Computation Of Water Surface Profiles Research Articles

Review paper on applications of the HEC-RAS model for flooding, agriculture, and water quality simulation

ABSTRACT The Hydrologic Engineering Center (HEC) of the United States Army Corps of Engineers (USACE) has developed the HEC-River Analysis System (RAS) hydraulic channel flow model as part of its portfolio of hydrologic and hydraulic modeling tools. HEC-RAS is a new version with capabilities to model flooding, modeling for agriculture production computations for water quality, and many more related to hydraulic modeling. The analysis components of the HEC-RAS system include one-dimensional steady flow water surface profile computations, one-dimensional and or two-dimensional unsteady flow simulation, one-dimensional and two-dimensional computations of quasi-unsteady or fully unsteady flow movable boundary sediment transport, and one-dimensional water quality analysis. The main objective of this paper is to review the use of HEC-RAS on flooding, agriculture, and water quality. The three primary components of the data input are plan data, geometry data, and flow data. Three of these scenarios applied to HEC-RAS and were proven by previous reviewers.

Analytical Solution of Gradually Varied Flow Equation in Non-prismatic Channels

Computation of water surface profile in open channel is considered as an essential component of channel design in open-channel hydraulics. In this regard, gradually varied flow (GVF) is enumerated as the most frequently occurring flow regime in artificial open channels. The analytical and/or semi-analytical solutions of GVF have been acquired for some types of open channels with prismatic channel cross section using both Manning’s and Chezy’s resistance equations. In conventional hydraulic textbooks, the interpretation of water surface profile is mainly based on prismatic channels. Indeed, the non-prismatic term in the numerator of the governing equation creates a further obstacle for proper interpretation. In this paper, an explicit closed-form semi-analytical solution is presented for a non-prismatic rectangular channel based on Chezy’s resistance equation using Adomian decomposition method. The developed semi-analytical solution compares well with both analytical and numerical solutions obtained from predictor–corrector method with very fine spatial resolution. The derived semi-analytical solution can be effectively used to conduct sensitivity analysis of pertinent parameters and compute channel discharge for a given water surface profile.

Normal depth and wetted perimeter in general power-law channels

Open channel cross section is an important element in water structures engineering. A general power-law section allows simulation and modeling of natural rivers and man-made open channels. Given simple forms and superior properties, the power-law sections are of interest to water resources engineers. The power-law exponent, m, is a parameter for which the open channel takes different shapes. The range of practical interest for the parameter m is 1 <m< ∞. Normal flow depth is of high importance and used for design and computation of water surface profiles in open channels with different shapes. The calculation of wetted perimeter and normal flow depth in power-law channels, ends up the hypergeometric functions and thus has been the main challenge over the years. Direct and simple solutions for these key quantities are not available in technical literature over the entire practical range of m> 1. Some studies are only valid over m> 2.5 while the others are applicable in the range of 1 <m< 2. This study presents direct and simple solutions for the normal flow depth and wetted perimeter in power-law channels over the wide practical range of 1.05 <m< 50. The maximum relative error of the proposed approximations for the normal flow depth and wetted perimeter are less than 1.2% and 0.3%, respectively. The proposed superior approximations can be used for channel section construction and optimization.

Semi-analytical solution and numerical simulation of water surface profile along duckbill weir

ABSTRACT Duckbill weir is one type of long crested weirs which passes more flow with less head variation on the weir than standard weirs. Due to contraction and decreasing discharge along the weir, a gradual variation in the water surface is occurred such as spatially varied flow phenomena. Therefore, in this study by solving the spatially varied flow equation, the water surface profile of duckbill weir is obtained when the bottom slots were used along the weir. Furthermore, Flow-3D software is used to simulate the water surface profile along the weir. The results of dimensional analysis showed that the discharge coefficient of the weir is increased by increasing of length and opening of slots. The results also show that the discharge coefficient of the weir is more affected by slot opening rather than the slot length. By solving the spatially varied flow equation along the weir one can found that there is a threshold value of H/P (H is the head of water over the weir and P is weir height) for a given θ (the angle between side wall and flow direction of the weir) in which the water surface tends to drop by entering to the weir and then a gradual rise in the water surface as it approaches the downstream end of the weir. The results also show that the calculated water surface profile along the weir by using spatially varied flow equation and Flow-3D software is close to experimental results. The maximum errors in computation of water surface profile for solving spatially varied flow equation and Flow-3D software are 6.8% and 3.05%, respectively.

