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14.2: Fluids, Density, and Pressure (Part 1)

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    Learning Objectives
    • State the different phases of matter
    • Describe the characteristics of the phases of matter at the molecular or atomic level
    • Distinguish between compressible and incompressible materials
    • Define density and its related SI units
    • Compare and contrast the densities of various substances
    • Define pressure and its related SI units
    • Explain the relationship between pressure and force
    • Calculate force given pressure and area

    Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common phases of matter. We will look at each of these phases in detail in this section.

    Characteristics of Solids

    Solids are rigid and have specific shapes and definite volumes. The atoms or molecules in a solid are in close proximity to each other, and there is a significant force between these molecules. Solids will take a form determined by the nature of these forces between the molecules. Although true solids are not incompressible, it nevertheless requires a large force to change the shape of a solid. In some cases, the force between molecules can cause the molecules to organize into a lattice as shown in Figure \(\PageIndex{1}\). The structure of this three-dimensional lattice is represented as molecules connected by rigid bonds (modeled as stiff springs), which allow limited freedom for movement. Even a large force produces only small displacements in the atoms or molecules of the lattice, and the solid maintains its shape. Solids also resist shearing forces. (Shearing forces are forces applied tangentially to a surface, as described in Static Equilibrium and Elasticity.)

    Characteristics of Fluids

    Liquids and gases are considered to be fluids because they yield to shearing forces, whereas solids resist them. Like solids, the molecules in a liquid are bonded to neighboring molecules, but possess many fewer of these bonds. The molecules in a liquid are not locked in place and can move with respect to each other. The distance between molecules is similar to the distances in a solid, and so liquids have definite volumes, but the shape of a liquid changes, depending on the shape of its container. Gases are not bonded to neighboring atoms and can have large separations between molecules. Gases have neither specific shapes nor definite volumes, since their molecules move to fill the container in which they are held (Figure \(\PageIndex{1}\)).

    Figure A shows an arrangement of atoms in a solid. The atoms are in close contact with neighboring atoms and are held in place by forces represented by springs. Figure B shows an arrangement of atoms in liquid. Atoms are also in close contact but can slide over one another. Figure C shows an arrangement of atoms in gas. Atoms move about freely and are separated by large distances.
    Figure \(\PageIndex{1}\): (a) Atoms in a solid are always in close contact with neighboring atoms, held in place by forces represented here by springs. (b) Atoms in a liquid are also in close contact but can slide over one another. Forces between the atoms strongly resist attempts to compress the atoms. (c) Atoms in a gas move about freely and are separated by large distances. A gas must be held in a closed container to prevent it from expanding freely and escaping.

    Liquids deform easily when stressed and do not spring back to their original shape once a force is removed. This occurs because the atoms or molecules in a liquid are free to slide about and change neighbors. That is, liquids flow (so they are a type of fluid), with the molecules held together by mutual attraction. When a liquid is placed in a container with no lid, it remains in the container. Because the atoms are closely packed, liquids, like solids, resist compression; an extremely large force is necessary to change the volume of a liquid.

    In contrast, atoms in gases are separated by large distances, and the forces between atoms in a gas are therefore very weak, except when the atoms collide with one another. This makes gases relatively easy to compress and allows them to flow (which makes them fluids). When placed in an open container, gases, unlike liquids, will escape.

    In this chapter, we generally refer to both gases and liquids simply as fluids, making a distinction between them only when they behave differently. There exists one other phase of matter, plasma, which exists at very high temperatures. At high temperatures, molecules may disassociate into atoms, and atoms disassociate into electrons (with negative charges) and protons (with positive charges), forming a plasma. Plasma will not be discussed in depth in this chapter because plasma has very different properties from the three other common phases of matter, discussed in this chapter, due to the strong electrical forces between the charges.


    Suppose a block of brass and a block of wood have exactly the same mass. If both blocks are dropped in a tank of water, why does the wood float and the brass sink (Figure \(\PageIndex{2}\))? This occurs because the brass has a greater density than water, whereas the wood has a lower density than water.

