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Valerio Caleffi - One of the best experts on this subject based on the ideXlab platform.
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depth energy and depth force relationships in open Channel flows ii analytical findings for power law cross sections
Advances in Water Resources, 2009Co-Authors: Alessandro Valiani, Valerio CaleffiAbstract:Abstract In a recent work [Valiani A, Caleffi V. Depth–energy and depth–force relationships in open Channel flows: analytical findings. Adv Water Resour 2008;31(3):447–54], the authors analytically inverted the depth–specific energy and depth–total force relationships for flows in open Channels with wide rectangular cross-sections. In the present work, the previous results are extended using a simple analytical perturbation technique to the important class of power-law cross-sections, which can often be used to approximate real fluvial geometry. Assuming the river cross-section slightly different from the rectangular form, the exponent of the power-law defining the river cross-section is subsequently small. The expressions for the specific energy and total force as functions of the water depth are considered in dimensionless form. The inversion of these functions begins with the exact analytical solutions for wide rectangular sections. A perturbation analysis is carried out taking the exponent of the power-law as a small parameter. For a known discharge and for each meaningful value of the specific energy, a subcritical and a supercritical depth are analytically determined, expanding the depth in terms of this small parameter up to the second-order. Similarly, for each meaningful value of the total force, a subcritical and a supercritical depth are found analytically, also using a second-order expansion of the flow depth. Examples from classical open Channel Hydraulics show the consistency of these analytical solutions. An error analysis is presented to provide limits of presented solutions and an analytical technique is proposed to further refine the solutions.
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depth energy and depth force relationships in open Channel flows analytical findings
Advances in Water Resources, 2008Co-Authors: Alessandro Valiani, Valerio CaleffiAbstract:Abstract In the present work the depth–specific energy relationship and the depth–total force relationship in open Channel flows of wide rectangular cross-section are analytically inverted. The nondimensional expressions of the specific energy and of the total force, as functions of the nondimensional water depth, are considered. The inversion of such functions consists of finding the roots of third degree algebraic equations; simple analytical solutions are obtained. More specifically, for a given specific discharge and for each meaningful value of the specific energy, a subcritical and a supercritical depth are found analytically. Similarly, for a given specific discharge and for each meaningful value of the total force, a subcritical and a supercritical depth are found analytically. For both functions, it is also shown that the third root corresponds to a negative depth, which can be discarded on the basis of physics. Examples from classical open Channel Hydraulics and a numerical application show the consistency of these analytical solutions.
Alessandro Valiani - One of the best experts on this subject based on the ideXlab platform.
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depth energy and depth force relationships in open Channel flows ii analytical findings for power law cross sections
Advances in Water Resources, 2009Co-Authors: Alessandro Valiani, Valerio CaleffiAbstract:Abstract In a recent work [Valiani A, Caleffi V. Depth–energy and depth–force relationships in open Channel flows: analytical findings. Adv Water Resour 2008;31(3):447–54], the authors analytically inverted the depth–specific energy and depth–total force relationships for flows in open Channels with wide rectangular cross-sections. In the present work, the previous results are extended using a simple analytical perturbation technique to the important class of power-law cross-sections, which can often be used to approximate real fluvial geometry. Assuming the river cross-section slightly different from the rectangular form, the exponent of the power-law defining the river cross-section is subsequently small. The expressions for the specific energy and total force as functions of the water depth are considered in dimensionless form. The inversion of these functions begins with the exact analytical solutions for wide rectangular sections. A perturbation analysis is carried out taking the exponent of the power-law as a small parameter. For a known discharge and for each meaningful value of the specific energy, a subcritical and a supercritical depth are analytically determined, expanding the depth in terms of this small parameter up to the second-order. Similarly, for each meaningful value of the total force, a subcritical and a supercritical depth are found analytically, also using a second-order expansion of the flow depth. Examples from classical open Channel Hydraulics show the consistency of these analytical solutions. An error analysis is presented to provide limits of presented solutions and an analytical technique is proposed to further refine the solutions.
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depth energy and depth force relationships in open Channel flows analytical findings
Advances in Water Resources, 2008Co-Authors: Alessandro Valiani, Valerio CaleffiAbstract:Abstract In the present work the depth–specific energy relationship and the depth–total force relationship in open Channel flows of wide rectangular cross-section are analytically inverted. The nondimensional expressions of the specific energy and of the total force, as functions of the nondimensional water depth, are considered. The inversion of such functions consists of finding the roots of third degree algebraic equations; simple analytical solutions are obtained. More specifically, for a given specific discharge and for each meaningful value of the specific energy, a subcritical and a supercritical depth are found analytically. Similarly, for a given specific discharge and for each meaningful value of the total force, a subcritical and a supercritical depth are found analytically. For both functions, it is also shown that the third root corresponds to a negative depth, which can be discarded on the basis of physics. Examples from classical open Channel Hydraulics and a numerical application show the consistency of these analytical solutions.
