energy dissipation and residual energy on embankment ... - UQ eSpace

ENERGY DISSIPATION AND RESIDUAL ENERGY ON EMBANKMENT DAM STEPPED SPILLWAYS Stefan FELDER (1) and Hubert CHANSON (2) ( ) Research student, E-mail: [email protected] (2) Professor in Civil Engineering, The University of Queensland, Brisbane QLD 4072, Australia, E-mail: [email protected] 1

Abstract: Stepped spillways are designed to increase the rate of energy dissipation on the chute and to reduce the size of the downstream energy dissipator. It is essential to predict accurately the turbulent dissipation above the steps for large discharges per unit width corresponding to the skimming flow regime. New measurements were conducted in a large facility with a channel slope of 21.8º and a step height of 0.05 m. The experiments were performed with dimensionless discharges dc/h between 1.17 and 3.16, and flow Reynolds numbers up to 7.2×105. The waters were highly turbulent and they dissipated a major proportion of the flow kinetic energy. Taking into account the free-surface aeration, the present results showed a decreasing rate of energy dissipation on the steps with increasing discharge: from about 80% for small discharges to less than 60% for medium to large flow rates. The residual energy data were compared with earlier studies conducted with step heights from 0.025 to 0.143 m, and invert slope between 3.4 and 26.6°. The results implied that the dimensionless residual head was about 2.7 ≤ Hres/dc ≤ 3.1 with a median value of 3.0 for θ = 21.8 and 26.6°, and between 3.7 ≤ Hres/dc ≤ 5 with a median value of 4.5 for θ = 3.4 and 15.9° independently of the step height and discharge. Altogether the comparative analysis yields some simple and basic design guidelines for embankment dam stepped spillways. Keywords: stepped spillways, turbulent kinetic energy dissipation, residual energy, air-water flows, embankment structures. INTRODUCTION A number of embankment overtopping protection systems were developed (ASCE 1994) and a common technique is the construction of a stepped spillway on the downstream slope (Fig. 1). Figure 1 illustrates an embankment whose primary spillway is a stepped spillway on the embankment slope. Stepped spillways are designed to increase the rate of energy dissipation on the chute and to reduce the size of the downstream energy dissipator (Fig. 1). Therefore it is essential to predict accurately the turbulent dissipation above the steps for large discharges per unit width corresponding to the skimming flow regime. Skimming flows are highly aerated (RAJARATNAM 1990, MATOS 2000). Through the air-water interface, air is continuously trapped and released, and the resulting two-phase mixture interacts with the flow turbulence yielding a complicated air-water structure. The high level of free-surface aeration is a characteristic feature of the stepped chute flows, and a number of in-stream stepped cascades were built along polluted and eutrophic streams to re-oxygenate the water (GOSSE and GREGOIRE 1997, TOOMBES and CHANSON 2005). New two-phase turbulent flow measurements were conducted in a large facility with a channel slope angle of 21.8º (1V:2.5H). Experiments were performed with dimensionless discharge dc/h between 1.17 and 3.16, and Reynolds numbers ranging from 1.7 105 to 7.2 105. The data were analysed in terms of the rate of energy dissipation and flow resistance, and the results were compared with relevant literature. The aim of this work is to characterise the energy dissipation performances of moderate slope stepped spillways.

33rd IAHR Congress: Water Engineering for a Sustainable Environment c 2009 by International Association of Hydraulic Engineering & Research (IAHR) Copyright ° ISBN: 978-94-90365-01-1

33rd IAHR Congress: Water Engineering for a Sustainable Environment

Fig. 1 - Stepped spillway of Salado Creek Dam Site 15R (Courtesy of Craig SAVELA, USDA-NRCSNDCSMC) - Roller compacted concrete construction, θ = 21.8º, h = 0.61 m

