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, - -\ I b6ll HYDRAULIC ENGINEERING '94 The aforementioned equations are convenient to simplify now eq~alion .of open channel hydraulic and .he estimation of their p~...mele~. ~erefore. dl~fic~lues occur in the determination of parameters and 10 vcnficauon of resuhs by measurements. An approach to detennine parameters of Ch6zy equation is presenled by /lodel, Kersten and Slorchenegger (/994). Evaluating t~e ':'Iooff models, Ihe Kirp" h equation was tested with rravcl limes by the salt-dilution method In the mountainous watershed ~Grosser Runs' (Storchenegger, 1984). just only fe~ observations pointed out, that the travel time is reciprocal to channel slope. ~IS gross diSl.Tepancy between measured travel time and c~lcul~ted time of concentntllon demonstrale the necessity for measurements of ttaveluR1eS 10 natural channels. 2. Data acquisition . Measurements of the travel limes were performed in tribularies and in the maIO stream of ~Grosser Runs' river basin by dilution method with salt and "uorescent U1lcers (SIOTcheneBger, /984). "inally'-the sel of coll<<1 dala counts aboul 100 U1lvel times from 20 different reaches with variation on i) slope 5 30 %, ii) calchmenl area 0.03 - 6.5 km2, iii) reach le"glh 0.25 - 1.7 km. Measurements by dilution method during floods in steep torrent are very dangerous. Furthermore, it is difficult to be present during the flood periods. Thus, the development of automatic dilution measurements has become a must (Grun~w. 1986). But this measurements instruments can be distrOyed by some facts hke lighlning slTOke, big floods, deelS, and hik~. . . In addition, measurements perfonned 1R 5 catchments with different and ~ accu-rate methods. Finally, 450 salt dilution measuremenLS (mean velocity, discharge, dispersion factor) from 31 reaches with the following variation were available (/lodel, /993) i) slope ii) catchment area iii) reach lenglh iv) discharge v) mean velocity 1.2 - 90.5 0.04 - 25.3 0.02 - 1.6 0.05 - 2.89 0.04 - 1.14 %, km2, km, m'/s, mls. 3. Evaluation Trying to fit data to several fonnulas, we encountersome difficulties because the paramelers of equalions derived from hydr.lulics equations ar~ highly (,:orrelaled in a nBlur...1 river bassin (e. g: area and slope, area and channel Size, roughness ~nd slope). To avoid singularities in regression analysis probably caused by correlation among independanl variabk!<. ::i'-' vlU"iables were prilrnuily tra?sfonned. In~le~ t~ apply principal compoooRlanalysis, which often leads 10 meanmgless ~omblOal.~ons of factors, the devlations of influenlial variables from geomorphological relanoos were inlroduced in equations to be filled by regression. Best fit was achieved ~y a uncommonly strange structured dimensionfree equ.ilum. Following this equauon, flow velocily is strongly related to discharge and position in stream nelwork but reciprocally related to slope. Area of upstream river basin seems 10 be best parameler - MEAN VELOCITY-NEW fORMUI.A 669 for position in stream network and this value is not affected by map scale. Relating velocity only 10 channel widlh and slope. representing channel size and roughness _ reduces multiple correlalion coefficient squares R2 from 0.85 10 0.80 and relating only; to stream-order of reach reduces 100.78. This n:lation was suspicious and the reciprocal effect of slope to velocity encoumered many doubls. The doubts were justfled by the inaccurracy of dischalge measurements and the difficulties 10 compare with Ch~zyIS equation for unifoml flow. The wide scope of unanswered questions forced Hodel to investigations emphasizing more accurale observalions in river bassins wilh different geology and morphology. 4. The derived formula The objective of the statistical evaluation of the travel lime measuremems is to derive a Cannula which allows a reliable determination of the mean velocity in lorrents. This fannula should conlents only variables. which can be detennined exaclly and wilh justifiable expense in field. from maps or hydrological yearbooks. 1ltis Connula for the mean velocity is based on lite non-linear characler oC Ihe runoff process in torrents and contains the variables discharge. slope of channel and reference discharge. v = a . (Q/(Q. .,0.5))" Fonnula for the eSlimation of the mean velocity in lorrents (Hodel 1993 ). As it can be seen from the ronnula above, there is a strong dependence between mean velocity and discharge. The process of bed-building is partly laken into consideration by using the reference discharge. . The lested torrent reaches can be divided into two groups. Very sleep IOrrents (Flgu~~ I) have a sequence of cascades and basins with extrem vnrying mean velocmes. The runoff characleristics of this type of lorrent (Figure 2) are the fasl falls over drops followed by slower flow in scour-like basins between cascades. But, ~ost imponant and surprising is Ihe simple fonn of the equation, which describes dlfferenl types of watersheds. For the eslimation of Ihe mean velocity in lorrems, Ihe use of following coefr.cienls can be recommended: lorrent mean velocily formula coefficient or sail-dilution reaches (willi insened coeffICients) determination measuremens lorrenls withoul man cascades v - 0.19. 90 377 very steep lorrenls wilh man cascades v-O.46* 97 19 Table I: Fonnula with coefficients for the eSlimation of mean velocily in torrenls. ~