Eine neue, auf der Impulsbilanz basierende Theorie zur Hydraulik des Schützes — ein Diskussionsbeitrag

Malcherek, Andreas

doi:10.1007/s35147-018-0062-7

Cited by 4 publications

(13 citation statements)

References 2 publications

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“…Elevated momentum coefficient

β_{a}

in the gap, associated with nonuniform vertical velocity distribution (Chow, 1959) has previously been described with a Rayleigh‐Weibull distribution (Equation 11 in Malcherek, 2018). Varying

β_{a}

is analogous to varying discharge coefficient

C_{d g}

in an energy‐based approach, with

C_{d g}

empirically observed to vary with

a / h_{0}

[

C_{d g} = \frac{C_{c}}{1 + C_{c} \frac{a}{h_{0}}}

(Henderson, 1966)].…”

Section: Theorymentioning

confidence: 98%

“…We first consider conservation of momentum for solid, vertical sluice gates extending from

z = a

to the water surface in a rectangular open channel with slope

S

and width

B

. Conservation of momentum (Malcherek, 2018) was considered for the blue control volume in Figure 2 extending vertically from

z = 0

z = h_{0}

and over longitudinal distance

L_{c v}

from the gate upstream edge (

x = x_{a}

) to a distance upstream (

x = x_{0}

) where the influence of near‐gate water surface set up is not present and

z = h_{0}

\underset{net pressure force}{\underset{⎵}{F_{p}}} + \underset{net change in momentum}{\underset{⎵}{ρ B q^{2} (\frac{1}{h_{0}} - \frac{β_{a}}{a})}} - \underset{shear stress at bed and sidewalls}{\underset{⎵}{\frac{1}{2} ρ C_{f} U^{2} L_{c v} (B + 2 h_{0})}} + \underset{bed slope}{\underset{⎵}{ρ g B h_{0} L_{c v} S}} = 0,

with momentum correction factor

β_{a} = 1

for flow under the gate (

h_{0} < a

) and for high relative submergence depths (

h_{0} / a ≫ 1

), and

β_{a} > 1

for intermediate relative submergence (Malcherek, …”

Section: Theorymentioning

confidence: 99%

“…(Malcherek, 2018), with bottom pressure

p_{b}

x = x_{a}

. Note that between

z = a

and

h_{0}

the net hydrostatic pressure force is the same on both faces of the control volume, so that this region was excluded from the force balance.…”

Section: Theorymentioning

confidence: 99%

“…Note that between

z = a

and

h_{0}

the net hydrostatic pressure force is the same on both faces of the control volume, so that this region was excluded from the force balance. The bottom pressure along the centerline of a channel with a solid sluice gate was measured by Roth & Hager (1999), from which Malcherek (2018) defines the bottom pressure at the sluice gate,

p_{b} (x_{a}) = ρ g (0.5 h_{0} + 0.5 a)

. Combining Equation and Equation yields the following expression for the net pressure force in Equation ,

F_{p} = F_{p 0} - F_{p a} = C_{p 0} ρ g B a (h_{0} - a)

with

C_{p 0} = 2 / 3

.…”

Section: Theorymentioning

confidence: 99%

“…Varying

β_{a}

is analogous to varying discharge coefficient

C_{d g}

in an energy‐based approach, with

C_{d g}

empirically observed to vary with

a / h_{0}

[

C_{d g} = \frac{C_{c}}{1 + C_{c} \frac{a}{h_{0}}}

(Henderson, 1966)]. Relative submergence depths of primary interest for logjams lie in the transitional region (

h_{0} / a < 10

) with elevated

β_{a}

(Malcherek, 2018). To ensure a smooth transition between unobstructed uniform flow when water depth is below the jam lower edge (

h_{0} < a

) and low relative submergence depths (

h_{0} / a \approx 1

), we define

β_{a}

following the semiempirical functional form

C_{p} = \frac{C_{p 0}}{false(1 + C_{b} \frac{a}{h_{0}} false)}

used for solid gates, with bottom coefficient

C_{b} = \frac{C_{p 0} C_{f}}{S} - 1

, which matches uniform flow when

h_{0} / a = 1

.…”

Section: Theorymentioning

confidence: 99%

See 4 more Smart Citations

Logjams With a Lower Gap: Backwater Rise and Flow Distribution Beneath and Through Logjam Predicted by Two‐Box Momentum Balance

Follett

Schalko

Nepf

2021

Geophysical Research Letters

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show abstract

“…Elevated momentum coefficient

β_{a}

in the gap, associated with nonuniform vertical velocity distribution (Chow, 1959) has previously been described with a Rayleigh‐Weibull distribution (Equation 11 in Malcherek, 2018). Varying

