Application of Displacement Height and Surface Roughness Length to Determination Boundary Layer Development Length over Stepped Spillway
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One of the most uncertain parameters in stepped spillway design is the length (from the crest) of boundary layer development. The normal velocity profiles responding to the steps as bed roughness are investigated in the developing non-aerated flow region. A detailed analysis of the logarithmic vertical velocity profiles on stepped spillways is conducted through experimental data to verify the computational code and numerical experiments to expand the data available. To determine development length, the hydraulic roughness and displacement thickness, along with the shear velocity, are needed. This includes determining displacement height d and surface roughness length z0 and the relationship of d and z0 to the step geometry. The results show that the hydraulic roughness height ks is the primary factor on which d and z0 depend. In different step height, step width, discharge and intake Froude number, the relations d/ks = 0.22–0.27, z0/ks = 0.06–0.1 and d/z0 = 2.2–4 result in a good estimate. Using the computational code and numerical experiments, air inception will occur over stepped spillway flow as long as the Bauer-defined boundary layer thickness is between 0.72 and 0.79.Keywords:
Froude number
Roughness length
Crest
Hydraulic roughness
Spillway
Froude number
Hydraulic jump
Baffle
Wedge (geometry)
Hydraulic roughness
Inflow
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Results of laboratory experiments carried out to determine the effective surface roughness for shallow overland flow as a function of the runoff rate, roughness element height, and underlying soil condition are presented. This work was conducted to extend the understanding of the mechanics of shallow overland flows based on the relationships between the Reynolds number, Froude number, and surface resistance over a wide range of conditions. Results exhibit a strong dependence of the effective roughness on the ratio between the depth of flow and the height of the roughness element, and a strong inverse relationship was found between Manning's n (and the Darcy-Weisbach friction factor f) and the Froude number. Three distinct subcritical flow regimes were identified: (1) Submerged flow (R < 300); (2) sheet flow (R > 1,200); and (3) transitional (partially submerged) flow (300 < R < 1,200). Analysis and synthesis of laboratory data allowed relationships between the Reynolds and Froude numbers, and Manning's n, which are suitable for practical engineering applications, to be established in this study.
Froude number
Hydraulic roughness
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The variations of hydro-dynamic parameters(Reynolds number,Froude number,average flow velocity,water depth and resistance coefficient) of overland flows were characterized under different flow discharge,slope gradient and roughness based on flume experiments.The research results indicated that Reynolds number,Froude number,average flow velocity,water depth and resistance coefficient of the overland flows increased with flow discharge for the artificial beds with same roughness and slope gradient.Under the conditions of same gradient and flow discharge,Reynolds number,Froude number and average flow velocity of the overland flows decreased with increasing roughness,while resistance coefficient and flow depth increased.Flow discharge and slope gradient were found closely correlated with the hydraulic parameters such as average flow velocity,water depth,and resistance coefficient,which could be well described by simple power functions.Furthermore,the influences of flow discharge were dominant.
Froude number
Flume
Hydraulic roughness
Discharge coefficient
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This paper presents a new method that is able to define the hydraulic jump peculiarities in rough-bed conditions. The findings of this paper improve the literature and guidelines on the design of a stilling basin over a rough bed, taking into account both the Froude number and bottom roughness. It starts with experimental evidence on the flow field and considers the characteristic length scale of the phenomenon as drawn from velocity measurements in the hydraulic jump region. The assumption in the length scale leads to different results compared with the known formulas in the literature related to the hydraulic jump on a rough bed. The formulas in the literature consider the effects of gravel roughness only, neglecting the effects due to the incident Froude number in the evaluation of integrated bottom shear stress. The comparison of the presented results with experimental measurements in the literature highlights the reliability and accuracy of this novel method. This method is theoretically based, but because it needs experimental data in application, it can be considered semiempirical. The results presented here allow for the design of hydraulic jump stilling basins over rough beds.
