Skip to main content
SpringerLink
Log in

Darcyan flow with relaxation effect

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

The equation for the flow of a liquid through a porous medium is either elliptic or parabolic which implies that a disturbance in pressure or head is transmitted with infinite velocity. This is unsatisfactory from a physical viewpoint, although not necessarily from a practical one. If Darcy's law is completed with an inertial term the flow equation becomes a strongly damped wave equation. The proposed additional term can be identified from experiments with confined flow and free surface flow when the pressure or head varies harmonically with time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

c 0 :

characteristic speed

c 1 :

characteristic speed

c w :

characteristic speed

C :

auxiliary parameter

d :

diameter of a bead

E :

modulus of elasticity

F :

auxiliary function

h :

piezometric height

H :

height of groundwater table

I 0(x):

modified Bessel function

I 1(x):

modified Bessel function

k :

permeability

K :

hydraulic conductivity

L :

tube length or channel length

L 0 :

reference length

m :

auxiliary parameter

n :

porosity

p :

pressure

Q :

mass flux

r=(x, y, z):

Cartesian coordinates

\(\hat r = (\xi ,n,\zeta )\) :

dimensionless Cartesian coordinates

r(p):

tube radius

r 0 :

tube radius

R 0 :

tube radius

r p :

equivalent pore radius

t :

time

\(\bar \upsilon = (u,\upsilon ,w)\) :

velocity vector

V :

volume

α :

coefficient of compressibility

β :

coefficient of compressibility

κ :

coefficient of compressibility

γ :

expansibility

ε :

relaxation time

μ :

dynamic viscosity

ν :

Poisson's ratio

ϱ :

density

τ :

dimensionless time

ω :

angular frequency

References

  1. H.C. Brinkmann: A calculation of the viscous force excited by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1 (1947) 27–34.

    Google Scholar 

  2. C.S. Yih: Stratified Flows. A.P. (1980).

  3. P.M. Morse and H. Feshback: Methods of Theoretical Physics. McGraw-Hill (1953).

  4. P. Szymanski: Quelque solutions exactes des equations de l'hydrodynamique du fluide visqueux dans le cas d'in tube cylindrique. Journ. de math. pures et appliqueé. Series 9, 11, 67 (1932).

    Google Scholar 

  5. J. Dupit: Études Théoriques et Pratiques sur le Mouvement des Eaux dans les Canaux Découverts et à Travers les Terrains Permeables. Paris (1863).

  6. M.A. Biot: Mechanics of deformation and acoustic propagation in porous media. Journ. of Appl. Phys. 33(4) (1962) 1482–1498.

    Google Scholar 

  7. M.K. Hubbert: Journal of Geol. 48 (1940) 785–944.

    Google Scholar 

  8. J.M.R. De Wiest (ed.): Flow Through Porous Media. A.P. (1969).

  9. R.M. Fand et al.: Resistance to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres. Journ. of Fluids Engin. 109 (1987) 268–274.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Swedish State Power Board, S-162 87, Vällingby, Sweden

    Göran Rehbinder

Authors
  1. Göran Rehbinder
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rehbinder, G. Darcyan flow with relaxation effect. Appl. sci. Res. 46, 45–72 (1989). https://doi.org/10.1007/BF00420002

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00420002

Keywords

Search

Navigation