# GASES LIQUID AND DENSITY

A fluid is any substance that can flow and change the shape of the volume that
it occupies. (By contrast, a solid tends to maintain its shape.) We use the term
“fluid” for both gases and liquids. The key difference between them is that a
liquid has cohesion, while a gas does not. The molecules in a liquid are close
to one another, so they can exert attractive forces on each other and thus tend to
stay together (that is, to cohere). That’s why a quantity of liquid maintains the
same volume as it flows: If you pour 500 mL of water into a pan, the water
will still occupy a volume of 500 mL. The molecules of a gas, by contrast,
are separated on average by distances far larger than the size of a molecule.
Hence the forces between molecules are weak, there is little or no cohesion,
and a gas can easily change in volume. If you open the valve on a tank of
compressed oxygen that has a volume of 500 mL, the oxygen will expand to
a far greater volume.

An important property of any material, fluid or solid, is its density, defined as its mass per unit volume. A homogeneous material such as ice or iron has the same density throughout. We use Þ (the Greek letter rho) for density. For a homogeneous material

Two objects made of the same material have the same density even though they
may have different masses and different volumes. That’s because the ratio of
mass to volume is the same for both objects (Fig. 12.1).
The SI unit of density is the kilogram per cubic meter 11 kg/m3. The cgs
unit, the gram per cubic centimeter 11 g/cm3, is also widely used:

1 g/cm3 = 1000 kg/m3

The densities of some common substances at ordinary temperatures are given in
Table 12.1. Note the wide range of magnitudes. The densest material found on
earth is the metal osmium 1r = 22,500 kg/m3, but its density pales by comparison
to the densities of exotic astronomical objects, such as white dwarf stars
and neutron stars.

The specific gravity of a material is the ratio of its density to the density of
water at 4.0°C, 1000 kg/m3
; it is a pure number without units. For example, the
specific gravity of aluminum is 2.7. “Specific gravity” is a poor term, since it has
nothing to do with gravity; “relative density” would have been a better choice.
The density of some materials varies from point to point within the material.
One example is the material of the human body, which includes low-density fat
) and high-density bone (from 1700 to 2500 kg/m3
). Two others
are the earth’s atmosphere (which is less dense at high altitudes) and oceans
(which are denser at greater depths). For these materials, Eq. (12.1) describes the
average density. In general, the density of a material depends on environmental
factors such as temperature and pressure.

SOLVED EXAMPLE OF THIS TOPIC

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Ans: Fluids play a vital role in many aspects of everyday life. We drink them, breathe them, swim in them. They circulate through our bodies and control our weather. The physics of fluids is therefore crucial to our understanding of both nature and technology view more..
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Ans: summary of equilibrium and elasticity view more..
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Ans: Hooke’s law—the proportionality of stress and strain in elastic deformations— has a limited range of validity. In the preceding section we used phrases such as “if the forces are small enough that Hooke’s law is obeyed.” Just what are the limitations of Hooke’s law? What’s more, if you pull, squeeze, or twist anything hard enough, it will bend or break view more..
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Ans: A fluid is any substance that can flow and change the shape of the volume that it occupies. (By contrast, a solid tends to maintain its shape.) We use the term “fluid” for both gases and liquids. The key difference between them is that a liquid has cohesion, while a gas does not. The molecules in a liquid are close to one another, so they can exert attractive forces on each other and thus tend to stay together (that is, to cohere). That’s why a quantity of liquid maintains the same volume as it flows: If you pour 500 mL of water into a pan, the water will still occupy a volume of 500 mL. The molecules of a gas, by contrast, are separated on average by distances far larger than the size of a molecule. Hence the forces between molecules are weak, there is little or no cohesion, and a gas can easily change in volume. If you open the valve on a tank of compressed oxygen that has a volume of 500 mL, the oxygen will expand to a far greater volume. view more..
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Ans: A fluid exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid. This is the force that you feel pressing on your legs when you dangle them in a swimming pool. Even when a fluid as a whole is at rest, the molecules that make up the fluid are in motion; the force exerted by the fluid is due to molecules colliding with their surroundings view more..
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Ans: If the weight of the fluid can be ignored, the pressure in a fluid is the same throughout its volume. We used that approximation in our discussion of bulk stress and strain in Section 11.4. But often the fluid’s weight is not negligible, and pressure variations are important. Atmospheric pressure is less at high altitude than at sea level, which is why airliner cabins have to be pressurized. When you dive into deep water, you can feel the increased pressure on your ears. view more..
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Ans: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. view more..
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Ans: If the pressure inside a car tire is equal to atmospheric pressure, the tire is flat. The pressure has to be greater than atmospheric to support the car, so the significant quantity is the difference between the inside and outside pressures. When we say that the pressure in a car tire is “32 pounds” (actually 32 lb>in.2 , equal to 220 kPa or 2.2 * 105 Pa), we mean that it is greater than atmospheric pressure (14.7 lb>in.2 or 1.01 * 105 Pa) by this amount. view more..
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Ans: The simplest pressure gauge is the open-tube manometer . The U-shaped tube contains a liquid of density r, often mercury or water. The left end of the tube is connected to the container where the pressure p is to be measured, and the right end is open to the atmosphere view more..
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Ans: A body immersed in water seems to weigh less than when it is in air. When the body is less dense than the fluid, it floats. The human body usually floats in water, and a helium-filled balloon floats in air. These are examples of buoyancy, a phenomenon described by Archimedes’s principle: view more..
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Ans: We’ve seen that if an object is less dense than water, it will float partially submerged. But a paper clip can rest atop a water surface even though its density is several times that of water. This is an example of surface tension: view more..
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Ans: We are now ready to consider motion of a fluid. Fluid flow can be extremely complex, as shown by the currents in river rapids or the swirling flames of a campfire. But we can represent some situations by relatively simple idealized models. An ideal fluid is a fluid that is incompressible (that is, its density cannot change) and has no internal friction (called viscosity). view more..
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Ans: The mass of a moving fluid doesn’t change as it flows. This leads to an important relationship called the continuity equation view more..
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Ans: According to the continuity equation, the speed of fluid flow can vary along the paths of the fluid. The pressure can also vary; it depends on height as in the static situation (see Section 12.2), and it also depends on the speed of flow. We can derive an important relationship called Bernoulli’s equation, view more..
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Ans: To derive Bernoulli’s equation, we apply the work–energy theorem to the fluid in a section of a flow tube. In Fig. 12.23 we consider the element of fluid that at some initial time lies between the two cross sections a and c. The speeds at the lower and upper ends are v1 and v2. In a small time interval dt, the fluid that is initially at a moves to b, a distance ds1 = v1 dt, and the fluid that is initially at c moves to d, a distance ds2 = v2 dt. The cross-sectional areas at the two ends are A1 and A2, as shown. The fluid is incompressible; hence by the continuity equation, Eq. (12.10), the volume of fluid dV passing any cross section during time dt is the same. That is, dV = A1 ds1 = A2 ds2. view more..
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Ans: HERE ARE SOME EXAMPLES TO DEAL WITH view more..
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Ans: Viscosity is internal friction in a fluid. Viscous forces oppose the motion of one portion of a fluid relative to another. Viscosity is the reason it takes effort to paddle a canoe through calm water, but it is also the reason the paddle works. Viscous effects are important in the flow of fluids in pipes, the flow of blood, the lubrication of engine parts, and many other situations view more..
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Ans: When the speed of a flowing fluid exceeds a certain critical value, the flow is no longer laminar. Instead, the flow pattern becomes extremely irregular and complex, and it changes continuously with time; there is no steady-state pattern. This irregular, chaotic flow is called turbulence view more..

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