EXPERIMENTAL FACILITIES New experiments were conducted at the University of Queensland in a 3.2 m long, 1 m wide chute with flow rates ranging from 43 to 181 L/s. The chute consists of a broad-crest followed by 20 identical steps (h = 0.05, l = 0.125 m, 21.8º slope). The cascade geometry and range of flow rates were selected to be a 1:2 scale model of the geometry used by CAROSI and CHANSON (2008) and CHANSON and TOOMBES (2003). Waters are supplied by a pump controlled with adjustable frequency AC motor drive enabling an accurate discharge adjustment. The water discharge was measured from the upstream head above the crest, and the head-discharge relationship was checked with detailed velocity distribution measurements on the crest itself (GONZALEZ and CHANSON 2007). The air-water flow properties were measured using a single-tip resistivity probe (∅ = 0.35 mm, Pt) and a double-tip resistivity probe (∅ = 0.25 mm, Pt). In the latter, the longitudinal separation between tips was 7.0 mm. Both phase detection probes were excited by an electronic system (Ref. UQ82.518) designed with a response time less than 10 µs and calibrated with a square wave generator. The probe signals were sampled at 20 kHz per sensor for 45 s. The translation of the probes in the direction normal to the pseudo-bottom formed by the step edges was controlled by a fine adjustment traverse mechanism connected to a MitutoyoTM digimatic scale unit with an accuracy of less than 0.2 mm. Experimental flow conditions On a stepped chute, the waters flow as a succession of free-falling nappes (i.e. nappe flow) at low flow rates. At large flow rates with an identical chute geometry (step height, mean slope), the water skims over the pseudo-invert formed by the step edges (i.e. skimming flow). For some intermediate discharges, a transition flow regime is observed, characterised by a chaotic behaviour and strong splashing and droplet projections downstream of the inception point of free-surface aeration. The present observations indicated a nappe flow regime for dc/h < 0.6 and a skimming flow regime for dc/h > 1.0, where dc is the critical flow depth and h is the vertical step height. The results were in agreement with the literature (CHANSON 1995,2001) suggesting no effect of the step height on the change in flow regimes. The detailed air-water flow measurements were conducted in the skimming flow regime for 1.17 < dc/h < 3.16. The flow conditions corresponded to flow Reynolds numbers ranging from 1.7 105 to 7.2 105. BASIC OBSERVATIONS In skimming flows, the free-surface was clear and transparent on the upper steps. Significant aeration took place when the turbulence generated by the step cavities reached the free-surface. This location is called the inception point of free-surface aeration. Downstream the turbulence next to the free-surface is large enough to initiate substantial flow aeration. Typical dimensionless distributions of void fraction and interfacial velocity measured downstream of

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the inception point of free-surface aeration are presented in Figure 2. The blue square are void fraction data and the empty triangles are the dimensionless velocity data V/V90 where Y90 is the characteristic distance where C = 0.9, and V90 is the characteristic velocity where C = 0.9. The data presented in Figure 2 were measured four step cavities downstream of the inception point of free-surface aeration. The void fraction data compared favourably with an advective diffusion model developed for smooth-invert chute flows: 3  1     y'−    y' 3  (1) + C = 1 − tanh 2  K '−  3 Do  2 Do      where y' = y/Y90, y is the distance normal to the pseudo-bottom formed by the step edges, K' is an integration constant and Do is a function of the depth-averaged void fraction Cmean (CHANSON and TOOMBES 2003). Equation (1) is shown in Figure 2. The velocity measurements performed at step edges showed that, within the main body of the flow (C < 90%), the data compared favourably with a power law: V (2) = y'1 / N V90 In the present study, the velocity power law exponent 1/N was 1/10 in average (i.e. N = 10), although it varied between adjacent step edges. Such fluctuations were believed to be caused by some interference between adjacent shear layers and cavity flows. In the upper flow region (y > Y90), the velocity profile was pseudo-uniform: V (3) =1 V90 This trend (Eq. (3)) implied that the spray was little affected by air resistance. The result was consistent with the earlier findings of CAROSI and CHANSON (2008) in a stepped spillway model, and DODU (1957) and BRATTBERG et al. (1998) who investigated high-velocity water jets discharging into air. Equations (2) and (3) are shown in Figure 2, and the agreement with experimental data was consistent with earlier studies (MATOS 2000, CAROSI and CHANSON 2008). A characteristic feature of all experiments was a distinct seesaw pattern in terms of the longitudinal distributions of dimensionless air-water depth Y90/dc, dimensionless maximum bubble count rate Fmaxdc/Vc and characteristic velocity V90/Vc where Vc is the critical flow velocity. Further the maximum bubble count rate did not reach uniform equilibrium before the end of the chute. It increased sharply with longitudinal distance immediately downstream of the inception point (i.e. (x-LI)/dc < 10), while they continued to increase gradually with increasing distance further downstream.

