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Introduction. An analysis of mathematical models of two-dimensional planned flows was carried out. Such flows are characterized by local depth-averaged velocities and local depths at each point of the flow. The mathematical model formation of the water flow is based on its division into several sections. There is a section where the flow parameters (velocity, depth, width) are kept constant at the stage of flow exit from the pipe — the inertial front. The purpose of the article and its relevance are defined.Materials and methods. By introducing dimensionless complexes on the basis of π-theorem, the formula for the length of inertial front of the water flow at its spreading from a rectangular pipe into a wide diverting channel is derived. An analogy from gas dynamics is used, namely, the transition to the plane of the velocity hodograph. Using the velocity hodograph, the distribution of depths and velocities of the flow along its longitudinal axis of symmetry and along the extreme line of current was obtained. The main computation tasks for the flow parameters have been formulated.Results. Numerical calculations of the formulated main tasks for determining flow parameters are described. Comparison with experimental data is given and the adequacy of the refined mathematical model of a two-dimensional planned flow is confirmed.Conclusions. The resulting formula for the length of the inertial front makes it possible to achieve the desired error in calculating the parameters of the water flow. With flow expansions up to 5, the relative error of the ordinates and flow velocities does not exceed 7–10 %. Calculation formulas and implemented programs will allow HTS designers to quickly and accurately determine the boundaries, speed and depth of free flow on the culvert.

In the planar hydraulics, the problems with previously unknown boundaries are most difficult. The best adequacy in terms of flow parameters is provided by simplified analytical methods based on a potential flow model. A mathematical model of a stationary, potential, 2D planar high-velocity open water flow of an ideal fluid, freely spreading back from a non-pressure orifice is studied. The boundary problem of flow free spreading in plane were formulated. Studying the system of dimensionless equations of motion resulted in identification of the criteria influencing the process of flow spreading. A critical analysis was carried out and a description of various methods for solving the problem of free spreading of a high-velocity water flow was given. The problem in an analytical form was solved in the velocity hodograph plane. All flow parameters are determined in the physical plane. For the first time, the conjugating flow "simple wave" was applied. The proposed analytical method for solving the problem of flow free spreading is effective, unambiguous and has no singularities and discontinuities, particularly, at the outlet of a non-pressure pipe. The adequacy of the mathematical model was verified on a test example. The relative error of the flow parameters does not exceed 10 % compared to the experimental data.

The spatial prediction of flood inundation, in the monsoon months (July–October), around the downstream southern part of the Damodar River Basin (Hooghly and Howrah districts of West Bengal) is very uncertain due to analytical lack of database, channel hydraulics and steady or unsteady flow anomaly. Using techniques of flood hydrology and HEC-RAS module of flood prediction, this study estimated the critical hydrological range of recurrent floods (1651–1822 m3 s−1 peak discharge) which are annually observed in the low-lying active floodplains of lower basin. The four days heavy rainfall (52.5 to 268 mm), yielded a runoff range of 10–207 mm which triggered maximum discharge of 7035 m3 s−1, causing havoc flood at downstream. There is possibility of channel shifting and embankmnet breaching during floods in the Mundeswari and Damodar/Amta channel, as Unit Stream Power can exceed 30 Wm−2 in tweleve cross-section stations. During 5-year and 10-year flood event (6676 m3 s−1) the floodplain inundation depth can reach 4–12 m in the Khanakul, and Udaynarayanpur region, having maximum chance of overbank flow. The most vulnerable site of embankment failure and overbank flow is stretch between Rajbalhat and Udaynarayanpur where the flood depth can cross 10 m limit for the critical discharge of 1811 m3 s−1. The flood risk is aggravated because within 42.5 km stretch of lower Damodar the channel can accommodate maximum flow of 1378 m3 s−1 (average flow area of 687 m2) at upstream cross-sections, but at downstream cross-sections the carrying capacity of channel is reduced to 1081 m3 s−1 (21.55 percent reduction) due to increasing siltation and decreasing average flow area (478 m2). [ABSTRACT FROM AUTHOR]