β_{a}

is analogous to varying discharge coefficient

C_{d g}

in an energy‐based approach, with

C_{d g}

empirically observed to vary with

a / h_{0}

[

C_{d g} = \frac{C_{c}}{1 + C_{c} \frac{a}{h_{0}}}

(Henderson, 1966)].…”

Section: Theorymentioning

confidence: 98%

“…We first consider conservation of momentum for solid, vertical sluice gates extending from

z = a

to the water surface in a rectangular open channel with slope

S

and width

B

. Conservation of momentum (Malcherek, 2018) was considered for the blue control volume in Figure 2 extending vertically from

z = 0

z = h_{0}

and over longitudinal distance

L_{c v}

from the gate upstream edge (

x = x_{a}

) to a distance upstream (

x = x_{0}

) where the influence of near‐gate water surface set up is not present and

z = h_{0}

\underset{net pressure force}{\underset{⎵}{F_{p}}} + \underset{net change in momentum}{\underset{⎵}{ρ B q^{2} (\frac{1}{h_{0}} - \frac{β_{a}}{a})}} - \underset{shear stress at bed and sidewalls}{\underset{⎵}{\frac{1}{2} ρ C_{f} U^{2} L_{c v} (B + 2 h_{0})}} + \underset{bed slope}{\underset{⎵}{ρ g B h_{0} L_{c v} S}} = 0,

with momentum correction factor

β_{a} = 1

for flow under the gate (

h_{0} < a

) and for high relative submergence depths (

h_{0} / a ≫ 1

), and

β_{a} > 1

for intermediate relative submergence (Malcherek, …”

Section: Theorymentioning

confidence: 99%

“…(Malcherek, 2018), with bottom pressure

p_{b}

x = x_{a}

. Note that between

z = a

and

h_{0}

the net hydrostatic pressure force is the same on both faces of the control volume, so that this region was excluded from the force balance.…”

Section: Theorymentioning

confidence: 99%

“…Note that between

z = a

and

h_{0}

p_{b} (x_{a}) = ρ g (0.5 h_{0} + 0.5 a)

. Combining Equation and Equation yields the following expression for the net pressure force in Equation ,

F_{p} = F_{p 0} - F_{p a} = C_{p 0} ρ g B a (h_{0} - a)

with

C_{p 0} = 2 / 3

.…”

Section: Theorymentioning

confidence: 99%

“…Varying

β_{a}

is analogous to varying discharge coefficient

C_{d g}

in an energy‐based approach, with

C_{d g}

empirically observed to vary with

a / h_{0}

[

C_{d g} = \frac{C_{c}}{1 + C_{c} \frac{a}{h_{0}}}

(Henderson, 1966)]. Relative submergence depths of primary interest for logjams lie in the transitional region (

h_{0} / a < 10

) with elevated

β_{a}

(Malcherek, 2018). To ensure a smooth transition between unobstructed uniform flow when water depth is below the jam lower edge (

h_{0} < a

) and low relative submergence depths (

h_{0} / a \approx 1

), we define

β_{a}

following the semiempirical functional form

C_{p} = \frac{C_{p 0}}{false(1 + C_{b} \frac{a}{h_{0}} false)}

used for solid gates, with bottom coefficient

C_{b} = \frac{C_{p 0} C_{f}}{S} - 1

, which matches uniform flow when

h_{0} / a = 1

.…”

Section: Theorymentioning

confidence: 99%

See 3 more Smart Citations

Logjams With a Lower Gap: Backwater Rise and Flow Distribution Beneath and Through Logjam Predicted by Two‐Box Momentum Balance

Follett

Schalko

Nepf

2021

Geophysical Research Letters

View full text Add to dashboard Cite

show abstract

Diskussionsbeitrag zum Artikel von Andreas Malcherek in der WasserWirtschaft 5/2018

Wiesbaden¹

2018

Wasserwirtsch

View full text Add to dashboard Cite

Testing the stage-discharge relationship of a sharp crested sluice gate deduced by the momentum equation for a free-flow condition

Ferro

2018

Flow Measurement and Instrumentation

View full text Add to dashboard Cite

Eine neue, auf der Impulsbilanz basierende Theorie zur Hydraulik des Schützes — ein Diskussionsbeitrag

Cited by 4 publications

References 2 publications

Logjams With a Lower Gap: Backwater Rise and Flow Distribution Beneath and Through Logjam Predicted by Two‐Box Momentum Balance

Logjams With a Lower Gap: Backwater Rise and Flow Distribution Beneath and Through Logjam Predicted by Two‐Box Momentum Balance

Diskussionsbeitrag zum Artikel von Andreas Malcherek in der WasserWirtschaft 5/2018

Testing the stage-discharge relationship of a sharp crested sluice gate deduced by the momentum equation for a free-flow condition

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