2.162. A vessel filled with air under pressure P
o
contains a soap
bubble of diameter
d.
The air pressure having been reduced isother-
mally n-fold, the bubble diameter increased mfold. Find the surface
tension of the soap water solution.
2.163. Find the pressure in an air bubble of diameter
d =
4.0 pm,
located in water at a depth
h =
5.0 m. The atmospheric pressure
has the standard value P
o
.
2.164. The diameter of a gas bubble formed at the bottom of a pond
is
d =
4.0 1.tm. When the bubble rises to the surface its diameter
increases n = 1.1 times. Find how deep is the pond at that spot.
The atmospheric pressure is standard, the gas expansion is assumed
to be isothermal.
2.165. Find the difference in height of mercury columns in two
communicating vertical capillaries whose diameters are
= 0.50 mm and
d
2
=
1.00 mm, if the contact angle 0 = 138°.
2.166. A vertical capillary with inside diameter 0.50 mm is
submerged into water so that the length of its part protruding over
the water surface is equal to
h =
25 mm. Find the curvature radius
of the meniscus.
2.167. A glass capillary of length
1 =
110 mm and inside dia-
meter
d =
20 pAn is submerged vertically into water. The upper end
of the capillary is sealed. The outside pressure is standard. To what
length
x
has the capillary to be submorged to make the water levels
inside and outside the capillary coincide?
2.168. When a vertical capillary of length
1
with the sealed upper
end was brought in contact with the surface of a liquid, the level
of this liquid rose to the height
h.
The liquid density is p, the inside
diameter of the capillary is
d,
the contact angle is 0, the atmospheric
pressure is P
o
. Find the surface tension of the liquid.
2.169. A glass rod of diameter d
1
= 1.5 mm is inserted sym-
metrically into a glass capillary with inside diameter
d
2
=
2.0 mm.
Then the whole arrangement is vertically oriented and brought in
contact with the surface of water. To what height will the water rise
in the capillary?
2.170. Two vertical plates submerged partially in a wetting liquid
form a wedge with a very small angle 6cp. The edge of this wedge is
vertical. The density of the liquid is p, its surface tension is a, the
contact angle is 0. Find the height
h,
to which the liquid rises, as a
function of the distance
x
from the edge.
2.171. A vertical water jet flows out of a round hole. One of the
horizontal sections of the jet has the diameter
d =
2 0 mm while
the other section located / = 20 mm lower has the diameter which
is n = 1.5 times less. Find the volume of the water flowing from
the hole each second.
2.172. A water drop falls in air with a uniform velocity. Find
the difference between the curvature radii of the drop's surface at
the upper and lower points of the drop separated by the distance
h =
2.3 mm.
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