    Figure A is a photo of a large block of wood and a small block of brass located on a scale. Scale indicates an identical weight of both blocks. Figure B is a photo of a large block of wood in a fish tank filled with water. The small brass block sinks to the bottom while the block of wood floats.
    Figure \(\PageIndex{2}\): (a) A block of brass and a block of wood both have the same weight and mass, but the block of wood has a much greater volume. (b) When placed in a fish tank filled with water, the cube of brass sinks and the block of wood floats. (The block of wood is the same in both pictures; it was turned on its side to fit on the scale.)

    Density is an important characteristic of substances. It is crucial, for example, in determining whether an object sinks or floats in a fluid.


    The average density of a substance or object is defined as its mass per unit volume,

    \[\rho = \frac{m}{V} \label{14.1}\]

    where the Greek letter \(\rho\) (rho) is the symbol for density, m is the mass, and V is the volume.

    The SI unit of density is kg/m3. Table 14.1 lists some representative values. The cgs unit of density is the gram per cubic centimeter, g/cm3, where

    \[1\; g/cm^{3} = 1000\; kg/m^{3} \ldotp\]

    The metric system was originally devised so that water would have a density of 1 g/cm3, equivalent to 103 kg/m3. Thus, the basic mass unit, the kilogram, was first devised to be the mass of 1000 mL of water, which has a volume of 1000 cm3.

    Table 14.1 - Densities of Some Common Substances

    Solids (0.0 °C) Liquids (0.0 °C) Gases (0.0 °C, 101.3 kPa)
    Substance \(\rho\)(kg/m3) Substance \(\rho\)(kg/m3) Substance \(\rho\)(kg/m3)
    Aluminum 2.70 x 103 Benzene 8.79 x 102 Air 1.29 x 100
    Bone 1.90 x 103 Blood 1.05 x 103 Carbon dioxide .1.98 x 100
    Brass 8.44 x 103 Ethyl alcohol 8.06 x 102 Carbon monoxide 1.25 x 100
    Concrete 2.40 x 103 Gasoline 6.80 x 102 Helium 1.80 x 10-1
    Copper 8.92 x 103 Glycerin 1.26 x 103 Hydrogen 9.00 x 10-2
    Cork 2.40 x 102 Mercury 1.36 x 104 Methane 7.20 x 10-2
    Earth's crust 3.30 x 103 Olive oil 9.20 x 102 Nitrogen 1.25 x 100
    Glass 2.60 x 103 Nitrous oxide 1.98 x 100
    Granite 2.70 x 103 Oxygen 1.43 x 100
    Iron 7.86 x 103
    Lead 1.13 x 104
    Oak 7.10 x 102
    Pine 3.73 x 102
    Platinum 2.14 x 104
    Polystyrene 1.00 x 102
    Tungsten 1.93 x 104
    Uranium 1.87 x 103

    As you can see by examining Table 14.1, the density of an object may help identify its composition. The density of gold, for example, is about 2.5 times the density of iron, which is about 2.5 times the density of aluminum. Density also reveals something about the phase of the matter and its substructure. Notice that the densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. The densities of gases are much less than those of liquids and solids, because the atoms in gases are separated by large amounts of empty space. The gases are displayed for a standard temperature of 0.0 °C and a standard pressure of 101.3 kPa, and there is a strong dependence of the densities on temperature and pressure. The densities of the solids and liquids displayed are given for the standard temperature of 0.0 °C and the densities of solids and liquids depend on the temperature. The density of solids and liquids normally increase with decreasing temperature.

    Table 14.2 shows the density of water in various phases and temperature. The density of water increases with decreasing temperature, reaching a maximum at 4.0 °C, and then decreases as the temperature falls below 4.0 °C. This behavior of the density of water explains why ice forms at the top of a body of water.

