Modeling of Relative Length and Relative Energy Loss of Free Hydraulic Jump in Horizontal Prismatic Channel
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Abstract:
Hydraulic jump is a phenomenon caused by change in stream regime from supercritical to sub - critical flow with considerable energy dissipation and rise in depth of flow. Hydraulic jump primarily serves as an energy dissipater to dissipate excess energy of flowing water downstream of hydraulic structures, such as spillway, sluice gates etc. This excess energy, if left unchecked, will have adverse effect on the banks and the bed. A review of literature has shown that earlier researcher have studied the hydraulic jump characteristics in terms of approach Froude number (Fr1) only. In the present paper hydraulic jump in horizontal prismatic channel has been studied and analyzed considering the effect of both approach Froude number and incoming Reynolds number (Re1). Empirical models for relative length and relative energy loss of free hydraulic jump based on experimental data using Buckingham jc- theorem and regression analysis have been developed considering the effect of approach Froude number and incoming Reynolds number. The developed empirical computational model is validated using Bhutto (1987) data.Keywords:
Hydraulic jump
Froude number
Supercritical flow
Sluice
Hydraulics
Hydraulic jump is a phenomenon caused by change in stream regime from supercritical to sub - critical flow with considerable energy dissipation and rise in depth of flow. Hydraulic jump primarily serves as an energy dissipater to dissipate excess energy of flowing water downstream of hydraulic structures, such as spillway, sluice gates etc. This excess energy, if left unchecked, will have adverse effect on the banks and the bed. A review of literature has shown that earlier researcher have studied the hydraulic jump characteristics in terms of approach Froude number (Fr1) only. In the present paper hydraulic jump in horizontal prismatic channel has been studied and analyzed considering the effect of both approach Froude number and incoming Reynolds number (Re1). Empirical models for relative length and relative energy loss of free hydraulic jump based on experimental data using Buckingham jc- theorem and regression analysis have been developed considering the effect of approach Froude number and incoming Reynolds number. The developed empirical computational model is validated using Bhutto (1987) data.
Hydraulic jump
Froude number
Supercritical flow
Sluice
Hydraulics
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This note presents experimental measurements on the turbulence characteristics in the transition region from the end of a hydraulic jump to open channel flow in a rectangular channel. An acoustic Doppler velocimeter was used to measure mean velocities, turbulent intensities, Reynolds stress and turbulent kinetic energy for two supercritical Froude numbers. General correlations for the variation of the normalized maximum values of the Reynolds normal stresses as well as the shear stress and the turbulent kinetic energy have been developed, using the present results and those from the literature. The supercritical Froude number was found to be an effective scale in addition to the supercritical approach flow velocity in obtaining the general correlations.
Froude number
Hydraulic jump
Supercritical flow
Reynolds stress
Acoustic Doppler velocimetry
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Abstract The hydraulic jump is a rapid transition state from supercritical to subcritical flow that occurs commonly in rivers, prismatic channels and downstream of spillways. In this study, the characteristics of the hydraulic jump in a stilling basin downstream of the spillway chute channel with the slopes of α = 12 o and 30 o were investigated experimentally for different Froude numbers of incoming flow, Fr 1 = 7, 7.5, 8, 9, 10 and 12, and relative heights of sill in the range of 4 < h s /h 1 (S) < 13 (S relative height). In the experiments, in which velocity field measured by laser Doppler Anemometry, it was particularly focused on the effects of both different structural configuration and flow conditions on the hydraulic jump and energy dissipation ratio. Experimental measurements showed that the length of hydraulic jump and the roller zone increases with the decrease of the sill height for α = 12 o and 30 o . In addition, the length of the hydraulic jump and roller zone increased with decreasing Froude numbers. The turbulence intensity in the jump region was determined to be greater than the turbulence intensity in the region near the bottom of stilling basin. The turbulence intensity, in general, tended to decrease with decreasing Froude number.
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Hydraulic jump
Supercritical flow
Sill
Spillway
Intensity
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A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-averaged void-fraction data highlight a rapid deaeration of the jump roller. The results suggest that the hydraulic jumps are effective aerators and that the rate of detrainment is comparatively smaller at the largest Froude numbers.
Froude number
Hydraulic jump
Supercritical flow
Air entrainment
Entrainment (biomusicology)
Inflow
Hydraulics
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In open channels, the transition from supercritical to subcritical flows is called a hydraulic jump. For low upstream Froude numbers, free-surface undulations develop downstream of the jump and the hydraulic jump is called an undular jump. New experiments on undular hydraulic jumps were performed in a rectangular channel in which the upstream flows were fully developed turbulent shear flows. In this paper, the main flow patterns are described. Visual and photographic observations indicate five types of undular jumps. One of the main flow characteristics is the presence of lateral shock waves for Froude numbers larger than 1.2. The results show that the disappearance of undular jump occurs for Froude numbers ranging from 1.5 to 2.9, and the wavelength and amplitude of free-surface undulations are functions of the upstream Froude number and the aspect ratio y c /W.
