FLUID MECHANICS

INTRODUCTION
States of Matter
Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common
phases of matter.

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). 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 ((see Figure 1)).
Figure 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.
Fluid Properties

Density

Density is an important characteristic of substances. It is crucial, for example, in determining

whether an object sinks or floats in a fluid.
Density
The average density of a substance or object is defined as its mass per unit volume,

The SI unit of density is kg/m3. (Table 1) lists some representative values. The cgs unit of density is
the gram per cubic centimeter, g/cm3, where
As you can see by examining Table 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 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 2 : Densities of Water

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, ρ=ρ(x,y,z)

Figure 2 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,
where ρ 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.