Environmental Engineering FOURTH EDITION

110 ENVIRONMENTAL, ENGINEERING

where v’ = the actual velocity in the soil, and a = the area available for flow. Solving
for v’,

If a sample of soil is of some length L, then

v’ = (Av)/a = (AvL)/(uL) = v/porosity. (6.4)

Water flowing through the soil at a velocity v’ loses energy, just as water flowing
through a pipeline or an open channel. The head loss is defhed as

• Ah
  AL ’

where h is the pressure head. The flow through a porous medium such as soil is related
to the head loss using the Darcy equation,

Ah

AL

Q = KA-,

where

K = coefficient of permeability (m3/day-m’), and

A = cross-sectional area (m’).

The coefiient of permeability varies dramatically for different soils ranging from
about 0.04 m3/day-m’ for clay to over 200 m3/day-m2 for gravel.
Trpical values of porosity specific yield and the coefficient of permeability are
shown in Table 6-1. The coefficient of permeability is measured commonly in the
laboratory using a permeameter, which consists of a soil sample through which a fluid
like water is forced. The flow rate is measured for a given driving force, and the
permeability calculated.

Table 6-1. Estimate of Average Permeability and Porosity for Selected Materialsa

Permeability KP

Material % Porosity % Specific yield (gavday-ft’) (m3/day-m’)

Clay 45

Sand 35

Gravel 25

Sandstone 15

Granite 1

3 1 0.04

25 800 32

22 5000 200

8 700 28

0.5 0.1 0.004

aSoum: R. K. Lmsley and J. B. Franzini, Elemenrs of Hydrology, McGraw-Hill, New York. Copyright

Q 1958. Used with permission of the McGraw-Hill Book Capany.