Ellen Wohl - One of the best experts on this subject based on the ideXlab platform.
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large woody debris and flow resistance in step pool Channels cascade range washington
Geomorphology, 2003Co-Authors: Janet H Curran, Ellen WohlAbstract:Abstract Total flow resistance, measured as Darcy–Weisbach f, in 20 step-pool Channels with large woody debris (LWD) in Washington, ranged from 5 to 380 during summer low flows. Step risers in the study streams consist of either (1) large and relatively immobile woody debris, bedrock, or roots that form fixed, or “forced,” steps, or (2) smaller and relatively mobile wood or clasts, or a mixture of both, arranged across the Channel by the stream. Flow resistance in step-pool Channels may be partitioned into grain, form, and spill resistance. Grain resistance is calculated as a function of particle size, and form resistance is calculated as large woody debris drag. Combined, grain and form resistance account for less than 10% of the total flow resistance. We initially assumed that the substantial remaining portion is spill resistance attributable to steps. However, measured step characteristics could not explain between-reach variations in flow resistance. This suggests that other factors may be significant; the coefficient of variation of the hydraulic radius explained 43% of the variation in friction factors between streams, for example. Large woody debris generates form resistance on step treads and spill resistance at step risers. Because the form resistance of step-pool Channels is relatively minor compared to spill resistance and because wood in steps accentuates spill resistance by increasing step height, we suggest that wood in step risers influences Channel Hydraulics more than wood elsewhere in the Channel. Hence, the distribution and function, not just abundance, of large woody debris is critical in steep, step-pool Channels.
Bethany T Neilson - One of the best experts on this subject based on the ideXlab platform.
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impacts of beaver dams on Channel Hydraulics and substrate characteristics in a mountain stream
Ecohydrology, 2017Co-Authors: Trinity Stout, M Majerova, Bethany T NeilsonAbstract:Beaver dams have significant impacts on the hydrology, temperature, biogeochemical processes, and geomorphology of streams and riparian areas. They have also been used as a viable tool in restoring impaired riverine systems. Because of the dynamic nature of beaver dams, these influences vary and are difficult to quantify. To begin understanding the impacts of beaver dams in mountain streams, we developed 1D hydraulic models for a beaver impacted reach that includes eight dams and a non-impacted reach to compare hydraulic responses (e.g. Channel depth, width, and velocity distributions). We also compared observations of substrate size distributions for different geomorphic/habitat units within each reach. Results from the models indicated shifts in Channel Hydraulics through statistically significant increases in depths and widths as well as a decrease in flow velocities through the beaver impacted reach. These hydraulic adjustments, as a result of beaver dams, are consistent with observed changes in the increased variability and spatial heterogeneity in sediment size distributions. Through the application of three different modelling approaches, we found that a relatively low number of beaver dams would result in significant changes in Channel Hydraulics. These results provide preliminary information regarding the number of dams per unit stream length required to begin meeting various restoration goals.
Janet H Curran - One of the best experts on this subject based on the ideXlab platform.
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large woody debris and flow resistance in step pool Channels cascade range washington
Geomorphology, 2003Co-Authors: Janet H Curran, Ellen WohlAbstract:Abstract Total flow resistance, measured as Darcy–Weisbach f, in 20 step-pool Channels with large woody debris (LWD) in Washington, ranged from 5 to 380 during summer low flows. Step risers in the study streams consist of either (1) large and relatively immobile woody debris, bedrock, or roots that form fixed, or “forced,” steps, or (2) smaller and relatively mobile wood or clasts, or a mixture of both, arranged across the Channel by the stream. Flow resistance in step-pool Channels may be partitioned into grain, form, and spill resistance. Grain resistance is calculated as a function of particle size, and form resistance is calculated as large woody debris drag. Combined, grain and form resistance account for less than 10% of the total flow resistance. We initially assumed that the substantial remaining portion is spill resistance attributable to steps. However, measured step characteristics could not explain between-reach variations in flow resistance. This suggests that other factors may be significant; the coefficient of variation of the hydraulic radius explained 43% of the variation in friction factors between streams, for example. Large woody debris generates form resistance on step treads and spill resistance at step risers. Because the form resistance of step-pool Channels is relatively minor compared to spill resistance and because wood in steps accentuates spill resistance by increasing step height, we suggest that wood in step risers influences Channel Hydraulics more than wood elsewhere in the Channel. Hence, the distribution and function, not just abundance, of large woody debris is critical in steep, step-pool Channels.