Geotechnical Engineering

DHARM

120 GEOTECHNICAL ENGINEERING

Equation 5.13 indicates that the seepage velocity is also proportional to the hydraulic
gradient. It may be rewritten as follows :

vs = ki/n = (k/n)i = kp. i ...(Eq. 5.14)

where kp, the constant of proportionality, is called the ‘Coefficient of Percolation’, and is given
by :

kp = k/n ...(Eq. 5.15)

5.4.4 Energy Heads

In the study of fluid flow it is convenient to express energy in any form in terms of ‘head’,
which is energy per unit mass :

1. Pressure head, hp = the pressure divided by the unit weight of fluid = p/ρ.

Pressure engery = Head =

energy

mass

pM M

L

ML

M

ML

ML

M

L

...
,
ρ

== ==

F

HG

I

(^2) KJ
3

2. Elevation or datum head, hc = the height from the datum (Elevation or potential
   energy = ML)


3. Velocity Head, hv = square of velocity divided by twice acceleration due to gravity

=

v

g

2

2

Kinetic energy =

Mv^2

g

ML T

TL

ML

2

22

== 2

F

HG

I

KJ

−

−.

Here,
M = Mass, v = Velocity, g = Acceleration due to Gravity
L = Length, T = Time, p = Pressure.
In dealing with problems involving fluid flow in soil, the velocity head is taken to be
negligible, and as such, the total head will be the sum of pressure head and elevation head. In
dealing with problems involving pipe and channel flow, total head is defined as the sum of
pressure head, elevation head and velocity head ; the sum of pressured head and elevation
head is usually called the ‘Piezometric’ head. In the case of flow through soils, the total head
and the piezometric head are equal.

Since both pressure head and elevation head can contribute to the movement of fluid
through soils, it is the total head that determines flow, and the hydraulic gradient to be used in
Darcy’s law is computed from the difference in total head. Unless there is a gradient of total
head, no flow can occur.

Pressure head or water pressure at a point in a soil mass can be determined by a
piezometer; the height to which water rises in the piezometer above the point is the pressure
head at that point. The manometer or standpipe and the Bourdon pressure gauge are two
simple piezometers, which require a flow of water from the soil into the measuring system to
actuate each device. This flow may require a significant time-lag if the soil is a relatively
impermeable one such as silt or clay. To measure pore pressures under ‘no-flow’ conditions