Permeability and Flow of Water in Soils - Elements of Soil Mechanics - page 55

Fig. 2.14 Capillary effects.

Let

Height of water column = h c
Radius of tube = r
Unit weight of water = γ w

If we take atmospheric pressure as datum, i.e. the air pressure = 0, we can equate the vertical forces
acting at the top of the column:

T 2 π r cos + α u r π

2

= 0

⇒ = −

2 cos α T

u

r

Hence, as expected, we see that u is negative which indicates that the water within the column is in a
state of suction. The maximum value of this negative pressure is γ w h c and occurs at the top of the column.
The pressure distribution along the length of the tube is shown in Fig. 2.14c . It is seen that the water
pressure gradually increases with loss of elevation to a value of 0 at the base of the column.
An expression for the height h c can be obtained by substituting u = − γ w h c in the above expression to
yield:

= 2 cos α
γ

T

h

c

r

w

From the two expressions we see that the magnitudes of both − u and h c increase as r decreases.