For a stationary potential 2D planar open high-velocity water flow of the ideal liquid, we propose a closed system of nonlinear equations considering the resistance forces to the flow from the channel bottom. Tangential stresses on jet interfaces are ignored. The resistance force components are expressed in terms of velocity components. In this case, the flow equations can be solved through the method of characteristics, and the surface forces are reduced to equivalent volumetric forces. The system of non-linear equations is solved in the velocity hodograph plane; further, the transition to the physical plane takes place. Since the value of the hydrodynamic pressure decreases downstream of the flow, the friction forces to the flow in the first approximation can be considered by using the integral laws of resistance. At that, the form of the equations of motion in the plane of the velocity hodograph does not change. This fact is proved in the article. An example of calculating the water flow is provided. The kinecity, ordinates, and velocities of the flow along its extreme line are calculated without considering resistance forces. Validation of the model in the real flow is performed. Acceptable accuracy relative to experimental data is obtained. [ABSTRACT FROM AUTHOR]

Widening of the A1 motorway between Köln‐Niehl and Leverkusen‐West – general planning of the motorway segment and design of the bridge over the Rhine River in Leverkusen The existing bridge over the Rhine River in Leverkusen is reaching its limit due to heavy load traffic having increased enormously since the 1960s. The replacement of the bridge over the Rhine River and the predicted future traffic volume require the widening of the A1 motorway segment between the Köln‐Niehl junction and the Leverkusen‐West interchange to eight continuous traffic lanes. For the first time in Germany, a cable‐stayed bridge over the Rhine River needs to be replaced. The construction of a new twelve‐lane bridge over the Rhine River while maintaining traffic on the six traffic lanes of the existing bridge goes hand in hand with the widening of the approx. 4.55 km motorway segment containing a total of 15 bridges, retaining walls, basin systems, noise barriers and traffic sign structures. A single general planner is responsible for nearly the entire planning of this construction project. Only surveying and landscape architecture services are provided by the client. The widening of the motorway and the replacement of the engineering structures within the secured former Dhünnaue landfill site represent a particular challenge. Efficient emission protection measures are to be provided for the work inside the landfill site. The site must be resealed, and the drainage and ventilation system connecting to the new traffic infrastructure and engineering structures must be restored. [ABSTRACT FROM AUTHOR]

A nonlinear system of differential equations in the problem of free flowing of supercritical flow is considered and a method of its solution is proposed. The analytical method is based on the introduction of the velocity hodograph plane and the obtaining of analytical solutions for the system of partial differential equations. It is pointed out that apart from being purely analytical, the potential flow model has a great practical demand due to its use as a base for the further research of the flow resistance forces. The proposed model can be developed by taking into account flow resistance and gradient, the bottom of the diverting channel flow. The theoretical results are complemented by numerical experiments and compared with experimental data. [ABSTRACT FROM AUTHOR]

Sediment transport has implications for activities such as fishing, flood control, scour countermeasures, and dredging through altered flow depths and sediment transport, bank erosion, and bridge scour. To estimate the changes in sediment transport and bridge scour, river discharge, water surface slope, water temperature, and tailwater depth (to simulate sea‐level rise) were altered in existing sediment transport and scour models. It was found that (a) in uniform flow upstream of sea‐level rise effects, sediment transport is sensitive to discharge but not to temperature; (b) in non‐uniform flow affected by sea‐level rise, sediment transport is sensitive to water surface slope and discharge but not to temperature; (3) the discharge value to restore the sediment transport rate existing before sea‐level rise is proportional to the water surface slope ratio to the fourth power; (4) the discharge value to restore the bed sediment size existing before sea‐level rise is proportional to the water surface slope ratio to the three‐fourth power; (5) abutment scour is weakly inversely proportional to the water surface slope but more strongly proportional to the discharge in a logarithmic relation; (6) pier scour is weakly proportional to the water surface slope but more strongly proportional to the discharge in a logarithmic relation; and (7) the discharge to restore both abutment and pier scour depths to their original values prior to sea‐level rise is proportional to the water surface slope ratio to the 9/25th power. Full equations for each of these relationships are given in the article. These relationships can be used for future application and planning purposes. [ABSTRACT FROM AUTHOR]