Sediment accumulation owing to backwater effect in the lower reach of the Stung Sen River, Cambodia

We examined channel bars at two sites in the lower reach of the Stung Sen River, which flows into Lake Tonle Sap, Cambodia, to identify sediment transport and accumulation processes during monsoon-related flood events and to investigate how sediment transport capacity changes as a result of enhanced backwater effect of the lake. Channel bars in the lower reach of the Stung Sen River that emerge in the dry season were classified into type A (lateral bars), type B (point bars), type C (concave-bank benches) and type D (diagonal and island bars, or fluvial dunes) based on Nagumo et al.'s previous study. Type B, type C, and type D channel bars were at our study sites of SEN-01 and SEN-02, about 83 and 77km from the river mouth respectively. Computation of water surface profiles showed that sediment transport capacity of the Stung Sen River decreased abruptly after the peak flow stage because of the backwater effect from Lake Tonle Sap during the decreasing flow stage. Our observations suggest that alternating layers of sand and silt to clay layers accumulate to form type C channel bars, corresponding to changes in sediment transport capacity controlled by backwater effects from Lake Tonle Sap and by changes in flow depths and associated slackwater systems. The accumulation of alternating silt and sand layers of type B channel bars results from lateral sediment transportation that is accelerated with an increase of secondary flow, whereas development of type D channel bars is related to bedload mobility.

Analytical solution of gradually varied flow equation in circular channels using variable Manning coefficient

The direct integration method is used to solve the equation of gradually varied flow (GVF) in open prismatic channels. The GVF is a non-uniform flow with gradual changes in flow depth. In circular channels, Manning roughness coefficient under the partially full flow condition varies with the flow depth, and thus a variable Manning coefficient should be used to calculate the water surface profile. It is accepted that the Manning coefficient varies with flow depth in accordance with Camp’s curve. Given that circular channels have an important application in sewer systems, this research presents a semi-analytical approach for establishing the gradually varied flow profiles in circular channels through application of a variable Manning coefficient. For this, using two approximation expressions, the integrand of the GVF equation is expanded into a finite set of partial fractions and then every term of them is integrated separately. The proposed semi-analytical solution uses a single step for the computation of water surface profiles and provides an accurate and simple way to compute GVF flow profiles.

Water surface profile along a side weir in a parabolic channel

A side weir is an overflow structure set into the side of a channel. This structure is used for water level control in channels, diverting excess water from a main channel into a side channel and as storm overflows from urban sewage systems. Computation of water surface profile over the side weirs is essential to determine the flow rate of the side weir. Discharge estimation of the side weir is still an important research subject. Most previous research works for the side weir were carried out in main channels with rectangular, triangular, trapezoidal and circular cross sections. Analytical solutions for water surface profile along a rectangular side weir are available only for the special cases of rectangular and trapezoidal main channels on the basis of a constant specific energy. No analytical solution is available for a rectangular side weir located in a parabolic channel. This research presents an elegant analytical solution for establishing the water surface profile along a side weir located in a parabolic channel which involves the use of incomplete elliptic integrals. The solution, which yields a direct computation, should be a useful computational tool for evaluation and design of rectangular side weirs in parabolic channels.

Analytical solution for water surface profile along a side weir in a triangular channel

Side weirs are widely used for water level control in irrigation and drainage systems. These structures are also used to divert excess water from a main channel into a side channel. Computation of water surface profile along the side weir is essential to determine the discharge over the side weir. Estimation of discharge over the side weirs is still an important issue. Most previous research works for side weirs were carried out in channels with rectangular, trapezoidal and circular cross sections. An analytical solution for the water surface profile along a side weir is available in the technical literature only for the special case of a rectangular channel on the basis of a constant specific energy assumption (De Marchi’s water surface profile). No analytical solution is available for the case of triangular channel. This research presents an elegant analytical solution for establishing the water surface profile along a side weir in a triangular channel. The solution, which yields a direct computation of the flow profile, should be a useful tool for evaluation and design of side weirs in triangular channels.

Direct integration of gradually varied flow equation in parabolic channels

The direct integration method is used to compute water surface profiles of gradually varied flow (GVF) in a prismatic open channel. No closed-form solution is available for the GVF equation in the case of general parabolic channels. Open channels with parabolic cross-sections are often a quite good approximation of the real geometry of natural rivers. Technology is also available for constructing this shape of channels. In the present study, by applying the Manning formula, a semi-analytical solution to compute the length of the gradually-varied-flow profile for parabolic channels is developed. The proposed solution uses a single step for the computation of water surface profiles and, as such, provides an accurate and yet simple way to compute GVF flow profiles; thus, it should be of interest to practitioners in the hydraulic engineering community.

