Journal of Hydraulic Engineering

Forum papers are thought-provoking opinion pieces or essays founded in fact, sometimes containing speculation, on a civil engineering topic of general interest and relevance to the readership of the journal. The views expressed in this Forum article do not necessarily reflect the views of ASCE or the Editorial Board of the journal.

Forum papers are thought-provoking opinion pieces or essays founded in fact, sometimes containing speculation, on a civil engineering topic of general interest and relevance to the readership of the journal. The views expressed in this Forum article do not necessarily reflect the views of ASCE or the Editorial Board of the journal.

Abstract

This paper presents a comparison of numerical properties of the fixed-grid method of characteristics resulting from space and time linear interpolation used for the solution of transient flow in pipe equations. Modified equation analysis method is applied, in which the modified equations derived for the simplified linear version of the transient pipe flow equations provide explicitly the coefficients of numerical diffusion and dispersion generated by the method of characteristics. Through this approach the value of the numerical diffusion coefficient generated in the solution can be precisely estimated. Consequently, the effects resulting from the interpolation in time and space can be compared. The conclusions presented were confirmed by the results of numerical calculations.

Practical Applications

If a valve is suddenly closed at the end of a pipeline in which water flows, a pressure wave will appear in it. This phenomenon, known as the water hammer, commonly occurs in water supply networks and in various industrial installations. The wave propagation process is described by a system of differential equations, which are solved using numerical methods. Numerical methods are approximate; they allow to solve the mathematical problems in which both the data and the results of calculations are given in the form of numbers. Numerical methods enable the calculation of approximate pressure and velocity values at selected cross-sections of the pipeline and at selected moments of time. The calculated values contain an error that depends on the solution method. This error determines the quality of the water hammer simulation results. There are a number of methods for numerical solution of water hammer equations. In this paper, the method of characteristics is used, which requires interpolating pressure and velocity values between selected points. The article shows that the generated numerical error depends on the applied technique of interpolation. Two techniques, interpolation in space and interpolation in time, are considered.

In recent years, the rehabilitation of spillways and design of new dam constructions have considered the combination of a stepped chute with a labyrinth weir crest, highlighting the need for hydraulic information for this specific spillway type. To address currently missing design guidance, a novel study was conducted on a 10.7° round-crested labyrinth weir with a $3H:1V$ sloped chute with multiple step heights. The results include guidance for estimating flow depths along the chute and selecting a chute wall height; the role of the labyrinth weir on aeration, streamwise and transverse flow uniformity, and general flow patterns; and energy dissipation by the labyrinth crest and by individual steps. It was found that stepped chutes with a labyrinth crest are aerated from the impact of the nappes in the labyrinth outlet cycles, which continued to the chute entrance where the maximum air concentrations and flow depths occurred. The labyrinth crest also generates nonuniform flow patterns and air-water flow properties that have a significant effect on energy dissipation as the nonuniformity and potential drag reduction (due to the stronger aeration) results in less energy dissipated compared with published literature of stepped spillways with linear crests. The present findings provide first guidance for practitioners to combine labyrinth weirs with stepped chutes.

Interaction between various components of bridge scour is a complex phenomenon. Bridge submergence during high flooding leads to the scour mechanisms becoming even more complex. Thus, to find the interaction between various components of bridge scour, a detailed investigation has been conducted by using scaled-down models in a hydraulic laboratory. Scour experiments were conducted with free, submerged-orifice, and overtopping flow (OT) under clear-water conditions. The results show that the total interactive scour caused by simultaneous effects of pier, abutment and contraction scour results in a reduced equilibrium scour depth compared to the sum of all individual components acting independently. A comparison with HEC-18 methodology shows that the large bias of over-estimation has been eliminated by the suggested model in this study. However, the interaction of pier scour with vertical contraction scour remains as a sum of individual scour components with the exception of the recommendation of using Lyn’s modified model to calculate vertical contraction scour. Field examples from past historical events have been used to validate the model, and they show good agreement with the suggested model.

This paper deals with the prediction of flows in open channels. For this purpose, models based on partial differential equations are used. Such models require the estimation of constitutive parameters based on available data. After this estimation, the solution of the equations produces predictions of flux evolution. In this work, we consider that most natural channels may not be well represented by deterministic models for many reasons. Therefore, we propose to estimate parameters using stochastic variations of the original models. There are two types of parameters to be estimated: constitutive parameters (such as roughness coefficients) and the parameters that define the stochastic variations. Both types of estimates will be computed using the maximum likelihood principle, which determines the objective function to be used. After obtaining the parameter estimates, due to the random nature of the stochastic models, we are able to make probabilistic predictions of the flow at times or places where no observations are available.

