An Analytical Solution for Finding the Deflection Point of the Wetted Perimeter – Discharge Curve by Hydraulic Methods for the Determination of Environmental Flow requirements

Document Type : Research Article


1 Graduate M.Sc. Student of Water Engineering Department, Imam Khomeini International University, Qazvin, Iran

2 Associate Professor of Water Resources Engineering, Faculty of Technical and Engineering, Imam Khomeini International University, Qazvin, Iran


In this paper, an analytical solution for determining the minimum water requirement by hydraulic methods (the wetted perimeter approach) is presented. The numerical methods (semi analytical – semi graphical methods) used for solving the non-linear and complex equations of the Hydraulic Method are strongly affected by elements such as the solution method, the increments of independent variable, the geometric properties of the section used to derive the required parameters, and the huge amount of calculations to achieve a reliable result. Indirect approach and reverse solution of the achieved equation to determine the environmental discharge, is another problem when using the Hydraulic Method. The common method of employing an index section or making an index section via averaging different sections, which could impose uncertainty with unknown sources to the solution, is not used in the presented approach. The case study on the Kazemroud River, as a perennial river in the west of Mazanderan Province, showed the complete agreement between the two analytical approach and numerical method. The Hydraulic Method gives the minimum environmental water requirement approximately as much as the annual average discharge of the river, while the Tenant (Montana) Method introduces just 10% of that discharge as the minimum discharge that could lead the river towards a critical situation. If the simplicity of application and insufficient amount of time is the reasons for accepting the Hydrologic Methods like the Tenant Method, the results of this research gives those advantages to the Hydraulic Method that makes it an incomparable approach for the minimum environmental water allocation in rivers.


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