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33rd IAHR Congress: Water Engineering for a Sustainable Environment 2 C Data V/V90 Data C Theory V/V90 1/10 power law

1.8 1.6 1.4 y/Y90

1.2 1 0.8 0.6 0.4 0.2 0 0

0.1

0.2

0.3

0.4

0.5

0.6 0.7 C, V/V90

0.8

0.9

1

1.1

1.2

Fig. 2 - Dimensionless distribution of void fraction C and air-water velocity V/V90 - Qw = 0.1222 m3/s, dc/h = 2.39, Re = 5.1 105, Step edge 18, Y90 = 0.061 m, V90 = 3.46 m/s - Comparison with Equations (1) and (2)

ENERGY DISSIPATION AND FLOW RESISTANCE On the stepped chute, the skimming flows dissipated a major proportion of the flow kinetic energy. The rate of energy dissipation ∆H/Hmax and the dimensional residual energy Hres/dc were estimated at three steps along the chute (steps 10, 18 & 20) based upon the air-water flow measurements. Herein Hmax is the upstream total head above the sampling location (step 10, 18 or 20), and the residual head Hres is the specific energy of the flow at the sampling location : Uw2 (4) 2g where Uw is the flow velocity (Uw = qw/d), qw is the water discharge per unit width and d is the equivalent clear-water depth defined as: H res = d cos θ +

Y90

d=

∫ (1 − C) dy

(5)

y =0

with y the distance normal to the pseudo-bottom formed by the step edges. The present results showed a decreasing rate of energy dissipation on the stepped chute with increasing discharge from about ∆H/Hmax = 80% for dc/h < 1.2 to less than 60% for dc/h > 3. The trend was consistent with earlier studies (MATOS 2000, CHANSON 1995) and very close to the results of CAROSI and CHANSON (2008) with the same bed slope. For design engineers, the dimensionless residual head Hres/dc is a critical parameter since it characterises the kinetic energy to be dissipated in a downstream stilling structure. The residual energy data are shown in Figure 3 together with earlier experimental results. The comparative data sets regroup results derived from detailed air-water flow measurements on three chute slopes (θ = 3.4, 15.9° & 21.8°) and for a range of step heights (0.05 ≤ h ≤ 0.143 m), as well as clear-water flow data for one slope (θ = 26.6°) and two step heights (h = 0.025 & 0.05 m). The comparison implied that the dimensionless residual head was about 2.7 ≤ Hres/dc ≤ 3.1 with a median value of 3.0 for θ = 21.8 and 26.6 °, and between 3.7 ≤ Hres/dc ≤ 5 with a median value of 4.5 for θ = 3.4 and 15.9°, independently of the step height and discharge (Fig. 3). The data of MEIRELES et al. (2006) are recorded in the region upstream of the inception point and not at the downstream end. The residual energy was calculated for the last step edge before the inception point. The results show that the data are in good agreement with the data for aerated flow at the downstream end of the chute. Furthermore the clear water flow depth data

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of MEIRELES et al. illustrate also a seesaw pattern with a wave length of two steps.

6 5

Hres/dc

4 3 2 1

θ=21.8°, h=0.05 m θ=21.8°, h=0.10 m θ=15.9°, h=0.05 m

0 0.4 0.6 0.8

θ (°) 21.8

15.9

3.4 26.6

h (m) 0.05 0.10 0.05 0.10 0.07 0.143 0.025 0.050

1

θ=15.9°, h=0.10 m θ=3.4°, h=0.071 m θ=3.4°, h=0.143 m

1.2 1.4 1.6 1.8

2 2.2 2.4 2.6 2.8 dc/h

Instrumentation Single-tip conductivity probe (∅=0.35 mm)

θ=26.6°, h=0.025 m θ=26.6°, h=0.05 m

3

3.2 3.4 3.6

Single-tip conductivity probe (∅=0.35 mm)

Reference Present study CAROSI & CHANSON (2008) GONZALEZ & CHANSON (2004) CHANSON & TOOMBES (2003), GONZALEZ (2005) CHANSON & TOOMBES (2002)

