1) Capillary rise occurs when a liquid rises in a narrow tube due to surface tension. The height it rises to depends on factors like tube radius and liquid properties. 2) In an inclined tube, the height of liquid rise remains the same but the length increases to maintain the relationship between height, radius, and surface tension. 3) Examples of capillary rise include water transport in plant stems, liquid rising in wicks, towels wicking up water, coffee dissolving, and ink rising in pen nibs. Proper soil management can also use or prevent capillary rise of water.

1. Special Cases of
Capillary Rise
The following are some special cases of
capillary rise

2. Rising of a liquid in a
capillary tube if
insufficient length
• Suppose a liquid of density p and surface tension
T rises in a capillary tube to a height h. Then,
hpg= 2T/R
• where R is the radius of curvature of the liquid
meniscus in the tube. From this we may write
2T hR/pg= = constant (for a given liquid).
• When the length of the tube is greater than h, the
liquid rises in the tube to a height so as to satisfy
the above relation. But if the length of the tube is
less than h, say h', then the liquid rises up to the
top of the tube and then spreads out until its
radius of curvature R increases to R', such that
h'R' = hR=2T/pg
• It is clear that liquid cannot emerge in the
form of a fountain from the upper end of a
short capillary tube.

3. Rise of Liquid in an
Inclined Capillary
Tube
• The height of the liquid column in a glass
capillary tube of radius r is
h=2T cosA /rpg
• where T is surface tension of the liquid and A is
the angle of contact f liquid glass.
• If we incline the capillary tube at an angle B with
the vertical, then for balancing the weight of the
liquid column raised in the tube by the force of
surface tension, the 'vertical' height of the liquid
in the capillary tube will still be h. For this, the
'length' of the liquid in the tube will increase to h',
where
h’=h/cosB
• Substituting the value of h from eq. (i), we have
• h'= 2 T cos A/rpg cosB.

4. Some Examples of
Capillarity
The Water given to the
fields rises in the
innumerable capillaries
formed in the stems of
plants and trees and
reaches the branches and
the leaves

5. Some Examples of
Capillarity
The kerosene oil in
lanterns and the melted
wax in a candle , rise in
capillaries formed in the
cotton wick and burns

6. Some Examples of
Capillarity
If one end of a towel is
dipped in a vessel filled with
water then the water began
to rise in the innumerable
holes (which act like
capillaries ) formed in
between the threads of the
towel and ultimately the
entire towel is wetted

7. Some Examples of
Capillarity
Coffee powder is easily
soluble in water because
water immediately wets
the fine granules of
coffee by the actin of
capillary.

8. Some Examples of
Capillarity
Writing nib is split in
the middle so that a
fine capillary is formed
in it, when it is dipped
in ink the ink rises in
the capillary

9. Some Examples of
Capillarity
The farmers plough their fields
after rains so that the capillaries
formed in the soil are broken a
the water remains in the lower
layers of the soil. This water is
taken up by plants. If ploughing is
done, the water of the lower
layers will rise through the
capillaries in the soil and
evaporate.

10. Pressure Difference
between the two sides of
a curved surface
• The Laplace pressure is the pressure
difference between the inside and the
outside of a curved surface that forms the
boundary between two fluid regions.The
pressure difference is caused by the
surface tension of the interface between
liquid and gas, or between two immiscible
liquids.
• The Laplace pressure is determined from
the Young–Laplace equation given as