An analysis of the accuracy of the peak flow branching coefficient of watersheds in line with planning for flood control (case example: Faresban watershed of Hamadan province)
Alireza Gholami
1
(
Ph.D educated of hydraulic structures, Boali Sina University
)
Majid Heydari
2
(
Associate Professor, Department of Water Engineering, Faculty of Agriculture, Bou Ali Sina University
)
bahram Rezaei
3
(
assistant Civil, Bualisina university
)
Keywords: Dynamic Wave, flood, Saint-Venant Equations, Inverse trend finding, Partition coefficient,
Abstract :
Flood is one of the phenomena that endangers the life and property of many people in every corner of the world. More than half of global flood damage occurs in Asia (Thingsanchal 2012). Since the flood discharge is very important in water resources utilization plans, flood control, dam construction, flood control operations and most hydrological studies, therefore, the accuracy of studies and the degree of safety in the design of water facilities and structures are highly dependent on the method of conducting studies. Depending on the conditions and available information about the river, solving the problems of the flood process can be done by hydraulic and hydrological methods. The lack of statistics in some basins practically makes it impossible to make the necessary forecasts to prevent flood damage. In some areas, due to the large distance between two stations, the information on intermediate points is not available. Therefore, in order to prevent flood damage, the flood hydrograph should be developed in these places. Estimating the downstream hydrograph using the characteristics of the upstream hydrograph or vice versa is considered a type of trending method. In some routes, the incoming or outgoing branches have a direct effect on the output hydrographs, so knowing the branching coefficient is a very good help for finding the flood hydrograph. Based on this, research is done in two ways, direct or reverse. The basis of trend finding is based on the theory of unsteady flows, assuming that the flow in rivers or flumes is one-dimensional, this problem can be analyzed based on the Saint and Nantes equations (flow continuity equation and momentum equation) (Abbasizadeh and colleagues, 1389).
Methodology
First, the data collected from the Faresban watershed near Nahavand city in Hamedan province with geographical characteristics of 48 degrees, 7 minutes and 5 seconds east and 34 degrees, 14 minutes and 39 seconds north were modeled after mathematical calculations and matching with laboratory conditions. For modeling, the Saint-Venant equations were simplified by the four-point finite difference method and the boundary conditions of the model were considered in the water engineering department laboratory of Boali Sina University, Hamedan. This model was used in the form of a rectangular flume with a length of 11 meters, a width of 48 cm, and a slope of 0.003 At a distance of 6.5 meters from the beginning of the flume, there is a branch to the left with a width of 34 cm, a length of 490 cm, and a slope of 0.003 and it was built with a 39 degree deviation angle which was modeled according to the conditions of one of the rivers in the basin. The flow of water enters the flume by a pump from the ground tank through a 6-inch pipe on which a gate valve was installed and controlled by an electric motor, inverter and smart board. Also, a vectorino single-point sonic speedometer was used to measure the speed.
Results and discussion
This research was carried out on 9 inlet and outlet hydrographs with different flow rates in the flume, and according to the measuring range of the speedometer device and the maximum height of the channel, the numerical values of the hydrographs were close to each other. The percentage of branching division was calculated from the ratio of output hydrograph to input hydrograph multiplied by percent and the average was calculated for each harvest. The outlet hydrograph in the branch and the main branch was considered as the downstream boundary condition, and then reverse trending was done up to the connection point, the division coefficient was calculated using trended hydrographs up to the point of division (odd hydrographs). Using the numbers obtained for the remaining hydrographs, the distribution coefficient was estimated by fitting the curve between the distribution coefficients and the volume of water entering the branch. The results of the inverse trending of the designed flood and the comparison of its results with the numerical methods obtained from the Saint-Venant equations are presented in the figures and tables below. These measurements were made on 9 hydrographs, which were considered as known for the accuracy of the odd-numbered hydrographs, and then using the simplified equations of continuity and movement size, the even-numbered hydrographs were calculated and the results The results were compared with the collected values.
Conclusion
In this research, the inverse hydraulic trending equations were done with the four-point finite difference method. For the reverse trend, the exit hydrograph of the branches was used, and the hydraulic characteristics of the route were also considered. Considering the short distance of the branches to the connection point and from the connection point of the two branches to the input hydrograph measurement location, the rising slope, peak point and descending slope of the measured and calculated hydrographs were in good agreement with each other; Also, as seen in the presented tables, the maximum amount of maximum error is related to hydrograph number 4. In the graphs presented, which are related to the calculated and measured hydrographs, it is clearly stated that the prediction of the branching coefficient can be a good help in finding the entrance or exit hydrograph of the branch in cases where the branching information is not available.
In watersheds with incomplete flood hydro graph statistics, one of the most useful methods is trend finding. One of the subcategories of trending is the hydraulic method, which is used in multi-branches and with incomplete statistics. In this regard, the dynamic wave method is one of the most complex and accurate hydraulic trending methods, which is done by fully numerically solving the Saint-Venant equations.Considering the output hydro graph of a flow as the information of the problem and the characteristics of the flow path, Saint-Venant's equations are solved by the finite difference method and the input hydro graph is calculated. In this research, the mentioned method was studied as reverse trending and its results were compared with observations.An unsustainable flow was created and withdrawals were made without considering the loss of the route. Then, the obtained data were controlled in the MATLAB coding environment and for trending. After this stage, the division coefficients of the branch for a number of hydrographs entering the branch were measured and the rest of the division coefficients were calculated by mathematical methods.After that, using statistical parameters mean square error, relative error percentage, maximum error percentage and minimum error percentage, the obtained results were analyzed and it was shown that the created model for calculating input hydro graphs has high accuracy.The results of inverse trending in 9 created hydro graphs showed that there is a good match between the outputs of the program and the observations, while the examination of the flow distribution coefficients indicated that these coefficients correspond to the percentage of permissible error.This issue was expressed by obtaining the maximum and minimum relative error of less than 10% in the division coefficients. The results of this research can be used after verification in the field in order to estimate the characteristics of floods in a channel that has not been properly surveyed in the flood measuring stations along the route.
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