Froude number
Hydraulic jump
Hydraulic roughness
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The roughness Froude number is a relatively new dimensionless parameter that began appearing in the hydraulic engineering literature in the late 1970s, first for the analysis of aeration inception in smooth chutes, and then later in connection with stepped chutes. This article reviews its foundations, historical development, alternative forms, present-day applications, and physical significance, which has received little attention previously. In addition to its empirically demonstrated connection to aeration inception, this paper shows that one form of a roughness Froude number has a strong relation to the transition between nappe and skimming flow regimes of stepped chutes, while another combines the dimensionless flow friction factor and the relative submergence of roughness elements.
Froude number
Hydraulic roughness
Dimensionless quantity
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Gravel bed flow resistance is affected by the shape and size of the roughness elements and their arrangement on the channel bed surface (spacing between elements, direction with respect to flow streamlines, and protrusion of the elements from the channel bed). Previous studies demonstrated that the flow resistance of open channel flows can be obtained by integrating the power velocity profile. This paper aims to study flow resistance in gravel-bed channels with different concentrations of boulders having staggered arrangements. At first, the equation relating Γ coefficient of the power velocity profile, and the Froude number was calibrated using measurements performed in a flume covered by hemispheric roughness elements for partially submerged and completely submerged hydraulic conditions. The roughness elements were evenly spaced (staggered) and arranged using three different concentrations of 9, 25, and 49%. Moreover, the relationship between Γ, slope, and the Froude number, calibrated using literature measurements performed with the same experimental setup but with a square arrangement, was tested for the measurements obtained with the staggered arrangement. The results showed that i) the Darcy-Weisbach friction factor can be accurately estimated by the proposed flow resistance equation, ii) the differences in flow resistance behavior between the two different investigated arrangements (staggered, square) occur only for the partially submerged hydraulic condition, and iii) for the staggered arrangement, skimming flow is reached for lower element concentrations as compared to the square one.
Froude number
Flume
Hydraulic roughness
Flow resistance
Hydraulics
Square (algebra)
Inflow
Power function
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Following the verification of the logarithmic nature of the wind profile and the establishment of a non-dimensional expression relating the shear velocity and surface roughness, a Froude number is proposed for scaling the wind stress at the air-water interface. A correlation curve for wind stresses determined at all fetches is presented and is shown to interrelate successfully the available data compiled from 42 independent investigations consisting of 12 laboratory studies and 30 oceanic observations.
Froude number
Wind Stress
Roughness length
Log wind profile
Shear velocity
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Velocity at the toe of structures, such as spillways, drops, and chutes, plays an important role in designing protective and control hydraulic structures. In this study, laboratory experiments were conducted to investigate velocity at an inclined surface with a height of 40 cm made up of galvanized steel in a flume 20 m long and 0.6 m wide. Using three different slopes, five different discharges and five kinds of roughness, 75 experiments were done. Comparison of measured and theoretical (measured by energy equation without considering losses) flow velocities showed that over the inclined bed, the correction coefficient of theoretical velocity for different Froude numbers varied from 0.87 to 0.88, reducing with roughness size. Roughness size, Froude number and the ratio of water head to the length of bed play a dominant role in the prediction of velocity.
Froude number
Flume
Hydraulic roughness
Paraboloid
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The mean flow in a nature-like fishpass can be highly modified by the Froude number. It is important to understand this evolution to correctly design the structure. The studied configuration is an emergent staggered arrangement of obstacles. The hydraulic resistance of a fishpass is experimentally investigated that depends on several geometric parameters: block shape, ramp slope, block density, and bed roughness. An analytical model based on the balance momentum allows one to quantify the influence of each hydraulic parameter. The bed roughness has a weak influence, whereas the block shape and the Froude number are significant. The variation of the drag coefficient was analyzed to improve the stage-discharge relationship. To this end, a correlation with the block diameter and water level is proposed. The maximal velocity reached in the fishpass can also be estimated. These results have to be compared with the fish swimming ability to assess the fishpass passability.
Froude number
Hydraulic roughness
Hydraulic resistance
Hydraulics
Momentum (technical analysis)
Flow resistance
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