Introduction A variety of formulae have been developed for estimating mixing length in open channels. Some of these formulae hav
6、e been developed for special flow conditions. Most mixing-length formulae have been developed for injection of a tracer at the centre of flow. Mixing theory will also allow these formulae to be used for the injection of a tracer at one edge of the flow. However, there are times when, for a variety o
7、f reasons, a tracer is injected at a point other than the centre or edge of flow. Also, the tracer may be in- jected from a line source or from a multiple-point source. Thus, a mixing-length formula is needed that can estimate the mixing length for different injection situations. Mixing-length formu
8、lae are generally developed for a condition which assumes complete mixing. However, an examination of the mixing process indicates that an infinite distance is required for theoretically complete mixing (100 Oh). If this theory is correct, then the existing mixing-length formulae only approximate co
9、mplete mixing. Experience shows that satisfactory flow measurements can be made with less than complete mixing. Special methods can be used to minimize errors re- sulting from measurements at considerably less than complete mixing. For these reasons, it is important to provide an objective means of
10、de- fining the degree of mixing, and to estimate the mixing distance associ- ated with various specified degrees of mixing. These results may lead to the elaboration of a future International Standard. iv Copyright International Organization for Standardization Provided by IHS under license with ISO
11、 Licensee=Rock Island Arsenal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction or networking permitted without license from IHS -,-,- TECHNICAL REPORT ISOlTR 11656:1993(E) Measurement of liquid flow in open channels - Mixing length of a tracer 1 Scope This
12、Technical Report investigates cross-channel mixing characteristics of solutes injected in streams. Specifically, it relates to the use of tracers for the measurement of discharge. A tracer must be well mixed, or compensating measures taken, in order to obtain a satisfactory dilution-type discharge m
13、eas- urement. The purposes of this Technical Repot-t are as fol- lows: a) to compare methods of defining the degree of mixing of a solute in a stream and to recommend a method; b) to compare methods of estimating the mixing length (the downstream distance required for a solute to thoroughly mix acro
14、ss a stream) and to recommend a particular method: c) to investigate the errors in dilution measure- ments associated with incomplete mixing; d) to discuss methods of reducing errors in dilution-discharge measurements when mixing is incomplete. 2 Reference The following standard contains provisions
15、which, through reference in this text, constitute provisions of this Technical Report. At the time of publication, the edition indicated was valid. All standards are subject to revision, and parties to agreements based on this Technical Report are encouraged to investi- gate the possibility of apply
16、ing the most recent edi- tion of the standard indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards. IS0 772:1988, Liquid flow measurement in open channels - Vocabulary and symbols. 3 Definitions For the purposes of this Technical Report, the deli- nit
17、ions given in IS0 772, except where noted, and the following definitions apply. 3.1 complete mixing: Mixing which occurs at a channel section, when the constant-injection method is used, if the steady-state tracer concentrations are equal at all points in the cross-section. Similarly, for the sudden
18、 injection method, mixing which occurs if the areas under the time/concentration curves are equal at all points sampled in a section. 3.2 degree of mixing: Measure of the extent to which mixing has been achieved in a cross-section downstream from the injection of a tracer. The degree of mixing may v
19、ary from nearly 0 % in a cross-section immediately downstream from the injection to 100 % at a cross-section in which the tracer has been completely mixed across the entire cross-section. 3.3 mixing length: Distance, measured along the general path of flow between the injection cross- section and th
20、e downstream cross-section, at which the specified degree of mixing is obtained. 1 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Rock Island Arsenal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction
21、or networking permitted without license from IHS -,-,- ISOITR 11656:1993(E) For given conditions, the mixing length is not a fixed value. it varies according to the specified degree of mixing. The higher the specified degree of mixing, the longer the mixing length. 4 Units of measurement The units o
22、f measurements used in this Technical Report are those of the International System (SI). 5 Determination of the degree of mixing 5.1 Criteria and concepts Determination of the degree of mixing should be readily conceptualized. It should also provide a unique value for the degree of mixing which can
23、be rationally related to the mixing observed in the channel. The values describing the degree of mixing range from 0 to 100 %. Where mixing has just begun, near the injection source, the degree of mixing approxi- mates 0, and where mixing is complete, it reaches 100 %. if a tracer has been injected
24、such that it is completely mixed in half of the flow and is not mixed at ail in the other half, the degree of mixing is 50 %. The concept should hold for conditions where the tracer is fully mixed in other specified parts of the flow and is not mixed at ail in the remaining flow. For a selected down
25、stream cross-section, the de- gree of mixing is determined by using the areas un- der N curves of concentration as a function of time for the sudden injection method, or by using N con- centration values on the plateau for the constant- injection method. The areas of the concentrations must be relat
26、ed to some cross-sectional flow char- acteristic. Because of the mass balance of tracer, the appropriate characteristic is cumulative dis- charge, or relative cumulative discharge, measured from one edge of flow. The preferred index is the relative cumulative discharge, ranging in value from 0 to 1.
