Journal of Hydraulics

Journal of Hydraulics

Experimental Study of the Equivalent Coefficients of the Forschheimer Equation in Vertical non-homogeneous Media of non-Darcy Flow in Gravel Materials

Document Type : Research Article

Authors
Hamid Azizkhani 1
Jalal Bazargan 2
Atefe Sadri 3
1 Master of Science in Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, University of Zanjan, Zanjan, Iran
2 2. Professor, Department of Civil Engineering, University of Zanjan, Zanjan, Iran
3 M.Sc. student in Architectural Engineering, Faculty of Architecture and Art, Islamic Azad University Abhar, Zanjan, Iran
10.30482/jhyd.2025.524010.1735
Abstract
The behavior of non-Darcy flow in gravel materials depends on the physical characteristics of the aggregate, the fluid properties and the flow characteristics. Non-Darcy flow in inhomogeneous environments also depends on the physical characteristics of each of the components of the environment, and the equivalent Forschheimer coefficients of the entire inhomogeneous environment are a function of the aforementioned coefficients of each of the components of the environment. The present study was conducted in the Hydraulic Laboratory of the University of Zanjan in a channel with a length of 5 meters, a width of 30 centimeters and a height of 30 centimeters for three aggregates: fine, medium and coarse. For this purpose, 90 experiments were conducted at different discharge rates and vertical homogeneous and inhomogeneous conditions. The equivalent Forschheimer coefficients of the vertical inhomogeneous environment were determined by three different methods based on the relationship between velocity and hydraulic gradient. In the first method, by equating the sum of the losses of each component of the medium with the total loss of the inhomogeneous medium, in the second method, by equating the values ​​of the friction force of each component with the total friction force, and the third method, which was estimated as an empirical relationship and has been developed into different relationships. Since Darcy's relationship is valid only in laminar flow, according to the experiments conducted in the present study and the invalidity of Darcy's relationship, the flow is always turbulent. The studies conducted show that the average error of the coefficient a in the first, second, and third methods was 87.32, 87.91, and 48.41 percent, respectively, and the average error of the coefficient b in the first, second, and third methods was 34.78, 32.31, and 33.24 percent, respectively. The average relative error of the hydraulic gradient estimated by the first, second, and third methods will be 8, 8.77, and 5.7 percent, respectively.
Keywords
steady flow
non-Darcy flow
Binomial Equations
hydraulic gradient
inhomogeneous porous media

Subjects

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  • Receive Date 19 May 2025
  • Revise Date 22 September 2025
  • Accept Date 09 October 2025