Geotechnical Engineering

DHARM

SEEPAGE AND FLOW NETS 189

It is interesting to note that this is a one-dimensional case, since the only space variable
is the radius. The seepage pattern is the same for any horizontal plane through the previous
stratum ; therefore, a flow net of the type shown in Fig. 6.24 (b) may be drawn.

Further, the seepage pattern is the same on all radial vertical planes through the centre
line of the well; hence a flow net of the radial type may also be drawn as shown in Fig. 6.24(c).

l

b

r

z

Pervious

Impervious

Z

(a) Well in a round island (b) Flow net for a horizontal plane

through the previous stratum

(c) Radial flow net
Fig. 6.24 Radial horizontal flow
This simple case of horizontal, radial flow is the only one for which it is possible to draw
both types of flow nets.
The special feature of radial flow is that a relatively large proportion of the head loss
occurs in the near vicinity of the well. In view of this, the radial extent of the cross section, the
depth below the well and the depth of the soil have little effect on the results.
The second one is the case of spherically radial flow, when the flow everywhere is di-
rected towards a single point. In this case the expression for flow is best written in spherical
coordinates; the area across which flow occurs at any given radius is the spherical surface of
area 4π(r′)^2 , where r′ is the spherical radius. Referring to Fig. 6.25, the discharge may be
written

Q = k.

dh

dr′

.4π(r′)^2
If the head is h at radius r′ and is zero at radius r 0 ′ the solution of the differential
equation is

h = Q

kr

r

4 r

1

0

0

π ′

−

′

′

F

HG

I

KJ

...(Eq. 6.29)