Pitot tube

MEIRELES et al. (2006)

Single-tip conductivity probe (∅=0.35 mm) Double-tip conductivity probe (∅=0.025 mm)

Fig. 3 - Dimensionless residual energy at the downstream end of the stepped chute - Median values are shown in dotted/dashed lines - Comparison with non-aerated flow results of MEIRELES et al. (2006)

FLOW RESISTANCE On the stepped chute, the skimming flows were characterised by significant form losses. Downstream of the inception point of free-surface aeration, the average shear stress between the skimming flow and the cavity recirculation was deduced from the measured friction slope Sf :  Y90    8 g S f  (1 − C) dy   y =0  8 τo   = fe = (6) 2 2 ρw U w Uw where fe is the equivalent Darcy-Weisbach friction factor, and the friction slope Sf is the slope of the total head line: Sf = -∂H/∂x (HENDERSON 1966). Equation (6) gives an estimate of the Darcy-Weisbach friction factor in the air-water flow region. The flow resistance results are presented in Figure 4. In Figure 4, the friction factor data are plotted as a function of the dimensionless step roughness height h cosθ/DH, where DH is the hydraulic diameter. In average, the equivalent Darcy friction factor was f e ≈ 0.25 downstream of the inception point of freesurface aeration for the present study.

∫

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θ=21.8°, h=0.05 m θ=21.8°, h=0.10 m θ=15.9°, h=0.05 m θ=15.9°, h=0.10 m θ=5.7-19°, Nihon θ=3.4°, h=0.071 m θ=18.4°, Brushes Clough θ=8.7°, Dneiper Eq. Mixing Layer

10 5 3 2 1 fe

0.5 0.3 0.2 0.1 0.05 0.03 0.02 0.01 0.05

θ (°) 21.8 15.9

3.4 5.7, 11.3, 18.8 8.75 18.4

h (m) 0.05 0.10 0.05 0.10

0.07

0.1

0.2 0.3 h cosθ/DH

Comment Laboratory model. Horizontal steps Laboratory model. Horizontal steps

0.07 Laboratory model. Horizontal steps 0.025 Laboratory model (Nihon University). Horizontal & 0.05 steps 0.405 Prototype data. Dneiper hydropower plant. Wedgeshaped blocks (horizontal). 0.19 Prototype data. Brushes Clough dam spillway. Wedge-shaped block (inclined downwards).

0.4

0.5 0.6 0.7 0.80.9 1

Reference Present study CAROSI & CHANSON (2008) GONZALEZ & CHANSON (2004) CHANSON & TOMBES (2003), GONZALEZ (2005) CHANSON & TOOMBES (2002) YASUDA & OHTSU (1999), CHANSON et al. (2002) GRINCHUK et al. (1977) BAKER (1994)

Fig. 4 - Darcy-Weisbach friction factor in air-water skimming flows down moderate-slope stepped spillways

The present results are compared with previous studies in Figure 4, including two sets of prototype observations (Dneiper and Brushes Clough) and several laboratory studies. All the laboratory data were close and suggested a larger flow resistance for θ = 21.8° than for the smaller slope angles (Fig. 4). This trend was consistent with the findings of OHTSU et al. (2004) and GONZALEZ and CHANSON (2006), although the discrepancy with the Brushes Clough prototype data remains unexplained (CHANSON et al. 2002). The flow resistance data were compared also with a simplified analytical model of the pseudoboundary shear stress in the developing shear layer downstream of each step edge that may be expressed in dimensionless form as: f = 2 /(K π ) where 1/K is the dimensionless expansion rate of the shear layer (CHANSON et al. 2002, GONZALEZ and CHANSON 2004). It predicts f ≈ 0.2 for K = 6 that is close to the observed friction factors (Fig. 4). Lastly, it must be noted that the results shown in Figure 7 applied to the aerated flow region only. In the developing boundary layer region, AMADOR et al. (2006) derived the flow resistance by applying an integral momentum method to PIV measurements and their results yielded f = 0.125 for dc/h = 2.1 and Re = 4.4 105. DISCUSSION The present data trend yielded some fundamental questions: (a) how do we define uniform equilibrium flow conditions (normal flow conditions) in skimming flow above a stepped spillway ? (b) is there an unique set of normal flow conditions for a given discharge on a stepped chute ? and (c) do the flow properties alternate between several modes of excitation

