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Flow Through Porous Media

•    Steady flow of a fluid such as water or ail flowing through porous soil mass is similar to Laminar flow in small diameter pipe.

•    In flow through porous media, a laminar flow though small irregular passage is consider instead of uniform size conduit.

•    The flow characterized by low velocity, high pressure drops and very small pore diameters so that conditions for laminar flow are fully satisfied.

•    The viscous force is predominant.

•    Consider a pipe filled with porous material as shown in and let the flow take place under geometric head different.

hf = h1 - h2

•    The apparent mean velocity of flow U is given by Q/A. However the flow velocity through the pore spaces will be more than U because part of cross-sectional area is blocked by material.

•    The actual area through which flow is taking place is given by ‘A’ e’ where ‘e’ is the porosity, hence the actual mean velocity through the porous medium is given by Q / Ae = U/e

•    It is also assumed that average size of pores is proportional to the grain diameter Ds.

•    The head loss by Hagen poiseuille equation is given by

P1 - P2 = K μ U L / e D2

hf = K μ  . U. L / γ. e. D2

U  = hf / L. γ e D2 / K μ

U = Ki


I = hydraulic gradient = hf / L

k = coefficient of permeability = γ e D2 / K μ

•    The equation U = Ki is known as Darcy’s Law and is useful in analysis of problem connected flow through porous material.

•    Darcy’s Law is applicable up to particles Reynolds’s number is one.

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