Regulated Rivers and Storm Sewer Systems †MyAssignmenthelp.com

Question: Discuss about the Regulated Rivers and Storm Sewer Systems. Answer: Introduction: There has been a large rate of urbanization in the metropolitan areas especially in the vicinity of the river basins. The rapid rate has caused resource planners and hydrologists to come up with better models of analysis of the urban hydrology. The kinematic wave model is used for the channel and the overland flow routing in the precipitation-runoff modelling system in the Distributed Routing Rainfall Runoff Model. The development of the theory and application of kinematic wave is complex but it is not readily available in a given text. It is an approximation of the dynamic wave model as there are developments of the models and the difficulty involved in applying the solution techniques, the theory is described as a dynamic wave theory applied to water routing problems. The open channel flow stand-out as the most experienced kind of flow in the catchment modelling processes over the recent years. When there is no acceleration experienced in the flow of the water or runoff, the system is considered to be in steady flow. When there is a change in the velocity, the flow is not considered steady any more. It is important to consider the impact of the unsteady flows; therefore, it is added as variable when performing the analysis of a catchment area. Another type of flow is the uniform flow which follows where the slope of the water surface does not change with flow. A large water surface slope change is used to demonstrate the rapidly varied flow. A general description of the runoff is given by the shallow water equations which are valid for surface flow, gutter flow and the flow in the sewer systems. The shallow water equations are two partial differential equation that are resultant of the mass and momentum conservation laws. The shallow water equatio ns are derived as demonstrated in the illustration below, The process of the open flow for an unsteady flow is expressed in mathematical terms as is described by the St. Venant equations as, The kinematic approach is analyzed as a product of the stage or depth versus the discharge relationship. It uses the momentum equations to perform the analysis such that the wave occurs when the process terms are deemed negligible. Such denotation allows a designer or the hydrologist to assume that the bed slope is very close to the friction slope. Every catchment area needs to acknowledge the backwater effect and the same is included in the analysis. On the other hand, the discharge is described as a function of depth of flow only. The run off process occurs in the surfaces, gutters, and sewers as described by one continuity and momentum equation for the shallow water equations. (Lyngfelt Arnell, n.d.). To advance run-off hydrographs by analyzing the relationship between the kinematic approach and the pond model approach. To deliberate the differences and reasons for the differences between the kinematic approach and the pond model At the outlet of the catchment area, the flow is considered uniform, unidirectional and one that flows instantaneously from the outlet to the next point in the analysis. Catchment area 2.25ha (150m x 150m) Slope 2.25% Roughness 0.150 Rainfall event 90mm/h for 60 mins Losses Initial losses of 4.5 mm and continuing losses of 3mm/h The kinematic data set as well as the pond approach model dataset are as described in the attached spreadsheet. The above values were used to provide the base ground information of the site being modelled. The design of a wet pond is modelled using several parameters. the primary parameter is the area ration which is designed not to be less than 100 for maximum efficiency. It is given as, The two approaches are used in the hydrological analysis of water flow on the ground surfaces. This refers to the water that flows in stream canals or the overland flow that flows on the land surface. As indicated in the introduction section, the St. Venant equations are used for the two-dimensional analysis. It is crucial to note that the kinematic wave approach models use the highlighted set of equations while considering the impacts of gravity and resistance on flow. The analysis provides a platform for the analysis of the 1-1 relationship between the depth or the stage and the discharge. This is done using the equation below, Unfortunately, the kinematic approaches do not manage to denote the flow at the low land regions or the very high points of the catchment area as a result of intense precipitation on the hillslope. The kinematic approach model assumes that the friction slope may be approached by the land surface slope making other effective components of the friction slope negligible. The pond model seeks to cater for the caveat or shortcomings of the kinematic approaches. The pond approach seeks to review the surface runoff that enter the drainage system through gulley and manholes. The sewer flows surcharge from the manhole and the surface overland flow in one or two dimensions. Once the sinks are full water is passed on to the catchment within which that sink and its corresponding sink lies in. Water tends to appear as output in the same water that is identified from the hydrograph. In the reality substantial portion of the water appearing as the old water. The water that has entered the watershed from a previous event. The unit hydrograph theory is as demonstrated below, One is able to determine the inflection point of the flow on the catchment area when a hydrograph is plotted. The plot uses the semi-logs or log scales as the data being addressed is very large. The designer notes the time when the recession side follows the trendline. (Li, et al., n.d.). One may wish to know why they would implement the kinematic approach over any other approach in the catchment modelling. It provides an alternative routing for the flow of water over the land surface. Some sections of the land are more pervious than other hence the water flowing may slip into the land causing a loss. Some of the portions of the catchment area may not allow the smooth flow as they act as obstacles. It allows non-linear response devoid of complex solution procedures or very complicated analytics. The parameters in a model are actively adjusted to account for the complexity of the catchment area. Some of the parameters considered in this are the channel shape, the boundary roughness, the catchment area length and width, the channel or area slope as well as the nature of the flow surface. The kinematic wave approach is acknowledged as the limiting case of an infinite number of non-linear reservoirs. The slope differs in terms of the flow rate at a given point in time depending on the section of the catchment area being analyzed. It can be observed that the after the 23rd minute of the hydrological analysis, the slope has a negative gradient as compared to the previous time. This demonstrates a catchment area that has an uphill section. The water flows downwards until it reaches a point where it stalls as it tries to manage the upward movement. The kinematic approach studies the motion of the fluid flow. The fluid flow tends to move at the same speed at a given point in time. Conclusion In a nutshell, the kinematic approach model assumes that the friction slope may be approached by the land surface slope making other effective components of the friction slope negligible. The run-off process occurs in the surfaces, gutters, and sewers is described by one continuity and momentum equation for the shallow water equations. The kinematic wave approximation is defined by a set of differential equations and boundary conditions. The development of the theory and application of kinematic wave is complex but it is not readily available in a given text. It is an approximation of the dynamic wave model as there are developments of the models and the difficulty involved in applying the solution techniques. It describes a characteristic type of wave motion that can occur in the many simplistic flow problems. References Li, R-M, S., Stevens, D. B. M, A., n.d. Non-linear Kinematic Wave Approximation for Water Routing. Water Resources Research, 11(2). Lyngfelt, S. Arnell, V., n.d. A mathematical runoff model for simulation of storm water runoff in urban areas. Chalmers university of Technology, Urban Geohydrology Research Group, Volume 12. Sjoberg, A., n.d. Calculation of Unsteady Flows in Regulated Rivers and Storm Sewer Systems. Department of Hydraulics, Chalmers University of Technology, Volume 87.