Section 7.7
Surface Tension 89 .62 g/cm3. The rest of its body has adensity of 1.067 g/cm3. We can find the percentage of the body volume occupied by the porous bone that makes the average density of the fish bethe same as the density of sea water (1.026 g/cm3) by using the followingequation (see Exercise 7-4): 1.026 0.62X + (100 − X) 1.067
(7.15)
100
In this case X 9.2%.
The cuttlefish lives in the sea at a depth of about 150 m. At this depth, the pressure is 15 atm (see Exercise 7-5). The spaces in the porous bone are filledwith gas at a pressure of about 1 atm. Therefore, the porous bone must be ableto withstand a pressure of 14 atm. Experiments have shown that the bone canin fact survive pressures up to 24 atm.
In fish that possess swim bladders, the decrease in density is provided by the gas in the bladder. Because the density of the gas is negligible comparedto the density of tissue, the volume of the swim bladder required to reducethe density of the fish is smaller than that of the porous bone. For example, to achieve the density reduction calculated in the preceding example, thevolume of the bladder is only about 4% of the total volume of the fish (seeExercise 7-6).
Fish possessing porous bones or swim bladders can alter their density.
The cuttlefish alters its density by injecting or withdrawing fluid from itsporous bone. Fish with swim bladders alter their density by changing theamount of gas in the bladder. Another application of buoyancy is examinedin Exercise 7-7.
7.7 Surface Tension
A molecule in the interior of the liquid is surrounded by an equal numberof neighboring molecules in all directions. Therefore, the net resultant intermolecular force on an interior molecule is zero. The situation is different,however, near the surface of the liquid. Because there are no moleculesabove the surface, a molecule here is pulled predominantly in one direction,toward the interior of the surface. This causes the surface of a liquid to contract and behave somewhat like a stretched membrane. This contracting tendency results in a surface tension that resists an increase in the free surface ofthe liquid. It can be shown (see reference [7-7]) that surface tension is aforce acting tangential to the surface, normal to a line of unit length on thesurface (Fig. 7.4). The surface tension T of water at 25◦C is 72.8 dyn/cm. The
90
Chapter 7 Fluids FIGURE 7.4 Surface tension.
total force FT produced by surface tension tangential to a liquid surface ofboundary length L is FT TL
(7.16)
When a liquid is contained in a vessel, the surface molecules near the wall are attracted to the wall. This attractive force is called adhesion. At the sametime, however, these molecules are also subject to the attractive cohesive forceexerted by the liquid, which pulls the molecules in the opposite direction.
If the adhesive force is greater than the cohesive force, the liquid wets thecontainer wall, and the liquid surface near the wall is curved upward. If theopposite is the case, the liquid surface is curved downward (see Fig. 7.5). Theangle θ in Fig. 7.5 is the angle between the wall and the tangent to the liquidsurface at the point of contact with the wall. For a given liquid and surfacematerial, θ is a well-defined constant. For example, the contact angle betweenglass and water is 25◦.
If the adhesion is greater than the cohesion, a liquid in a narrow tube will rise to a specific height h (see Fig. 7.6a), which can be calculated from the following considerations. The weight W of the column of the supported liquid is
W π R2hρg
(7.17)
where R is the radius of the column and ρ is the density of the liquid. The maximum force Fm due to the surface tension along the periphery of the liquid is
Fm 2π RT
(7.18)
The upward component of this force supports the weight of the column ofliquid (see Fig. 7.6a); that is, 2π RT cos θ π R2hρg
(7.19)
(7.15)
100
In this case X 9.2%.
The cuttlefish lives in the sea at a depth of about 150 m. At this depth, the pressure is 15 atm (see Exercise 7-5). The spaces in the porous bone are filledwith gas at a pressure of about 1 atm. Therefore, the porous bone must be ableto withstand a pressure of 14 atm. Experiments have shown that the bone canin fact survive pressures up to 24 atm.
In fish that possess swim bladders, the decrease in density is provided by the gas in the bladder. Because the density of the gas is negligible comparedto the density of tissue, the volume of the swim bladder required to reducethe density of the fish is smaller than that of the porous bone. For example, to achieve the density reduction calculated in the preceding example, thevolume of the bladder is only about 4% of the total volume of the fish (seeExercise 7-6).
Fish possessing porous bones or swim bladders can alter their density.
The cuttlefish alters its density by injecting or withdrawing fluid from itsporous bone. Fish with swim bladders alter their density by changing theamount of gas in the bladder. Another application of buoyancy is examinedin Exercise 7-7.
7.7 Surface Tension
A molecule in the interior of the liquid is surrounded by an equal numberof neighboring molecules in all directions. Therefore, the net resultant intermolecular force on an interior molecule is zero. The situation is different,however, near the surface of the liquid. Because there are no moleculesabove the surface, a molecule here is pulled predominantly in one direction,toward the interior of the surface. This causes the surface of a liquid to contract and behave somewhat like a stretched membrane. This contracting tendency results in a surface tension that resists an increase in the free surface ofthe liquid. It can be shown (see reference [7-7]) that surface tension is aforce acting tangential to the surface, normal to a line of unit length on thesurface (Fig. 7.4). The surface tension T of water at 25◦C is 72.8 dyn/cm. The
90
Chapter 7 Fluids FIGURE 7.4 Surface tension.
total force FT produced by surface tension tangential to a liquid surface ofboundary length L is FT TL
(7.16)
When a liquid is contained in a vessel, the surface molecules near the wall are attracted to the wall. This attractive force is called adhesion. At the sametime, however, these molecules are also subject to the attractive cohesive forceexerted by the liquid, which pulls the molecules in the opposite direction.
If the adhesive force is greater than the cohesive force, the liquid wets thecontainer wall, and the liquid surface near the wall is curved upward. If theopposite is the case, the liquid surface is curved downward (see Fig. 7.5). Theangle θ in Fig. 7.5 is the angle between the wall and the tangent to the liquidsurface at the point of contact with the wall. For a given liquid and surfacematerial, θ is a well-defined constant. For example, the contact angle betweenglass and water is 25◦.
If the adhesion is greater than the cohesion, a liquid in a narrow tube will rise to a specific height h (see Fig. 7.6a), which can be calculated from the following considerations. The weight W of the column of the supported liquid is
W π R2hρg
(7.17)
where R is the radius of the column and ρ is the density of the liquid. The maximum force Fm due to the surface tension along the periphery of the liquid is
Fm 2π RT
(7.18)
The upward component of this force supports the weight of the column ofliquid (see Fig. 7.6a); that is, 2π RT cos θ π R2hρg
(7.19)