EXPERIMENTAL STUDY OF THE ENERGY DISSIPATION IN THE STEPPED CHANNELS: COMPARISON WITH THE EMPIRICAL MODEL

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1 EXPERIMENTAL STUDY OF TE ENERGY DISSIPATION IN TE STEPPED CANNELS: COMPARISON WIT TE EMPIRICAL MODEL Nouis Messaad a, Djaid Naima a, Gafsi Mostefa a, Boutassouna Kheira a, Gahmani Ahmed a, and Kaouahi Anouar a a Researh Laboratory of Water Resoures, Soil and Environment Department of Civil Engineering, Faulty of Tehnology Amar Telidji University; Adress: Boulevard of the Martyrs P.O. Box 37.G, Laghouat 03000, Algeria. nouis989@gmail.om; djaid.dz@yahoo.fr; msgafsi@yahoo.fr; k.boutassouna@yahoo.fr; hydroahmed@hotmail.fr; a.kaouahi@lagh-univ.dz ABSTRACT Water flowing over stepped hute an dissipate a major proportion of its energy. To show the importane of studying these flows, we made an experimental approah in the laboratory of ivil engineering at the University of Laghouat (Algeria), in three models: model A (4m x 4m x7.5m), model B (8m x 8m x 7.5m), and model C (m x m x 7.5 m). In what follows, we set the rate of flow and vary the slope of the hannel. As result, the effet of the rate flow allowed us to see that: For low flows, the energy dissipation (nappe flow) is imum is around 95% for the three models. For a large flow, the energy dissipation (nappe flow) is minimal and in the order of 8%, 80% and 77% for models A, B and C respetively, The energy dissipation relative imum and minimum flows in skimming flow are of the order of 73% and 70% respetively. Keywords: energy dissipation, nappe flow, skimming flow, empirial model, omparison.. INTRODUCTION: Water flowing over stepped hute an dissipate a major proportion of its energy. On a spillway hute, the steps inrease substantially the energy dissipation taking plae on spillway fae, and lead to a redution in the depth and dimensions needed for the stilling basin at the toe of the hute (Very Dermawan and all, 00). Several researh models have distinguished themselves in the field of flow in hannels stairs, among the most reent works are Benmamar (006), Kerbahe and Benmamar (008a, 008b, 00, 0), Gafsi and Benmamar (0, 03a, 03b), and the most popular are those of Chanson (994, 996, 000). Our work is experiment and onerned with the study of different flows on the stepped hannels, the quantifiation of dissipative energy. To show the importane of studying these flows, we made an experimental approah in the laboratory of ivil engineering at the University of Laghouat (Algeria), in three redued stepped hannels models: model A (4m x 4m x 7.5m), model B (8m x 8m x7.5m), and model C (m x m x 7.5 m) developed "Plexiglas." In what follows, we set the rate of flow and vary the slope of the hannel to show the effet of the slope on the energy dissipation. As result, the effet of the rate flow allowed us to see that:

2 For low flows, the energy dissipation (nappe flow) is imum is around 95% for the three models. For a large flow, the energy dissipation (nappe flow) is minimal and in the order of 8%, 80% and 77% for models A, B and C respetively; The energy dissipation relative imum and minimum flows in skimming flow are of the order of 73% and 70% respetively.. PYSICAL MODEL Experimental studies were onduted on three (3) models stairs developed "Plexiglas". The model "A" onsists of hannel totaling (0) steps and model "B"(0) steps and model "B"(07) steps. Three slopes were studied in this experiment: α = 0, 30 and α = 45, with flow rates ranging from 0.07 l/s to.569 l/s. Photo. : Experimental devie (Gafsi et al, 03b) 3. ANALYSIS OF RESULTS : Figure.: Determination of the limits of different flow in the three models following of Simões (0) shemes (Gafsi et al, 03b) 3.. Determination of flow regime : From our observations and our measurements, we have observed two different flow regimes observed (see fig. ). The appearane of the nappe flow is leading for models B and C on the model A. This is explained by the fat that models B and C have large steps relative to model A. It an be inferred that the steps of important dimensions rather promote nappe flow that skimming flows. This result is onfirmed by Chanson (995) and Simões (0). 3.. Determination of energy dissipation: For a nappe flow with jump fully developed Chanson (994), give one expression adimensionnelle: For a spillway without valve: d d d d 3 d ()

