Geotechnical Engineering

DHARM

138 GEOTECHNICAL ENGINEERING

where γw is the unit weight of water and hc is the capillary rise.

∴ πdc. Ts = π γ

4

dh^2

ccw.

or hc =

4 T

d

s

γwc.

...(Eq. 5.36)

This equation helps one in computing the capillary rise of water in a glass capillary
tube.

The value of Ts for water varies with temperature. At ordinary or room temperature, Ts

is nearly 7.3 dynes/mm or 73 × 10–6 N/mm and γw may be taken as 9.81 × 10–6 N/mm^3.

∴ hc =

47310

981 10

(^630)
6
××
×
≈
−

. − d d
c c

...(Eq. 5.37)

where dc is the diameter of the glass capillary in mm, and hc is the capillary rise of water in the
glass tube in mm.
There are situations, however, in which the temperature effects should be considered.
Generally, as temperature increases, surface tension decreases, indicating a decrease in capil-
lary rise under warm conditions or an increase in capillary rise under cold conditions. The
effect of this on soil will be discussed in a later sub-section.

As the column of water stands in the capillary tube, supported by the surface tension at
the meniscus, the weight of the column is transmitted to the walls of the capillary tube creat-
ing a compressive force on the walls. The effect of such an action on soil is also discussed in a
later sub-section.

The height of the capillary rise is not dependent on the orientation of the capillary tube,
or on variations in the shape and size of the tube at levels below the meniscus as shown in
Fig. 5.13.

dc dc dc dc dc dc

hhcc

Fig. 5.13 Capillary heights of capillary tubes of various shapes

(These are equal if the diameters of their menisci are the same)

However, for water migrating up a capillary tube, a large opening can prevent further

movement up an otherwise smaller diameter tube. The determining factor is the relation be-

tween the size of the opening and the particular height of its occurrence above the source of

water.

In case the capillary rise computed on the basis of a larger opening is more than the

height of this section of the tube, the water would rise further, and the final level will depend

upon the capillary rise, computed and based upon the smaller opening above. In other words,

the capillary rise would be dependent upon the diameter of the meniscus in such cases. How-

ever, in case the capillary rise computed on the basis of a larger opening is less than the height

of this section, the water would rise no further, even if the section above is of a smaller size.