Geotechnical Engineering

DHARM

188 GEOTECHNICAL ENGINEERING

ht

r 0 l

r

b

Impervious

C of well of radius ro

Fig. 6.23 Radial flow net for seepage into a well (After Taylor, 1948)
If ∆Q and ∆h are to have the same values for every figure of the flow net, rb/l must be
the same for all the figures. Thus the requirement for a radial flow net is that the b/l ratio for
each figure must be inversely proportional to the radius, whereas in the other type of the
ordinary flow net this ratio must be a constant.

Also Q = nf. ∆Q and ht = nd. ∆h

Substituting in Eq. 6.26, we have

Q = 2πkht.

n

n

r

l

f

d

. b ...(Eq. 6.27)

Here, Q is the total time-rate of seepage for the well.
Two simple cases of radial flow lend themselves to easy mathematical manipulation.
The first one–the simplest case of radial flow–is that into a well at the centre of a round
island, penetrating through a pervious, homogeneous, horizontal stratum of constant thick-
ness. It is illustrated in Fig. 6.24.

When the water level is above the level of the previous stratum, the flow everywhere is
radial and horizontal; the gradient at all points is dh/dr for such a flow. The flow across any
vertical cylindrical surface at radius r is given by:

Q = k. dh

dr

. 2πr. Z

whence h =

Q

kZ

r

2 π er 0

log ...(Eq. 6.28)

Here h is the head loss between radius r and radius of the well rim.
Here Q is the seepage through the entire thickness Z of the pervious stratum. Eq. 6.1 for
q/L may be used with the flow net drawn. The value of Q obtained from the flow net would
agree reasonably well with that obtained from the theoretical Eq. 6.28, depending upon the
accuracy with which the flow net is sketched.