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Hydraulic jump
Supercritical flow
Free surface
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Froude number
Hydraulic jump
Supercritical flow
Sill
Spillway
Hydraulics
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Abstract
One of the most frequently encountered cases of rapid varied flow is the hydraulic jump. It occurs when a supercritical open channel flow changes into sub critical flow. In the present research, the experimental study of the hydraulic jump on seven sinusoidal corrugated beds with different wave steepness. The wave steepness of sinusoidal corrugated beds is in the range of 0.1667 to 0.75 and Froude number was in the range of 4.5 to 12.26. The results showed that the tail water depth of a jump on a corrugated bed is about 20% smaller than that on smooth bed in Froude number 12 and the length of jump on corrugated beds is about 35% less than that for smooth bed.
Keywords: Hydraulic jump, Corrugated bed, Wave steepness
Froude number
Hydraulic jump
Supercritical flow
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The conditions for hydraulic jump formation at the confluence to a supercritical flow are examined theoretically. One‐dimensional analysis for rectangular channels leads to approximate criteria for the channels discharge ratio in terms of the junction geometry and approaching flow conditions. The effect of the main factors, notably the Froude numbers and channels' width ratio, is determined. Experiments are carried out for junctions at a 90° and a 17° angle of a subcritical tributary flow to a weakly supercritical main flow with F1=1.5-2.0. The results of this study and other available experimental results covering a wider range of Froude numbers compare favorably to the theoretical predictions. The behavior of the water level at the end of the lateral channel is also presented in nondimensional diagrams.
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Hydraulic jump
Supercritical flow
Confluence
Hydraulics
Hydraulic structure
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Calculation methods of conjugate depth and hydraulic jump length of the roughened stilling basin with uniform gravel bed are proposed in this study. According to the test data given by Hughes on the conjugate depth and hydraulic jump length of the roughened stilling basin with the gravel bed,hydraulic jump equation and the change law of hudraulic jump length with the upstream Froude number,upstream supercritical flow depth, downstream subcritical flow depth and roughness height are analized through the dimension concordant principle. The conjugate depth is increasing with the increasing in Froude number and decreasing with increasing in the roughness height. The hydraulic jump length is also the function of the upstream Froude number,upstream supercritical flow depth,downstream subcritical flow depth and roughness height. Meanwhile,energy dissipation ratio in the hydraulic jump region is increasing with increasing in the roughness height. Calculation formulas of the conjugate depth and the hydraulic jump length of the roughened stilling basin with uniform gravel bed,verified by the test results of F. G. Carollo,are put forward.
Hydraulic jump
Froude number
Supercritical flow
Weir
Hydraulics
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There are multiple initiatives aimed at strengthening coastal communities against tsunami disaster risks, such as growing vegetation belts, construction of embankments, moats, and different hybrid alternatives. To find a solution for strengthening the coastal buildings themselves, we firstly reviewed the flow phenomena around a single emergent (circular and rectangular) cylinder (case C1), which was considered as a piloti-type column under different Froude conditions, and evaluated the formation of surface bow-waves, hydraulic jump detachment, and wall-jet-like bow-waves. Secondly, the flow characteristics were investigated under the same Froude conditions with side-by-side two-cylinder (case C2) and four-cylinder (case C4) arrays in an open channel. Surface bow-wave length (LBw) increased by 7–12% over the rectangular cylinders (RCs) compared to the circular cylinders (CCs) with a subcritical flow. For the supercritical flow with a 1/200 bed slope, hydraulic jump detachment was observed in relation to the Froude number. The observed length of the hydraulic jump detachment (Ljump) varied between 3.1–8.5% and 4.2–12.9% for the CCs and RCs in the supercritical flow with a 1/200 bed slope. In addition, the wall-jet-like bow-wave height (hjet) over the CCs was increased by 37% and 29% compared to the RCs with a supercritical flow and zero bed slope (orifice-type flow). For case C4, a hydraulic jump was observed for the supercritical flow over the horizontal channel bed. Finally, empirical equations were defined concerning the geometrical shape and arrangement based on the experiment data for the single and side-by-side configurations of the cylinders to validate the height of the wall-jet-like bow-wave as the most critical flow property.
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Supercritical flow
Hydraulic jump
Free surface
Potential flow
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