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which may be regarded as unstable equilibrium conditions ? The concept of uniform equilibrium flow conditions (normal flow) was developed for smooth-invert chutes (e.g. BAKHMETEFF 1932, HENDERSON 1966). It is not valid for skimming flows on a stepped chute. In a 24 m long chute, CHANSON and TOOMBES (2002) highlighted the longitudinal variations of the air-water flow properties between step edges, although uniform equilibrium flow conditions were not achieved at the downstream end of their chute despite near full-scale prototype dimensions. The experimental evidences tended overall to refute the uniqueness of normal flow conditions in skimming flows, although further works are required to present a conclusive statement.

CONCLUSION Detailed two-phase turbulent flow measurements were performed in a large facility with a moderate slope stepped invert (1V:2.5H). The experimental data were analysed in terms of the rate of energy dissipation, and flow resistance, while the results were compared with relevant literature. The data demonstrated significant energy dissipation of the flow for all investigated conditions. The median dimensionless residual head was about Hres/dc =3.0 for θ = 21.8°, while the re-analysis of earlier data sets gave Hres/dc = 4.5 for smaller slope (θ = 3.4° & 15.9°). The results were found to be independent of step heights and discharges. The flow resistance results yielded an equivalent Darcy friction factor f e ≈ 0.25 downstream of the inception point of free-surface aeration. A comparison with earlier studies showed a good agreement although it suggested a larger flow resistance for θ = 21.8° than for the smaller slope angles. The experimental data showed some distinctive seesaw pattern in the longitudinal distribution of air-water flow properties with a wave length of about two step cavities. It is thought that the trend was caused by the interactions between successive adjacent step cavities and their interference with the free-surface. The existence of such "instabilities" implies that the traditional concept of normal flow might not exist in skimming flows above moderate-slope stepped spillways. ACKNOWLEDGMENTS The writers acknowledge the financial support of the Australian Research Council. REFERENCES AMADOR, A., SANCHEZ-JUNY, M., and DOLZ, J. (2006). "Characterization of the Nonaerated Flow Region in a Stepped Spillway by PIV." Jl of Fluids Eng., ASME, Vol. 128, No. 6, pp. 1266-1273. ASCE Task Committee (1994). "Alternatives for Overtopping Protection of Dams." ASCE, New York, USA, Task Committee on Overtopping Protection, 139 pages. BAKER, R. (1994). "Brushes Clough Wedge Block Spillway - Progress Report No. 3." SCEL Project Report No. SJ542-4, University of Salford, UK, Nov., 47 pages. BAKHMETEFF, B.A. (1932). "Hydraulics of Open Channels." McGraw-Hill, New York, USA, 1st ed., 329 pages. BRATTBERG, T., CHANSON, H., and TOOMBES, L. (1998). "Experimental Investigations of FreeSurface Aeration in the Developing Flow of Two-Dimensional Water Jets." Jl of Fluids Eng., Trans. ASME, Vol. 120, No. 4, pp. 738-744. CAROSI, G., and CHANSON, H. (2008). "Turbulence Characteristics in Skimming Flows on Stepped Spillways." Canadian Journal of Civil Engineering, Vol. 35, No. 9, pp. 865-880 (DOI:10.1139/L08030). CHANSON, H. (1995). "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways." Pergamon, Oxford, UK, Jan., 292 pages. CHANSON, H. (2001). "The Hydraulics of Stepped Chutes and Spillways." Balkema, Lisse, The Netherlands, 418 pages. CHANSON, H., and TOOMBES, L. (2002). "Energy Dissipation and Air Entrainment in a Stepped Storm Waterway: an Experimental Study." Jl of Irrigation and Drainage Engrg., ASCE, Vol. 128, No. 5, pp. 305-315.

