Linear and angular momentum conservation in hydraulic jump in diverging channels

Valiani, Alessandro; Caleffi, Valerio

doi:10.1016/j.advwatres.2010.11.006

Cited by 5 publications

(21 citation statements)

References 21 publications

(55 reference statements)

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“…Using these hypotheses Valiani and Caleffi (2011) demonstrate that the only non-dimensional parameter governing the phenomenon is the specific energy ratio E R = E 2 /E 1 , whose completion to unity (1 − E R ) is the rate of mechanical energy per unit weight dissipated in the jump. The implicit expressions for the supercritical and subcritical free surface profiles are ξ = 1/ η sp 3 − 2 η sp ;…”

Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

“…The reference steady flow is characterised by a constant specific energy E 0 and a constant liquid discharge Q. and r c are defined as those minimising the specific energy and the total force, respectively (Valiani and Caleffi, 2011). The non-dimensional reference discharge is Γ = Q/ 2 α E 2 0 √ gE 0 .…”

Section: Basic Steady Flow Equationsmentioning

confidence: 99%

“…The jump is considered an inviscid shock of zerolength, including the entire energy dissipation. A more detailed treatment, which incorporates the gradual variability of the physical quantities inside the jump, which is inversely considered to have a finite length, is reported by Valiani and Caleffi (2011) and Valiani and Caleffi (2013). Here, the scheme concerning the mechanics is much more simple and general, even if less detailed.…”

Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

“…A comparison with experimental data from Rubatta (1963) and Rubatta (1964) is also shown. The selected dataset is chosen because experiments were performed at a quite large scale; further details are given in Valiani and Caleffi (2011) and Valiani and Caleffi (2013). The dashed lines represent existence limits for the direct jump.…”

Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

See 3 more Smart Citations

Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps

Valiani

Caleffi

2016

J. Hydraul. Eng.

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Free surface, axially symmetric shallow flow is analyzed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterized by a unique value of specific energy, the analytical sub- and supercritical solutions are determined. Furthermore, the sub- and supercritical steady solutions for the flow with friction over a flat plate are determined, provided that inertial terms are important compared with frictional terms. In the inviscid case, the sub- and supercritical solutions over a bottom topography are determined, provided that the bottom unevenness is compatible with a continuous solution. In the fundamental case of inviscid flow over a flat plate, the discontinuous solution also is analyzed for a direct hydraulic jump imposed by proper boundary conditions. In the simple scheme of an inviscid shock of zero length, the jump position and the sequent depths are analytically derived, thus indicating that all results are uniquely functions of one dimensionless number, i. e., the specific energy ratio between the sub- and supercritical flows

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Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

Section: Basic Steady Flow Equationsmentioning

confidence: 99%

Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

Section: Analytical Solution: Direct Hydraulic Jumpmentioning

confidence: 99%

See 2 more Smart Citations

Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps

Valiani

Caleffi

2016

J. Hydraul. Eng.

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confidence: 95%

Linear and angular momentum conservation for the hydraulic jump in converging channels

Valiani

Caleffi

2013

Journal of Hydraulic Research

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This note is the final completion of a previously published work concerning the integral conservation of linear and angular momentum in the steady hydraulic jump in a linearly diverging channel [Valiani, A., Caleffi, V. (2011). Linear and angular momentum conservation in hydraulic jump in diverging channels. Adv. Water Res. 34(2), 227–242]. The same reasoning is applied to a linearly converging channel, and the theoretical framework, which is almost completely the same, is shown to remain valid. Using a proper mechanical scheme, an analytical solution is obtained for the free surface profile of the flow. This solution allows the determination of the sequent depths and their positions. Thus, the length of the jump, which is assumed to be equal to the length of the roller, is also found. The mainstream and roller thicknesses can also be derived. This model may be used to derive the average shear stress exerted by the roller on the mainstream and the related exact expression for the total power loss in the jump, allowing to demonstrate the internal consistency of the proposed conceptual scheme

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A Petrov–Galerkin scheme for modeling 1D channel flow with varying width and topography

Atallah

Hazzab

2012

Acta Mech

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Linear and angular momentum conservation in hydraulic jump in diverging channels

Cited by 5 publications

References 21 publications

Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps

Free Surface Axially Symmetric Flows and Radial Hydraulic Jumps

Linear and angular momentum conservation for the hydraulic jump in converging channels

A Petrov–Galerkin scheme for modeling 1D channel flow with varying width and topography

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