Considerable parts of riparian forests around the world are covered by deciduous trees and tall shrub species with rigid trunk and flexible-broadleaf. Experiments are conducted on artificial rigid and flexible models to estimate drag coefficient and resistance to flow for deciduous trees in forest floodplains under nonsubmerged condition. The rigid and flexible models with similar size and configuration are tested in a laboratory flume to clearly determine the effects of vegetation flexibility and density, and the flow velocity and depth on the roughness coefficients. Ratios of the flexible to rigid drag forces and drag coefficients indicate considerable effects of flexibility on the roughness coefficients. In this study, the flexural rigidity of the tree leaf is used in the roughness equations to account for vegetation flexibility instead of the traditionally used tree trunk flexural rigidity. This is based on the assumption that foliage flexibility governs tree reaction to the flow for most species of deciduous trees and leafy tall shrub families. The developed roughness coefficient equations are scaled up to determine the variation of Manning’s $n$-value with increase of flow depth for a riparian canopy of black willow. The estimated Manning’s $n$-values are compared with the reported Manning $n$-values for the same black willow canopy.

This paper designs and builds a stormwater pipe-river/channel experimental system at the first attempt to observe hydraulic dynamics between pipe flow and downstream water levels under different steady state conditions. In addition, a three-dimensional (3D) model is developed to facilitate the understanding of this complex hydraulic interaction, and the reliability of a widely used one-dimensional (1D) model is first investigated. Experiment and simulation results show that (1) a high downstream water level can increase pipe flow capacity at the early stage, and the pipe flow is followed by a slightly downward trend and finally rapidly decreased, (2) pipe flows exhibit complex behaviors during the transition from nonfull to full pipe flow by altering flow area and velocity, and (3) the observed flows are significantly lower than those from the 1D model for the nonfull pipe flow scenario. This study offers insights to the underlying complex hydraulic properties between pipe flows and downstream water levels, and also shows that the 1D model is insufficient to reveal such an interaction process, which may underestimate the urban flooding risk.

Bernoulli’s equation is a famous, elegant fluid mechanics relation that, in its most popular version, relates pressure, velocity, and elevation changes along each streamline in a steady barotropic inviscid flow. Despite its simplicity and restrictive assumptions, this equation is a powerful and effective analysis tool in a variety of real-flow situations. However, the Bernoulli equation is unfortunately not Galilean-invariant, i.e., it does not satisfy the desirable property of remaining unchanged under a Galilean transformation between two inertial reference frames reciprocally moving with constant velocity. In a previous paper, the author presented a Galilean-invariant formulation of the Bernoulli equation, in which a new term is introduced in the definition of the Bernoulli constant. In the present technical note, this Galilean-invariant form of the Bernoulli relation is extended to (1) unsteady flow, (2) compressible flow, and (3) a noninertial frame of reference accelerating with constant rectilinear acceleration. Similar extensions are consolidated for the classic Bernoulli equation and treated in fundamental fluid mechanics textbooks. The use of the updated Galilean-invariant Bernoulli equation in these less-restrictive contexts is illustrated with typical engineering application examples. The results demonstrate that the extended version of the Bernoulli principle can also be applied along the same flow lines in a reference frame moving with constant velocity relative to another reference frame in which the conventional Bernoulli equation is valid, provided that the Bernoulli constant includes a suitable additional term.

Abstract

Blockage detection in circular open channels (partially filled pipes, e.g., gravity sewer pipes) has gained increasing interest in the water industry. While there have been significant advancements in monitoring technologies for such systems (e.g., smart sewer systems), there is a lack of quantification of the hydraulic impact of partial blockages in circular pipes, which is a limiting factor for cost-effective detection. This study presents and validates a numerical framework to quantify the changes in water depth caused by extended bottom blockages in circular open channels. The analysis is based primarily on continuity and energy conservation with the assumption of a lossless transition at the blockage. The proposed approach can determine the critical blockage height that would induce choking, therefore a change in the upstream depth. It can also calculate the changed upstream water depth for various bottom blockage height values (above the critical height) for both subcritical and supercritical conditions. The proposed approach is numerically implemented and then validated through a series of laboratory experiments under the subcritical flow condition (which is the most common condition for gravity sewer systems). The numerically determined water depth results are consistent with the experimental results, which confirms that the proposed approach can accurately estimate the new upstream depth under the choking condition induced by a bottom blockage in circular open channels. The results contribute to advancing the hydraulic understanding in circular open channels with extended partial blockages, which is useful in the development of smart sewer technologies.

Practical Applications

Spills and overflows out of the gravity sewer system damage the environment and bring risks to public health. The problem is typically caused by partial blockages, which can reduce the flow capacity of the sewer pipe and induce higher-than-designed flow depth on the upstream of the blockage (known as choked flow condition). This study helps water engineers and operators to understand how an extended bottom blockage affects the flow condition just upstream of the blockage in a circular gravity sewer pipe. Charts have been presented to enable the determination of (1) the critical height of an extended bottom blockage that would induce choking; (2) the expected upstream flow depth for blockages with various heights, with a given flow rate under choked flow condition; and (3) the expected upstream flow depth for various flow rates, with a given blockage height under choked flow condition. The results can be used to evaluate the risk of bottom blockage-induced spill for sewer pipes with various sizes, slopes and flow rates (e.g., some may be more tolerant to bottom blockages while some may be more sensitive). This information can then be used to prioritize preventative measures such as sewer depth monitoring or regular cleaning.