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CHANSON, H., and TOOMBES, L. (2003). "Strong Interactions between Free-Surface Aeration and Turbulence in an Open Channel Flow." Experimental Thermal and Fluid Science, Vol. 27, No. 5, pp. 525-535. CHANSON, H., YASUDA, Y., and OHTSU, I. (2002). "Flow Resistance in Skimming Flows and its Modelling." Can Jl of Civ. Eng., Vol. 29, No. 6, pp. 809-819. DODU, J. (1957). "Etude de la Couche Limite d'Air autour d'un Jet d'Eau à Grande Vitesse." ('Study of the Boundary Layer around a High Velocity Water Jet.') Proc. 7th IAHR Congress, Lisbon, Portugal, paper D6 (in French). GONZALEZ, C.A. (2005). "An Experimental Study of Free-Surface Aeration on Embankment Stepped Chutes." Ph.D. thesis, Department of Civil Engineering, The University of Queensland, Brisbane, Australia, 240 pages. GONZALEZ, C.A., and CHANSON, H. (2004). "Interactions between Cavity Flow and Main Stream Skimming Flows: an Experimental Study." Can Jl of Civ. Eng., Vol. 31, No. 1, pp. 33-44. GONZALEZ, C.A., and CHANSON, H. (2006). "Flow Characteristics of Skimming Flows in Stepped Channels. Discussion." Jl of Hyd. Engrg., ASCE, Vol. 132, No. 5, pp. 537-539 (DOI: 10.1061/(ASCE)0733-9429(2006)132:5(537)). GONZALEZ, C.A., and CHANSON, H. (2007). "Experimental Measurements of Velocity and Pressure Distribution on a Large Broad-Crested Weir." Flow Measurement and Instrumentation, Vol. 18, No. 34, pp. 107-113 (DOI 10.1016/j.flowmeasinst.2007.05.005). GOSSE, P., and GREGOIRE, A. (1997). "Dispositif de Réoxygénation Artificielle du Sinnamary à l'Aval du Barrage de Petit-Saut (Guyane)." ('Artificial Re-Oxygenation of the Sinnamary, Downstream of Petit-Saut Dam (French Guyana).') Hydroécol. Appl., Tome 9, No. 1-2, pp. 23-56 (in French). GRINCHUK, A.S., PRAVDIVETS, Y.P., and SHEKHTMAN, N.V. (1977). "Test of Earth Slope Revetments Permitting Flow of Water at Large Specific Discharges." Gidrotekhnicheskoe Stroitel'stvo, No. 4, pp. 22-26 (in Russian). (Translated in Hydrotechnical Construction, 1978, Plenum Publ., pp. 367-373). HENDERSON, F.M. (1966). "Open Channel Flow." MacMillan Company, New York, USA. MATOS, J. (2000). "Hydraulic Design of Stepped Spillways over RCC Dams." Intl Workshop on Hydraulics of Stepped Spillways, Zürich, Switzerland, H.E. MINOR & W.H. HAGER Editors, Balkema Publ., pp. 187-194. MEIRELES, I., CABRITA, J., and MATOS, J. (2006). "Non-Aerated Skimming Flow Properties on Stepped Chutes over Small Embankment Dams." Proc. Intl Junior Researcher and Engineer Workshop on Hydraulic Structures, IAHR, Montemor-o-Novo, Portugal, 2-4 Sept., J. MATOS and H. CHANSON Ed., Hydraulic Model Report No. CH61/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, pp. 91-99. OHTSU, I., YASUDA, Y., and TAKAHASHI, M. (2004). "Flow Characteristics of Skimming Flows in Stepped Channels." Jl of Hyd. Engrg., ASCE, Vol. 130, No. 9, pp. 860-869. Discussion: Vol. 132, No. 5, pp. 527-542. RAJARATNAM, N. (1990). "Skimming Flow in Stepped Spillways." Jl of Hyd. Engrg., ASCE, Vol. 116, No. 4, pp. 587-591. Discussion : Vol. 118, No. 1, pp. 111-114. TOOMBES, L., and CHANSON, H. (2005). "Air-Water Mass Transfer on a Stepped Waterway." Jl of Environ. Engrg., ASCE, Vol. 131, No. 10, pp. 1377-1386. YASUDA, Y., and OHTSU, I.O. (1999). "Flow Resistance of Skimming Flow in Stepped Channels." Proc. 28th IAHR Congress, Graz, Austria, Session B14, 6 pages.

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