27、 Width or other cross-section characteristics vary from one cross-section to another, and are not usually adequate for accounting for the mass bai- ante of tracer. 5.2 Formulae defining the degree of mixing Various formulae have been proposed for defining the degree of mixing. Five such formulae are
28、 pre- sented below. Coefficient of variation (see I, page 6 and 7, page 1073) x100 . Rimmar equation (see I, page 6) (1) Schuster equation (see I, page 6 and 8, page 134) N c 1 ci - c 1 n$is= I- i= L I NC x 100 . . , (3) Cobb-Bailey equation (see 9, page C5 and 5, iwe 48) . . (4) or, in discrete for
29、m Graphic (Cobb and Bailey, communication) M,=(- (5) (6) SC is the standard deviation of the concen- trations observed in a section; c is the observed tracer concentration; this is the steady-state concentration ob- served at a selected cross-section for the constant-injection method, or the area un
30、der the time/concentration curve for the sudden injection method; 2 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Rock Island Arsenal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction or networking p
31、ermitted without license from IHS -,-,- ISOlTR 1165 is the average concentration in the channel cross-section; is the concentration observed in the cross-section having the greatest deEar- ture from the average concentration C; is the number of observation points across a section; the observations a
32、re taken at the centre of equal increments of flow; is the total stream discharge; is the cumulative discharge at any point in a channel cross-section; the value of q is 0 at one bank and Q at the opposite bank; A and B are the areas associated with the cross- sectional distribution of tracer (see f
33、igure I). The characteristics of the various definitions of mix- ing may best be seen by looking at a number of ex- amples. The examples A, B, C and D which follow assume that the concentration was observed at 10 points across the section. The assumed concen- tration distributions are shown in ftgur
34、e2. The de- grees of mixing computed by the various formulae are shown in table 1. The concentration distributions shown in figure 2 are idealized distributions which can be approximated by a line injection across a part of a section. The distributions shown in figure2 are used to demon- strate vari
35、ous characteristics of the formulae. Table 1 - Degree of mixing computed by application of the various equations to the concentration distributions shown in figure 2 Values in percentage I I I Equation 1 D;ree,of mfingi M.tr errnre 1 (1) 200 100 50 0 (2) 400 100 -100 0 (3) - 60 0 60 100 (5) 20 50 80
36、 100 (6) 20 50 80 100 Figure 1 - Graphic description of the degree of mixing 3 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Rock Island Arsenal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction or n
37、etworking permitted without license from IHS -,-,- ISO/TR 11656:1993(E) I 0 O-2 1 q/Q 0 0.5 1 Example A Example B C c 1 1 0 088 1 q/Q 0 1 q/Q Example C Example II Example q/Q Concentration observed, C, for an average concentration, ?, across a section of 0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75 0,85
38、0.95 A 072 180 180 0 0 0 0 0 0 0 0 B 03 1,o 180 170 130 1,o 0 0 0 0 0 C 098 ItO 190 14 1,o 180 14 l,O 180 0 0 D 170 I,0 I,0 190 14 180 14 I.0 I,0 ItO I,0 I I Figure 2 - Hypothetical concentration distributions across a section (constant-injection method) A number of observations can be made from thi
39、s exercise. Equations (1) and (2) can give values which exceed 100 %. Equation (3) gives negative values for low degrees of mixing. Equation (2) can have negative values for some degrees of mixing. The definition of the coefficient of variation equation (I) appears to be uniquely valued but shows an
40、 inverse relation with the degree of mixing. That is, the lower the computed value, the higher the degree of mixing. The Cobb-Bailey formula equations (4) and (5) and the graphic formula equation (S) give identical numerical values. In fact, the Cobb-Bailey formula was developed to be consistent wit
41、h the graphic definition. Examination of the concentration distri- bution curve across the injection point cross-section will reveal by the graphic method that MG ap- proaches zero. This can also be shown mathemat- ically by the Cobb-Bailey formula. It is seen that only the Cobb-Bailey and the graph
42、ic formulae, equations (4), (5) and (6) fully meet the rec- ommended criteria. 5.3 Recommended formula Because of the above characteristics, as revealed in table 1, the definitions of mixing given by Rimmar and Schuster may be discarded. These equations do not define a unique degree of mixing at eve
43、ry condition of mixing. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Rock Island Arsenal/9983967100, User=Schabilion, Shelley Not for Resale, 04/10/2007 06:22:34 MDTNo reproduction or networking permitted without license from IHS -,-,- ISOl
44、TR 11656:1993(E) The coefficient of variation equation (l) exhibits an inverse relation with the degree of mixing and may also give values greater than 100 %. The graphic definition equation (S) provides a clear and easy-to-follow conceptual definition. Both the Cobb-Bailey and the graphic formulae
45、equations (4), (5) and (S) fit the criteria established earlier and provide identical results. These two definitions thus are recommended for determining the degree of mixing. In most cases, the discrete form, equation (5), will be necessary. The computed degree of mixing may vary slightly with the
46、number of cross-channel ob- servations. In a practical situation, the problem arises of how to determine the relative flow, q/Q, across a channel without increasing the number of sub-area and vel- ocity measurements across the channel. At times, information is available for defining the variation of
47、 the relative flow across a section. Otherwise, an approximate calculation can be made on the basis of width by substituting relative width in place of relative discharge, q/Q, in equations (4) and (5). Whether the values of q/Q are approximated or not, it is conceptually essential to have a definit
48、ion that requires each concentration observation to be weighted by flow, because this is the only means of accounting for the mass balance of the tracer. 6.2 Methods of estimating mixing length There are three general approaches to estimating mixing lengths: direct observation, the empirical method
49、and the theoretical method. 6.2.1 Direct observation Direct observation involves injecting a tracer into a channel and, from measurements, determining the distance required for mixing. The results are gener- ally valid only for that channel and for those flow conditions for which the observations were ma