Book Reviews

Book Reviews

Uncertainty in Water Surface Profile of Buried Stream Flowing under Coarse Material

Non-Darcy flow occurs when a hydraulic gradient is set up across a matrix of coarse porous media, resulting in turbulence in the void spaces. Buried streams that are formed at open-pit coal mines in mountainous areas (due to the disposal of large quantities of waste rock in valley terrain) are good examples of this phenomenon. An overview of the sources of uncertainty associated with non-Darcy water surface profile computations is presented. Numerical and experimental examples are used to illustrate how the mathematical developments presented in this paper can be used to quantify some of the inherent uncertainties. A model buried stream built as part of this study was used to test these mathematical developments. The performance of an equation for optimizing cross-section spacing is described. Uncertainty equations developed using first-order uncertainty analysis are applied to a rectangular stream. A procedure for quantifying the probable error in the computed depth of flow is illustrated herein by applying a simplified form of the total uncertainty equation to a model buried stream. Based on these results, guidance is provided for the uncertainty analysis of water surface profiles for field-scale buried streams.

Flow Transitions in Bridge Backwater Analysis

In the steady flow computation of water surface profiles with one-dimensional models, bridges across floodplains require special attention. Accurate prediction of energy losses in the reaches upstream and downstream of the bridge requires accurate evaluation of four parameters: the expansion reach length, the contraction reach length, the expansion coefficient, and the contraction coefficient. This study investigated these four parameters through the use of field data, two-dimensional hydraulic modeling, and one-dimensional modeling. In this paper, the findings of the study with regard to the transition reach lengths are presented. The traditional rule, which recommends an expansion rate of one unit outward for every four units downstream from a bridge, overestimates the reach length in many cases. The standard rule regarding contraction reach lengths, which assumes a one-to-one rate of contraction, was not refuted by this study, but more refined estimates are reported.

Random differential equation modelling for backwater profile computation

Two probabilistic models for backwater profile computation are developed by using the theory of random differential equations. The models can simultaneously consider uncertainties in boundary condition and hydraulic parameters, such as the Manning's resistance coefficient, channel slope, discharge rate, within the equation describing the one-dimensional steady state nonuniform flow. The probability density functions of the water profile are obtained by numerically solving Liouville and Fokker-Planck equations. The results indicate that the method of random differential equations is useful for uncertainty analysis of the water surface profile computations.

Generalized Water Surface Profile Computations

A computer model based on both the energy and momentum equations is developed. This generalized model can be used for the computation of water surface profiles through hydraulic jumps. It also allows computation of water surface profiles regardless of whether the bed slope is steep, mild, horizontal, adverse or a combination of these. The control section can be a lake, weir, gate or a natural river section. The Manning, Chezy or Darcy-Weisbach equations can be used for head loss computation. A detailed description of methods used and a step-by-step computation procedure is given in this paper. Examples are used to demonstrate the applications of this generalized model for water surface profile computations.

FRICTION SLOPE MODELS FOR M2 PROFILES1

ABSTRACT: Results of studies which have considered the relative merit of various friction slope averaging equations previously used in water surface profile computations are described. Limitations of the most accurate equation known for the M2 profile have indicated that a new equation which gives more emphasis to the upstream energy gradient is desirable. Based upon friction slope curves developed for M2 water surface profiles two new equations, one a parabolic and the other an elliptical approximation, are presented. The behavior of the new equations and of the previously most recommended equation is described by test calculations. The elliptical equation performed more satisfactorily than the harmonic method commonly recommended for M2 profile computations. Insertion of an additional cross‐section about 50 feet upstream from a critical depth section was found to reduce computational errors for any energy gradient averaging method.

Water Surface Profiles in Irregular Natural Streams

Simple, practical method is proposed for computation of water surface profiles; method is advantageous when several backwater profiles must be determined in channel; assumption is that velocity of flow is not uniformly distributed over area of any cross section; effect of bend losses, bridge-pier losses, and losses owing to change in shape of cross section can be included when necessary. (22 refs.)

Two Methods to Compute Water Surface Profiles

Two methods for computation of water surface profiles used for development of tail water rating curves and backwater profiles; examples of each method are included which show computational procedure; tail water curves are used in design of power plants, pumping plants, and energy dissipators such as stilling basins; use of backwater curve above dam for reservoir land acquisitions and easements, design of new pumping plants, bridges, power plants.