alinik
۱۳ مهر ۱۳۸۸, ۱۷:۰۷
At the interface between a liquid and a gas, or between two immiscible liquids, forces develop
in the liquid surface which cause the surface to behave as if it were a “skin” or “membrane”
stretched over the fluid mass. Although such a skin is not actually present, this conceptual
analogy allows us to explain several commonly observed phenomena. For example, a steel
needle will float on water if placed gently on the surface because the tension developed in
the hypothetical skin supports the needle. Small droplets of mercury will form into spheres
when placed on a smooth surface because the cohesive forces in the surface tend to hold all
the molecules together in a compact shape. Similarly, discrete water droplets will form when
placed on a newly waxed surface. (See the photograph at the beginning of Chapter 1.)
These various types of surface phenomena are due to the unbalanced cohesive forces
acting on the liquid molecules at the fluid surface. Molecules in the interior of the fluid mass
are surrounded by molecules that are attracted to each other equally. However, molecules
along the surface are subjected to a net force toward the interior. The apparent physical
consequence of this unbalanced force along the surface is to create the hypothetical skin or
membrane. A tensile force may be considered to be acting in the plane of the surface along
any line in the surface. The intensity of the molecular attraction per unit length along any
line in the surface is called the surface tension and is designated by the Greek symbol 1sigma2. For a given liquid the surface tension depends on temperature as well as the other
fluid it is in contact with at the interface. The dimensions of surface tension are with
BG units of and SI units of Values of surface tension for some common liquids 1in contact with air2 are given in Tables 1.5 and 1.6 and in Appendix B 1Tables B.1 and B.22
for water at various temperatures. The value of the surface tension decreases as the temperature
increases.
The pressure inside a drop of fluid can be calculated using the free-body diagram in
Fig. 1.7. If the spherical drop is cut in half 1as shown2 the force developed around the edge
lbft Nm.
FL1
s
is about At this temperature the vapor pressure of water is 10.1 psi 1abs2. Thus, boiling
can be induced at a given pressure acting on the fluid by raising the temperature, or at a
given fluid temperature by lowering the pressure.
An important reason for our interest in vapor pressure and boiling lies in the common
observation that in flowing fluids it is possible to develop very low pressure due to the fluid
motion, and if the pressure is lowered to the vapor pressure, boiling will occur. For example,
this phenomenon may occur in flow through the irregular, narrowed passages of a valve or
pump. When vapor bubbles are formed in a flowing fluid they are swept along into regions
of higher pressure where they suddenly collapse with sufficient intensity to actually cause
structural damage. The formation and subsequent collapse of vapor bubbles in a flowing fluid,
called cavitation, is an important fluid flow phenomenon to be given further attention in
Chapters 3 and 7.
193 °F.
In flowing liquids it
is possible for the
pressure in localized
regions to
reach vapor pressure
thereby causing
cavitation.
σ R
Δpπ R2 σ F I G U R E 1 . 7 Forces acting on one-half of a liquid drop.
V1.5 Floating razor
blade
due to surface tension is This force must be balanced by the pressure difference,
between the internal pressure, and the external pressure, acting over the circular area,
Thus,
or
(1.21)
It is apparent from this result that the pressure inside the drop is greater than the pressure
surrounding the drop. 1Would the pressure on the inside of a bubble of water be the same as
that on the inside of a drop of water of the same diameter and at the same temperature?2
Among common phenomena associated with surface tension is the rise 1or fall2 of a
liquid in a capillary tube. If a small open tube is inserted into water, the water level in the
tube will rise above the water level outside the tube as is illustrated in Fig. 1.8a.
in the liquid surface which cause the surface to behave as if it were a “skin” or “membrane”
stretched over the fluid mass. Although such a skin is not actually present, this conceptual
analogy allows us to explain several commonly observed phenomena. For example, a steel
needle will float on water if placed gently on the surface because the tension developed in
the hypothetical skin supports the needle. Small droplets of mercury will form into spheres
when placed on a smooth surface because the cohesive forces in the surface tend to hold all
the molecules together in a compact shape. Similarly, discrete water droplets will form when
placed on a newly waxed surface. (See the photograph at the beginning of Chapter 1.)
These various types of surface phenomena are due to the unbalanced cohesive forces
acting on the liquid molecules at the fluid surface. Molecules in the interior of the fluid mass
are surrounded by molecules that are attracted to each other equally. However, molecules
along the surface are subjected to a net force toward the interior. The apparent physical
consequence of this unbalanced force along the surface is to create the hypothetical skin or
membrane. A tensile force may be considered to be acting in the plane of the surface along
any line in the surface. The intensity of the molecular attraction per unit length along any
line in the surface is called the surface tension and is designated by the Greek symbol 1sigma2. For a given liquid the surface tension depends on temperature as well as the other
fluid it is in contact with at the interface. The dimensions of surface tension are with
BG units of and SI units of Values of surface tension for some common liquids 1in contact with air2 are given in Tables 1.5 and 1.6 and in Appendix B 1Tables B.1 and B.22
for water at various temperatures. The value of the surface tension decreases as the temperature
increases.
The pressure inside a drop of fluid can be calculated using the free-body diagram in
Fig. 1.7. If the spherical drop is cut in half 1as shown2 the force developed around the edge
lbft Nm.
FL1
s
is about At this temperature the vapor pressure of water is 10.1 psi 1abs2. Thus, boiling
can be induced at a given pressure acting on the fluid by raising the temperature, or at a
given fluid temperature by lowering the pressure.
An important reason for our interest in vapor pressure and boiling lies in the common
observation that in flowing fluids it is possible to develop very low pressure due to the fluid
motion, and if the pressure is lowered to the vapor pressure, boiling will occur. For example,
this phenomenon may occur in flow through the irregular, narrowed passages of a valve or
pump. When vapor bubbles are formed in a flowing fluid they are swept along into regions
of higher pressure where they suddenly collapse with sufficient intensity to actually cause
structural damage. The formation and subsequent collapse of vapor bubbles in a flowing fluid,
called cavitation, is an important fluid flow phenomenon to be given further attention in
Chapters 3 and 7.
193 °F.
In flowing liquids it
is possible for the
pressure in localized
regions to
reach vapor pressure
thereby causing
cavitation.
σ R
Δpπ R2 σ F I G U R E 1 . 7 Forces acting on one-half of a liquid drop.
V1.5 Floating razor
blade
due to surface tension is This force must be balanced by the pressure difference,
between the internal pressure, and the external pressure, acting over the circular area,
Thus,
or
(1.21)
It is apparent from this result that the pressure inside the drop is greater than the pressure
surrounding the drop. 1Would the pressure on the inside of a bubble of water be the same as
that on the inside of a drop of water of the same diameter and at the same temperature?2
Among common phenomena associated with surface tension is the rise 1or fall2 of a
liquid in a capillary tube. If a small open tube is inserted into water, the water level in the
tube will rise above the water level outside the tube as is illustrated in Fig. 1.8a.