3 Aording Chanson (994), the energy dissipated in skimming flow is expressed by: For ungated spillway: f e 8sin /3 os 3 d Where E is the orretion oeffiient of kineti energy: 3 3 f e E 8sin n (3) n n E 8 n (4) f Where K is the von Karman onstant, equal to 0.4 and f is the frition oeffiient for a non-aerated flow. In the ase of a stepped hannel, Chanson (994) reommends taking f =. d : eight of the dam rest above the foot downstream. f e : oeffiient of frition for an aerated flow. : Slope of the hannel. d : depth of ritial flow. : imum load available. The initial load of the total flow above the threshold is given by: d The residual harge av at the foot of weir is expressed by: av VE dav (6) g where V E is the flow veloity in the setion onsidered. Figures, 3and 4, show the omparison between experimental urves of energy dissipation based on Froude number in the three models A, B and C respetively, and analytial urves plotted aording to equation (). /3 () (5) Figure.: Variation of energy dissipation as a funtion of Froude number (nappe flow) on the Model A (Gafsi et al, 03b)

4 Figure.3: Variation of energy dissipation as a funtion of Froude number (nappe flow) on the model B (Gafsi et al, 03b) Figure.4: Variation of energy dissipation as a funtion of Froude number (nappe flow) on the model C (Gafsi et al, 03b) Figure.5: Variation of energy dissipation as a funtion of Froude number (skimming flow) on the model A (Gafsi et al, 03b). Comment: Energy dissipation in model A is greater than B and C models, and values as e.g. for α = 30 and Fr = 0.: / = % (model A), / = % (mode B), / = 8.4 % (model C); For a given (Figures, 3 and 4) rate flow, the energy dissipation inreases to a relative inrease in the slope. This is explained by the inrease in slope of the first hannel whih influenes the inrease in the height of the weir ( han = L.sinα), and therefore the inrease of the kineti energy. For a given (Figures, 3 and 4) slope, the energy dissipation dereases with inreased flow. This is explained by the effet of the inrease of maro-roughness with inreasing speed. Therefore the energy dissipation is redued.

5 4. GENERAL CONCLUSION: The experimental and analytial urves of energy dissipation show the same profiles, that is, dereasing trends, of low (low value of the Froude number) at high flow rate (high value of the Froude number). Also, theses urves merge almost for small flows, so that, for high flows, both urves show a visible differene. This is mainly due to the leakage rate is greater at high flow and low flow less. For steep slopes and low-flow steps, the flows in stepped hannels, ause signifiant dissipation of energy in the nappe flow and skimming flow. The flows with average to high flow rates, favor rather skimming flows on the steps of small dimensions than those large, whih verifies the assumption made by.canson 995. The influene of the slope of large energy dissipation is more visible on the nappe, those on skimming flows. The larger values of energy dissipation are obtained on the nappe flows, those on the skimming flows. This is explained by the effet of the maro-roughness whih is less on the small steps. The energy of dissipation on the nappe flow and skimming flow is influened by three parameters, namely: the slope of the hannel, the flow rate and the geometry of the stairs. Referenes :. Benmamar, S. (006). «Etude des éoulements dans les onduits à motifs périodiques Appliation aux évauateurs de rues». Thèse de dotorat, Eole Nationale Polytehnique d Alger, Algérie, 97 pages.. Chanson,. (994). Comparison of Energy Dissipation between Nappe and Skimming Flow Regimes on Stepped Chutes. Jour. of yd. Res., IAR, Vol. 3, N, pp 3-8. Errata:Vol. 33, No., p. 3. Disussion: Vol. 33, No., pp Chanson,. (995). ydrauli Design of Stepped asades, Channels, Weirs and Spillways. Pergamon, Oxford, Uk, Jan., 9 pages (ISBN ). 4. Chanson,. (996). Predition of the Transition Nappe/ Skimming Flow on a Stepped Channel. Jour. of yd. Res., MIAR, Vol. 34, N 3, pp Chen, C.L. (990). Unified Theory on Power Laws for Flow Resistane. Jour. of yd. Eng., ASCE, Vol. 7, N 3, pp Gafsi, M, Benmamar S, Djehihe A, and Kerbahe K. (0). Influene of the Flow Rates and the Channel Slope in the Energy Dissipation on Flows in the Stepped Channel. Wulfenia Journal (ISSN: 56-88X), Vol 9, No. ;Nov 0, pp Gafsi, M., Benmamar, S. (03a). Etude de l effet de la pente sur les aratéristiques hydraulique des éoulements dans les anaux a motifs périodiques. Thèse de Master en hydraulique, Université Ammar Telidji a Laghouat. 8. Gafsi, M. Benmamar, S. (03b). Etude de l effet du débit sur les aratéristiques hydraulique des éoulements dans les anaux a motifs périodiques. Thèse de Master en hydraulique, Université Ammar Telidji à Laghouat. 9. Kherbahe K., (008a) - Elaboration d un ode de alul régissant les éoulements sur les oursiers d évauateurs de rues. Mémoire de magister en hydraulique, Eole Nationale Polytehnique d Alger, p Very D. Nadjadji Anwar, E (00). ydrauli model of flow onditions on stepped spillway due to number of steps. International journal of aademi researh, Vol.. No. 5. September, 00, pp.: