DHARM

SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 127

∴ k

zz

q

r

er

.

()

(^2) (/ ) log
2
1
2
2
(^21)
2
−

R
S
T
U
V
W
π
∴ k =
q
zz
r
r
q
zz
r
π()e r
log
.( )
log
2
2
1
2
2
1 22 12
10 2
− (^1361)

−
...(Eq. 5.18)
k can be evaluated if z 1 , z 2 , r 1 and r 2 are obtained from observations in the field. It can be
noted that z 1 = (h – d 1 ) and z 2 = (h – d 2 ).
If the extreme limits z 0 and h at r 0 and R are applied,
Equation 5.18 reduces to
k =
q
hz
R
136 .(^202 )^10 r 0
.log
−
...(Eq. 5.19)
This may also be put in the form
k =
q
dd z
R
136 .( 0020 )^10 r 0
.log

• ...(Eq. 5.20)
  For one to be in a position to use (Eq. 5.19) or (Eq. 5.20), one must have an idea of the
  radius of influence R. The selection of a value for R is approximate and arbitrary in practice.
  Sichart gives the following approximate relationship between R, d 0 and k;
  R = 3000 d 0 k ...(Eq. 5.21)
  where,
  d 0 is in metres,
  k is in metres/sec,
  and R is in metres.
  One must apply an approximate value for the coefficient of permeability here, which
  itself is the quantity sought to be determined.
  Two observation wells may not be adequate for obtaining reliable results. It is recom-
  mended that a few symmetrical pairs of observation wells be used and the average values of
  the drawdown which, strictly speaking, should be equal for observation wells, located sym-
  metrically with respect to the central well, be employed in the computations. Several values
  may be obtained for the coefficient of permeability by varying the combination of the wells
  chosen for the purpose. Hence, the average of all these is treated to be a more precise value
  than when just two wells are observed.
  Alternatively, when a series of wells is used, a semi-logarithmic graph may be drawn
  between r to the logarithmic scale and z^2 to the natural scale, which will be a straight line.
  From this graph, the difference of ordinates y, corresponding to the limiting abscissae of one
  cycle is substituted in the following equation to obtain the best fit value of k for all the obser-
  vations :
  k = q/y ...(Eq. 5.22)
  This is a direct consequence of Eq. 5.18, observing that log 10 (r 2 /r 1 ) = 1 and denoting
  (z 22 – z 12 ) by y.
  Confined Aquifer
  A well penetrating a confined aquifer to its full depth is shown in Fig. 5.7.