Share This Article:

Open Channel Flow over a Permeable River Bed

DOI: 10.4236/oalib.1101475    809 Downloads   1,307 Views  

ABSTRACT

This paper presents results of a modeled open channel flow through a porous media (River). In the model, we considered water as an incompressible fluid; the flow as steady and uniform; the system is assumed to be isothermal and the flow pattern is laminar. We have solved the resulting Brinkman equation using analytical method. By some mathematical operation, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically using the standard solution technique for a second order ODE. The analysis of the result was done and plotted on graph using MATLAB to show the effect of permeability on flow parameters such as velocity, pressure gradient and height of the channel. It is found that velocity of the open channel decreases with increase in permeability. Also, increase in the height of the open channel results in increase in velocity of flow in the open channel. We also found that an increase in the permeability of an open channel resulted in decrease in pressure.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Mbah, G. and Udogu, C. (2015) Open Channel Flow over a Permeable River Bed. Open Access Library Journal, 2, 1-7. doi: 10.4236/oalib.1101475.

References

[1] How a River Flows. (From Wikipedia, the Free Encyclopaedia. Accessed 24th September, 2002)
http://chamisa.freeshell.org//flow.htm
[2] Batchelor, G.K. (1967) An Introduction to Fluid Dynamics. Cambridge University Press, New York, 223-224.
[3] Tritton, D.J. (1977) Physical Fluid Dynamics. Van Nostrand Reinhold (UK), 3-12.
http://dx.doi.org/10.1007/978-94-009-9992-3
[4] Calvert, J.B. (2003) Open Channel Flow.
http://mysite.du..edu/-etuttle/tech/opench.htm
[5] River. (From Wikipedia, the Free Encyclopaedia. Accessed 1st March 2012)
http://enWikipedia.org/wiki/river
[6] Stoesser, T., Frohlich, J. and Rodi, W. (2007) Turbulent Open Channel Flow over a Permeable Bed. Proceedings of 32nd IAHR Congress, Venice, 1-6 July 2007, 10p.
[7] Radiom, M., Khakbaz, M. and Kermani, M.J. (2007) Numerical and Analytical Calculation of Air flow through an Open Channel Linked to a Porous Media. Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, 15875-4413.
[8] Nabovati, A. and Sousa, A.C.M. (2007) Fluid Flow Simulation in Random Porous Media at Pore Level Using the Lattice Boltzmann Method. Journal of Engineering Science and Technology, 2, 226-237.
[9] Parvazinia, M., Nassehi, V. and Wakeman, R.J. (2006) Multiscale Finite Element Modelling of Laminar Steady Flow through Highly Permeable Media. Chemical Engineering Science, 61, 583-596.
http://dx.doi.org/10.1016/j.ces.2005.07.018
[10] Zagni, A.F.E. and Smith, K.V.H. (1976) Channel Flow over Permeable Beds of Graded Spheres. Journal of the Hydraulics Division, 102, 207-222.
[11] Aaltosalmi, U. (2005) Fluid Flow in Porous Media with the Lattice-Boltzmann Method. Academic Dissertation for PhD, University of Jyväskylä, Jyväskylä, 5-8.
[12] Heinemann, Z.E. (2005) Fluid Flow in Porous Media. Petroleum Engineering Science, 1, 6-12.
[13] Zippe H.J Graf. W.H. (1983) Turbulent Boundary Layer Flow over Permeable and Non-Permeable Rough Surfaces. Journal of Hydraulic Research, 21, 51-65.
http://dx.doi.org/10.1080/00221688309499450
[14] Obikwelu, D.O.N. (2003) Differential Equations and Application. AMDI-Nel Publishers Ogidi, Nigeria, 60-61.
[15] Wang, J., Gao, Z., Gan, G. and Wu, D. (2001) Analytical Solution of Flow Coefficients for a Uniformly Distributed Porous Channel. Chemical Engineering Journal, 84, 1-66.
http://dx.doi.org/10.1016/S1385-8947(00)00263-1
[16] Spiege, M.R. (1983) Advanced Mathematics for Engineers and Scientists. McGraw-Hill Book Company, Singapore, 74-83.
[17] Rajput, R.K. (1998) Fluid Mechanics and Hydraulic Machines. Schand and Company, Ram Nagar, New Dehi, 3-29, 867-871.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.