DHARMSOIL MOISTURE–PERMEABILITY AND CAPILLARITY 117
Permeability is one of the most important of soil properties. The path of flow from one point to
another is considered to be a straight one, on a macroscopic scale and the velocity of flow is
considered uniform at an effective value ; this path, in a microscopic scale, is invariably a
tortuous and erratic one because of the random arrangement of soil particles, and the velocity
of flow may vary considerably from point to point depending upon the size of the pore and
other factors.
According to fundamental hydraulics flowing water may assume either of two charac-
teristic states of motion—the ‘laminar flow’ and the ‘turbulent flow’. In laminar flow each
particle travels along a definite path which never crosses the path of other particles; while, in
turbulent flow the paths are irregular and twisting, crossing and recrossing at random. Osborne
Reynolds, from his classic experiments on flow through pipes, established a lower limit of
velocity at which the flow changes from laminar to a turbulent one; it is called the ‘lower
critical velocity’. In laminar flow, the resistance to flow is primarily due to the viscosity of
water and the boundary conditions are not of much significance; in turbulent flow, however,
the boundary conditions have a major influence and the effect of viscosity is insignificant.
The lower critical velocity vc is governed by a dimensionless number, known as Reynold’s
number :
R = vD.
υ...(Eq. 5.8)or R =
vD
g..w
.γ
μ...(Eq. 5.9)whereR = Reynold’s number
v = Velocity of flow
D = Diameter of pipe/pore
υ = Kinematic viscosity of water
γw = Unit weight of water
μ = Viscosity of water, and
g = Acceleration due to gravity.
Reynolds found that vc is governed by :
R = vDc.
υ= 2000 ...(Eq. 5.10)It is difficult to study the conditions of flow in an individual soil pore; only average
conditions existing at any cross-section in a soil mass can be studied. Since pores of most soils
are small, flow through them is invariably ‘laminar’ ; however, in the case of soils coarser than
coarse sand, the flow may be turbulent. (Assuming uniform particle size, laminar flow may be
considered to occur up to an equivalent particle diameter of 0.5 mm).
5.4.1 Darcy’s Law
H. Darcy of France performed a classical experiment in 1856, using a set-up similar to that
shown in Fig. 5.2, in order to study the properties of the flow of water through a sand filter bed.
By measuring the value of the rate of flow or discharge, q for various values of the
length of the sample, L, and pressure of water at top and bottom the sample, h 1 and h 2 , Darcy
found that q was proportional to (h 1 – h 2 )/L or the hydraulic gradient, i :
q = k[(h 1 – h 2 )/L] × A = k.i.A ...(Eq. 5.11)