Exact Solution of Optimum Hydraulic Power-Law Section with General Exponent Parameter

Han, Yan-Cheng; Easa, Said M.

doi:10.1061/(asce)ir.1943-4774.0001358

Cited by 9 publications

(6 citation statements)

References 19 publications

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“…Approximate solutions for the wetted perimeter in range of s∈ [1.5, 2] have been developed [17]. The approximate solution of the wetted perimeter presented by Han and Easa [21] for the range of 1.167 < s < 2 is only accurate for the shape factor a = 0.4 (they defined power-law section by y = ax k , where k = (s − 1) −1 ). Their solution is not accurate for other shape factors (for a = 0.5 and water surface width of 2 m, the relative error reaches up to 6.8% for s near 1.167).…”

Section: Complex Power-law Section (B ≠ 0)mentioning

confidence: 99%

“…Recently, Han and Easa [21] and Chen et al [22] presented optimum hydraulic power-law sections using the Lagrange multiplier optimization method. In practice, sometimes open channel sections are constrained by side slope (when slope stability and geotechnical conditions are important), but, the optimum hydraulic section for a given side slope has not been solved by the authors.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, sometimes open channel sections are constrained by side slope (when slope stability and geotechnical conditions are important), but, the optimum hydraulic section for a given side slope has not been solved by the authors. Analytical solutions for the wetted perimeter of the power-law sections are developed by Han and Easa [21] and Chen et al [22] using the Gaussian hypergeometric functions. They also proposed exact optimization model using the Gaussian hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%

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Optimum simple and complex power-law channels

Vatankhah

2020

SN Appl. Sci.

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This study develops solutions for the hydraulically and most hydraulically efficient power-law sections (simple and complex). For this, the dimensionless objective function is defined as the wetted perimeter to the square root of the flow area. The objective function is then minimized. This study uses a simple procedure to establish the optimum dimensions. In comparison with the Lagrange multiplier method, this approach without any constraints is very simple for implementation. The optimization model of the simple power-law section has two decision variables (dimensionless depth and exponent) while the optimization model of the complex power-law section has three decision variables (dimensionless depth, dimensionless width and exponent). Optimizing all decision variables results in the most hydraulically efficient section (best hydraulic section), while optimizing some of the decision variables results in the hydraulically efficient section. This study presents a novel graphical comparison between simple and complex optimum power-law sections and shows that the dimensionless decision variables are constant for the most hydraulically efficient sections while are not constant for the hydraulically efficient sections. The characteristics of the hydraulically efficient sections are presented in tabular forms and explicit equations. These solutions are easy to use for optimum design of the power-law sections.

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Section: Complex Power-law Section (B ≠ 0)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimum simple and complex power-law channels

Vatankhah

2020

SN Appl. Sci.

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“…The new sections included polygonal section by Kurbanov and Khanov [23], trapezoidal-rectangular section by Abdulrahman [24], parabolic sides with horizontal bottom (HB) by Das [25], trapezoidal section with round corners by Froehlich [26], and two-segment parabolic sides with HB by Easa [27]. These sections have subsequently inspired the development of more new sections (2010-2018), such as semi-regular polygon by Vatankhah [28], multiple-segment linear sides by Easa [29], standard elliptic sides by Easa and Vatankhah [30], general elliptic side by Easa [31], and cubic and power-law (PL) sections by Han and Easa [32,33]. As noted, the trend of recent advances in section shape has been to introduce additional linear or curved elements, such as HB and round bottom corners, to improve discharge (flow rate) and maintenance.…”

Section: Section Familymentioning

confidence: 99%

New Compound Open Channel Section with Polynomial Sides: Improving Cost and Aesthetics

Easa

Han

2019

Water

Self Cite

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Previous research on compound trapezoidal cross sections has mainly focused on improving the prediction of the discharge (flow rate) because of its inherent challenges. This paper focuses on two other important aspects: Section shape and optimal construction cost. First, the paper proposes a new compound section with third-degree polynomial sides of main channel with horizontal bottom (HB) that allows its top corners to be smooth, called herein compound polynomial section. The special cases of this versatile section include the simple polynomial section, polygonal section, trapezoidal-rectangular section, two-segment linear-side section, and parabolic bottom-trapezoidal section. The simple polynomial section, which is the bank-full part of the compound polynomial section, can further produce parabolic (with or without HB), trapezoidal, rectangular, and triangular sections. Second, an optimization model that minimizes construction cost (excavation and lining) of the compound (or simple) polynomial section is developed. The model includes discharge and physical constraints. Theoretical and empirical methods of discharge prediction were used in the model. The results show that the simple polynomial section was more economical than the popular parabolic section by up to 8.6% when the side slopes were restricted. The new polynomial-based sections not only reduced construction cost, but also improved maintenance and aesthetics. As such, the new sections should be of interest to researchers and practitioners in hydraulic engineering.

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“…Vatankhah [9] considered the relationship between the specific energy of a parabolic channel section and its depth and obtained the subcritical and supercritical depths analytically by solving a quartic equation. Han [10,11] used a complex function method and the undetermined Lagrange multiplier optimization algorithm to derive a theoretical solution for the hydraulic optimal section of a cubic parabola. Through a comparison, it was shown that the hydraulic performance of the cubic parabolic section was the best.…”

Section: Introductionmentioning

confidence: 99%

Research on the Comprehensive Optimization of the Hydraulic Performance and Frost-Heaving Resistance of a Parabolic Channel

Yang

Wang

et al. 2020

Water

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Hydraulic performance and frost-heaving resistance should be considered simultaneously in the channel design of seasonally frozen soil areas. Quadratic parabolic channels have good water and sand transport capacities and high frost-heaving resistances. The width–depth ratio of a parabola determines its section structural form, which in turn determines the hydraulic performance and frost-heaving resistance. In this research, based on the current lack of a comprehensive optimization method that accounts for the hydraulic performance and frost-heaving resistance of the cross-section structures of parabolic channels, a multi-objective optimization model was established with the goal of achieving a minimum cross-sectional flow area and a uniform channel section force. Taking the flow velocity, the width–depth ratio and the crack resistance of concrete lining plate as constraints, the α method of the linear weighted sum method was used to optimize the calculation, and the comprehensive optimal quadratic parabolic channel section was obtained. The comprehensive optimal section of an actual parabolic channel in the Shijin Irrigation District was determined using this method, and the comprehensive optimal section was analyzed and compared to the original design section and two typical parabolic channel sections. The comprehensive optimal section was compared with the original design section in the Shijin Irrigation District. The force uniformity of the optimal section was 23.2% better, the hydraulic performance was 1.96% better, and the land use was 12.35% less. Compared with the values for the hydraulic optimal section, the maximum positive and negative bending moments of the comprehensive optimal section decreased by 5.6% and 11.89%, respectively, and the force uniformity increased by 7.62%. Additionally, compared with the values for the practical economic section, the force uniformity and the hydraulic performance of the comprehensive optimal section increased by 1.79% and 0.2%, respectively, and the land use decreased by 4.49%. Thus, the comprehensive optimal section met the engineering requirements and it could provide a reference for the design and selection of parabolic channels in seasonally frozen soil areas.

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Exact Solution of Optimum Hydraulic Power-Law Section with General Exponent Parameter

Cited by 9 publications

References 19 publications

Optimum simple and complex power-law channels

Optimum simple and complex power-law channels

New Compound Open Channel Section with Polynomial Sides: Improving Cost and Aesthetics

Research on the Comprehensive Optimization of the Hydraulic Performance and Frost-Heaving Resistance of a Parabolic Channel

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