Transport in Porous Media

, Volume 104, Issue 3, pp 565–579 | Cite as

An Analytical Solution for 1-D Non-Darcy Flow Through Slanting Coarse Deposits

  • Mohammad Sedghi-Asl
  • Javad Farhoudi
  • Hassan Rahimi
  • Sven Hartmann


In this paper, an analytical solution to solve 1-D partial differential equation is presented for fully developed turbulent flow through highly permeable sloping deposited porous medium. The present solution will be applicable for a wide range of slopes varying from zero to relatively steep slopes. To confirm the solution, the analytical results have been validated using two sets of experimental data including rounded and crushed material. To see the compatibility of solution, a Darcy-based form of the solution is derived and compared with proposed solution and experimental data. The results showed a satisfactory agreement with experimental records from water surface profiles through rock cavities for both rounded and crushed rock materials. Finally, it may be concluded that the proposed solution could be used to analyze water surface profiles and normal depth in such slanting permeable porous media. This solution provides a reliable realization of the flow profiles in porous materials which are widely used in open-channel flow concepts.


Fully developed turbulent flow Coarse porous media Non-Darcy flow Analytical solution Slanting valley fills 

List of Symbols


Cross-sectional area


Constant coefficient of Izbach equation


Power constant of Izbach equation

\(C, C_2\)

Constants of integral


Piezometric head


Normal depth


Bed slope


Length of rock drain


Discharge through porous medium


Discharge per unit width


Flow velocity


Longitudinal coordinate


Depth of low normal to bed


Arbitrary variable

\(\alpha \)

Angle of bed related to horizontal

\(\eta \)

Dimensionless depth for Darcy flow

\(\varphi \)


\(\xi \)

Dimensionless depth

\(\chi (\xi )\)

Dimensionless depth function for positive slope

\(\psi (\xi )\)

Dimensionless depth function for negative slope

\(\phi (\eta )\)

Dimensionless depth function for Darcian flow


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Mohammad Sedghi-Asl
    • 1
  • Javad Farhoudi
    • 2
  • Hassan Rahimi
    • 2
  • Sven Hartmann
    • 3
  1. 1.Department of Soil Science, Faculty of AgricultureYasouj UniversityYasouj Iran
  2. 2.Department of Irrigation and Reclamation Engineering, College University of Agricultural and Natural ResourcesUniversity of TehranKarajIran
  3. 3.Department of Civil EngineeringStuttgart UniversityStuttgartGermany

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