New Flow-Resistance Law for Steep Mountain Streams Based on Velocity Profile

Ferro, Vito

doi:10.1061/(asce)ir.1943-4774.0001208

Cited by 37 publications

(142 citation statements)

References 25 publications

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“…Assuming the incomplete self‐similarity in u * y /ν k (Barenblatt & Monin, ; Barenblatt & Prostokishin, ; Ferro, ; Ferro & Pecoraro, ), Equation allows one to obtain the following velocity distribution:

\frac{v}{u_{*}} = normalΓ {(\frac{u_{*} y}{ν_{k}})}^{δ}

in which Γ is a function to be defined by velocity measurements and δ is an exponent that can be calculated by the following theoretical equation (Barenblatt, ; Castaing, Gagne, & Hopfinger, ):

δ = \frac{1.5}{ln Re}

in which Re = V h /ν k is the flow Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

“…Integrating the power velocity distribution (Equation ), the following expression of the Darcy–Weisbach friction factor f is deduced (Barenblatt, ; Ferro, ; Ferro & Porto, )

f = 8 {[\frac{2^{1 - δ} normalΓ {Re}^{δ}}{((), δ + 1) ((), δ + 2)}]}^{- 2 / ((), 1 + δ)} .

…”

Section: Introductionmentioning

confidence: 99%

“…Setting y = α h , the distance from the bottom at which the local velocity is equal to the cross‐sectional average velocity V , from Equation , the following estimate Γ v of Γ is obtained (Ferro, ):

Γ_{v} = \frac{V}{u_{*} {(\frac{u_{*} α h}{ν_{k}})}^{δ}}

in which α is a coefficient, less than one, taking into account that both the average velocity V is located below the water surface and a single velocity profile representing the whole cross section is considered (i.e., the velocity profile is the mean profile in the cross section, obtained by averaging for each distance y the velocity values v measured in different verticals, and its integration gives the cross‐sectional average velocity).…”

Section: Introductionmentioning

confidence: 99%

“…Ferro () theoretically deduced the equation for calculating α and Di Stefano et al () established that for 2,000 ≤ Re ≤ 10,000, which is usually the measurement range used in rill investigations, the calculated α values vary in a very narrow range and a constant value equal to the mean α = 0.124 can be used.…”

Section: Introductionmentioning

confidence: 99%

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Testing slope effect on flow resistance equation for mobile bed rills

Stefano

Ferro

Palmeri

et al. 2018

Hydrological Processes

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In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.

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\frac{v}{u_{*}} = normalΓ {(\frac{u_{*} y}{ν_{k}})}^{δ}

in which Γ is a function to be defined by velocity measurements and δ is an exponent that can be calculated by the following theoretical equation (Barenblatt, ; Castaing, Gagne, & Hopfinger, ):

δ = \frac{1.5}{ln Re}

in which Re = V h /ν k is the flow Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

“…Integrating the power velocity distribution (Equation ), the following expression of the Darcy–Weisbach friction factor f is deduced (Barenblatt, ; Ferro, ; Ferro & Porto, )

f = 8 {[\frac{2^{1 - δ} normalΓ {Re}^{δ}}{((), δ + 1) ((), δ + 2)}]}^{- 2 / ((), 1 + δ)} .

…”

Section: Introductionmentioning

confidence: 99%

Γ_{v} = \frac{V}{u_{*} {(\frac{u_{*} α h}{ν_{k}})}^{δ}}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Testing slope effect on flow resistance equation for mobile bed rills

Stefano

Ferro

Palmeri

et al. 2018

Hydrological Processes

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“…The aim of this paper is testing a theoretical flow resistance law (Di Stefano et al, ; Ferro, , , ; Palmeri, Pampalone, Di Stefano, Nicosia, & Ferro, ), deduced by dimensional analysis and self‐similarity theory, using the rill flow measurements by Jiang et al () under equilibrium bed‐load transport conditions. At date, at the best of our knowledge, the measurements by Jiang et al () are unique, since the hydraulic variables and the corresponding transport capacity values were published and cover a wide range of slope and flow conditions.…”

Section: Introductionmentioning

confidence: 99%

Rill flow resistance law under equilibrium bed‐load transport conditions

Stefano

Nicosia

Pampalone

et al. 2019

Hydrological Processes

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In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations and . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.

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Flow resistance law in channels with emergent rigid vegetation

Nicosia,

Palmeri,

Ferro

2024

Ecohydrology

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Flow resistance estimate is a challenging topic for establishing flooding propensity of streams, designing river restoration works, and evaluating the use of soil bioengineering practices. In this paper, flume measurements with rigid cylinders set in two arrangements (aligned, staggered) were used to evaluate the effect of rigid emergent vegetation on flow resistance. A well‐known theoretical flow resistance equation was firstly reviewed. Then, it was calibrated and tested by measurements performed for these arrangements with six concentrations (0.53–11.62 stems dm−2). The analysis was conducted using three approaches: (i) distinguishing the experimental runs corresponding to different arrangements and stem concentrations; (ii) using only a scale factor representing the effect of the stem concentration; and (iii) joining all available data. The results demonstrated that the flow resistance equation gives an accurate estimate of the Darcy–Weisbach friction factor f, characterized, for the best approach among the tested ones, by errors less than or equal to ±5% for 95.9% of the examined cases for the aligned arrangement and for the staggered arrangement less than or equal to ±5% for 94.2% of the examined cases. For both arrangements, the measurements demonstrated that, for a given longitudinal distance between vegetation elements, flow resistance increases for decreasing values of the transverse distance and, for a given transverse distance, f decreases for increasing values of the longitudinal distance between elements. Finally, in the range of the investigated stem concentrations, the influence of the arrangement on flow resistance resulted negligible.

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New Flow-Resistance Law for Steep Mountain Streams Based on Velocity Profile

Cited by 37 publications

References 25 publications

Testing slope effect on flow resistance equation for mobile bed rills

Testing slope effect on flow resistance equation for mobile bed rills

Rill flow resistance law under equilibrium bed‐load transport conditions

Flow resistance law in channels with emergent rigid vegetation

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