    Table 14.2 - Densities of Water

    Substance \(\rho\)(kg/m3)
    Ice (0 °C) 9.17 x 102
    Water (0 °C) 9.998 x 102
    Water (4 °C) 1.000 x 103
    Water (20 °C) 9.982 x 102
    Water (100 °C) 9.584 x 102
    Steam (100 °C, 101.3 kPa) 1.670 x 102
    Sea water (0°C) 1.030 x 103

    The density of a substance is not necessarily constant throughout the volume of a substance. If the density is constant throughout a substance, the substance is said to be a homogeneous substance. A solid iron bar is an example of a homogeneous substance. The density is constant throughout, and the density of any sample of the substance is the same as its average density. If the density of a substance were not constant, the substance is said to be a heterogeneous substance. A chunk of Swiss cheese is an example of a heterogeneous material containing both the solid cheese and gas-filled voids. The density at a specific location within a heterogeneous material is called local density, and is given as a function of location, \(\rho\) = \(\rho\)(x, y, z) (Figure \(\PageIndex{3}\)).

    Figure is a drawing of a container filled with a liquid. Small cubes are drawn in different regions of the container to indicate local density points.
    Figure \(\PageIndex{3}\): Density may vary throughout a heterogeneous mixture. Local density at a point is obtained from dividing mass by volume in a small volume around a given point.

    Local density can be obtained by a limiting process, based on the average density in a small volume around the point in question, taking the limit where the size of the volume approaches zero,

    \[\rho = \lim_{\Delta V \rightarrow 0} \frac{\Delta m}{\Delta V} \label{14.2}\]

    where \(\rho\) is the density, m is the mass, and V is the volume.

    Since gases are free to expand and contract, the densities of the gases vary considerably with temperature, whereas the densities of liquids vary little with temperature. Therefore, the densities of liquids are often treated as constant, with the density equal to the average density.

    Density is a dimensional property; therefore, when comparing the densities of two substances, the units must be taken into consideration. For this reason, a more convenient, dimensionless quantity called the specific gravity is often used to compare densities. Specific gravity is defined as the ratio of the density of the material to the density of water at 4.0 °C and one atmosphere of pressure, which is 1000 kg/m3:

    \[Specific\; gravity = \frac{Density\; of\; material}{Density\; of\; water} \ldotp\]

    The comparison uses water because the density of water is 1 g/cm3, which was originally used to define the kilogram. Specific gravity, being dimensionless, provides a ready comparison among materials without having to worry about the unit of density. For instance, the density of aluminum is 2.7 in g/cm3 (2700 in kg/m3), but its specific gravity is 2.7, regardless of the unit of density. Specific gravity is a particularly useful quantity with regard to buoyancy, which we will discuss later in this chapter.


    You have no doubt heard the word ‘pressure’ used in relation to blood (high or low blood pressure) and in relation to weather (high- and low-pressure weather systems). These are only two of many examples of pressure in fluids. (Recall that we introduced the idea of pressure in Static Equilibrium and Elasticity, in the context of bulk stress and strain.)


    Pressure (p) is defined as the normal force F per unit area A over which the force is applied, or

    \[p = \frac{F}{A} \ldotp \label{14.3}\]

    To define the pressure at a specific point, the pressure is defined as the force dF exerted by a fluid over an infinitesimal element of area dA containing the point, resulting in p = \(\frac{dF}{dA}\).

    A given force can have a significantly different effect, depending on the area over which the force is exerted. For instance, a force applied to an area of 1 mm2 has a pressure that is 100 times as great as the same force applied to an area of 1 cm2 . That is why a sharp needle is able to poke through skin when a small force is exerted, but applying the same force with a finger does not puncture the skin (Figure \(\PageIndex{4}\)).

    Figure A is a drawing of a person being poked with a finger in a shoulder. The force of the finger is shown taking up a larger area, which produces only a small amount of pressure. Figure B is a drawing of a person being poked with a syringe with needle in a shoulder. The force of the syringe is shown taking up a smaller area, which produces a large amount of pressure.
    Figure \(\PageIndex{4}\): (a) A person being poked with a finger might be irritated, but the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is enough to break the skin.

    Note that although force is a vector, pressure is a scalar. Pressure is a scalar quantity because it is defined to be proportional to the magnitude of the force acting perpendicular to the surface area. The SI unit for pressure is the pascal (Pa), named after the French mathematician and physicist Blaise Pascal (1623–1662), where

    \[1\; Pa = 1\; N/m^{2} \ldotp\]

    Several other units are used for pressure, which we discuss later in the chapter.

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