On the Current-Meter, Together with a Reason Why the Maximum Velocity of Water Flowing in Open Channels is below the Surface

Stearns, Frederic P.

doi:10.1061/taceat.0000467

Cited by 30 publications

(10 citation statements)

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“…However, in narrow open-channels involving an aspect ratio Ar < 5, where Ar = b/h is the ratio of the channel width b to flow depth, and near side walls or corner zones even for wide open-channels (Vanoni 1941), the maximum velocity appears below the free surface producing the velocity-dip-phenomenon, involving a deviation from the log-wake law. This phenomenon, which was reported more than a century ago (Francis 1878, Stearns 1883, was observed both in open-channels and rivers. It is related to secondary currents generated in three-dimensional (3D) open-channel flows (Imamoto andIshigaki 1988, Wang andCheng 2005).…”

Section: Introductionmentioning

confidence: 63%

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

Absi¹

2011

Journal of Hydraulic Research

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International audienceAn ordinary differential equation for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-Averaged Navier-Stokes equations and a log-wake modified eddy viscosity distribution. This proposed equation allows to predict the velocity-dip-phenomenon, i.e. the maximum velocity below the free surface. Two different degrees of approximations are presented, a semi-analytical solution of the proposed ordinary differential equation, i.e. the full dip-modified-log-wake law and a simple dip-modified-log-wake law. Velocity profiles of the two laws and the numerical solution of the ordinary differential equation are compared with experimental data. This study shows that the dip correction is not efficient for a small Coles' parameter, accurate predictions require larger values. The simple dip-modified-log-wake law shows reasonable agreement and seems to be an interesting tool of intermediate accuracy. The full dip-modified-log-wake law, with a parameter for dip-correction obtained from an estimation of dip positions, provides accurate velocity profiles

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Section: Introductionmentioning

confidence: 63%

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

Absi¹

2011

Journal of Hydraulic Research

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“…For the two-dimensional flow in narrow channels, it occurs below the free surface of water due to secondary currents. The occurrence of maximum flow velocity just below the water's free surface is known as the "dip phenomenon" (Stearns, 1883).…”

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confidence: 99%

Entropy Based River Discharge Estimation Using One‐Point Velocity Measurement at 0.6D

Vyas

Perumal

Moramarco

2021

Water Resources Research

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Entropy theory applied to hydrometric measurements enables establishing a relationship between the maximum and the mean velocities of flow passing a river section. In many developing countries, river discharge is still estimated by the velocity‐area method following the procedure established based on the point‐velocities measured at 0.6D depth from the water surface of many verticals of flow section. This study explores the establishment of a relationship between the maximum point‐velocity estimated at 0.6D depth of the vertical located at or nearer to the deepest flow depth, and the maximum point‐velocity occurring somewhere along the same vertical which in turn can be linked to the sectional mean flow velocity based on the established entropy theory. The appropriateness of the proposed two‐steps based approach of discharge estimation is first verified on the Tiber River and the Po River of Italy. The study finds that the values of the maximum point‐velocity estimated using the proposed approach closely matches with the recorded maximum flow velocity values along the same flow‐depths. After this verification, the proposed method was applied for discharge estimation at two Indian river gauging stations, where only the point‐velocity measurements at 0.6D depth locations of the verticals are recorded. The study finds that the discharges estimated by both the proposed approach and the velocity‐area method closely match with each other with the estimated Nash‐Sutcliffe Efficiency (NSE) values greater than 0.99. Thus the proposed two‐steps approach involving the entropy concept based relationship for discharge estimation enables to replace the tedious and time‐consuming velocity‐area approach.

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“…However, in Figure 8, we can see that the maximum velocity point is below the water surface, not on it. This phenomenon was first observed about a century ago [31,32], and further experimental studies showed that it was induced by the presence of secondary cross-sectional flow structures [33]. Due to the occurrence of anisotropic turbulence and cross-sectional secondary currents, which tend to shift the maximum velocity from the free surface to the bed, its identification is still a complex task in hydraulics [34].…”

Section: Analysis With Semi-circular Channelsmentioning

confidence: 99%

“…The mean velocity can be calculated from the value of Q/A, which can be expressed using Equation (31):…”

Section: Cpl Of Regions In Rectangular Channelmentioning

confidence: 99%

Study on the Characteristic Point Location of Depth Average Velocity in Smooth Open Channels: Applied to Channels with Flat or Concave Boundaries

Chen

Han

et al. 2020

Water

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Based on the flow partition theory, we derive a mathematical expression by using the log-law for the characteristic point location (CPL) of depth average velocity in channels with flat or concave boundaries. It can manifest the position of the characteristic points in the vertical direction relative to the channel side wall or bed. Taking rectangular and semi-circular channels as research objects, we put forward a method to calculate the discharge of channels with CPL. Additionally, we carried out some experiments on rectangular and semi-circular channel sections. CPL’s analytic expression is validated against experimental results through comparison of velocity and discharge. The proposed formulation of characteristic point location could be extensively employed in flow measurements of flat and concave boundary channels, which has practical application value in simplifying the flow measurement steps of open channels.

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On the Current-Meter, Together with a Reason Why the Maximum Velocity of Water Flowing in Open Channels is below the Surface

Cited by 30 publications

References 0 publications

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

Entropy Based River Discharge Estimation Using One‐Point Velocity Measurement at 0.6D

Study on the Characteristic Point Location of Depth Average Velocity in Smooth Open Channels: Applied to Channels with Flat or Concave Boundaries

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