# 14.2: Fluids, Density, and Pressure (Part 1) (2023)

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##### learning goals
• Name the different phases of matter.
• Describe the properties of the phases of matter at the molecular or atomic level.
• Distinguish between compressible and incompressible materials.
• Define density and its SI units
• Compare and contrast the densities of different substances.
• Define pressure and its 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.

## solid properties

Solids are rigid and have specific shapes and definite volumes. The atoms or molecules in a solid are very close to each other and there is a significant force between these molecules. Solids take a shape determined by the nature of these forces between molecules. Although true solids are not incompressible, it still takes a great force to change the shape of a solid. In some cases, the force between molecules can cause the molecules to arrange themselves into a lattice, as shown in the figure $$\PageIndex{1}$$. The structure of this three-dimensional network is represented as molecules connected by rigid links (modeled as rigid springs) that allow limited freedom of movement. Even a large force creates only small displacements in the atoms or molecules of the lattice, and the solid retains its shape. Solids also resist shear forces. (Shear forces are forces that act tangentially to a surface, as described inStatic balance and elasticity..)

## liquid properties

How are liquids and gases considered?liquidsbecause they yield to shear forces while solids resist them. Like solids, molecules in a liquid are linked to neighboring molecules, but they have far fewer of these links. Molecules in a liquid are not fixed and can move relative to each other. The distance between molecules is similar to the distance in a solid, 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 distances between molecules. Gases do not have defined shapes or defined volumes as their molecules move to fill the container in which they are contained (Figure $$\PageIndex{1}$$).

Fluids easily deform when stressed and will not return to their original shape once the force is removed. This happens because the atoms or molecules in a liquid are free to move around and change their neighbors. That is, liquids flow (so they are a type of liquid), with the molecules held together by mutual attraction. If a liquid is placed in a container without a lid, it remains in the container. Because the atoms are close together, liquids, like solids, resist compression; An extremely large force is required to change the volume of a liquid.

(Video) phys3A ch14.2 Fluids at Rest

By contrast, the atoms in gases are separated by great distances, and therefore the forces between the atoms in a gas are very weak, except when the atoms collide with each other. This allows gases to compress and flow (making them liquid) with relative ease. When placed in an open container, gases will escape, unlike liquids.

In this chapter we refer to both gases and liquids in general simply as fluids and distinguish between them only when they behave differently. There is another phase of matter, plasma, which exists at very high temperatures. At high temperatures, molecules can dissociate into atoms and atoms into electrons (with negative charges) and protons (with positive charges) and form a plasma. Plasma is not covered in detail in this chapter because plasma has very different properties from the other three ordinary phases of matter discussed in this chapter, due to the strong electrical forces between the charges.

## density

Suppose a block of brass and a block of wood have exactly the same mass. If both blocks fall into a tank of water, why does the wood float and the brass sink (Figure $$\PageIndex{2}$$)? This is because brass has a higher density than water, while wood has a lower density than water.

densityIt is an important characteristic of tissues. For example, it is decisive whether an object sinks or floats in a liquid.

##### density

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

$\rho = \frac{m}{V} \label{14.1}$

(Video) Thermal expansion and Ch 14.2 Fluid properties

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

The SI unit of density is kg/m.3. Table 14.1 lists some representative values. The cgs unit of density is grams per cubic centimeter, g/cm3, is

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

The metric system was originally designed so that water has a density of 1 g/cm3, corresponds to 103 kg/m3. Therefore, the basic unit of mass, the kilogram, was first developed as the mass of 1000 ml of water with a volume of 1000 cm.3.

### Table 14.1 - Densities of some common substances

solid (0.0 C) liquids (0.0 C) gas (0,0 °C, 101,3 kPa)
substance $$\rho$$(kg/m3) substance $$\rho$$(kg/m3) substance $$\rho$$(kg/m3)
Aluminum 2,70x103 Benzene 8,79x102 Luft 1.29x100
Bone 1,90x103 sangre 1.05x103 carbon dioxide .1,98 x 100
dirty 8,44x103 ethyl alcohol 8.06x102 carbon monoxide 1,25x100
Concrete 2.40x103 Gasoline 6,80x102 Helio 1,80x10-1
copper 8,92x103 Glycerin 1,26x103 hydrogen 9.00x10-2
Cap 2.40x102 mercurio 1,36x104 methane 7,20x10-2
Cortex 3,30x103 olive oil 9,20x102 Nitrogen 1,25x100
glass 2,60x103 laughing gas 1,98x100
granite 2,70x103 oxygen 1.43x100
Eisen 7,86x103
Oak 7,10x102
Kiefer 3,73x102
platinum 2,14x104
polystyrene 1.00x102
tungsten 1,93x104
Carrera 1,87x103

As you can see in Table 14.1, the density of an object can help determine its composition. For example, the density of gold 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 matter and its substructure. Note 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 lower than those of liquids and solids because the atoms of gases are separated by large amounts of empty space. Gases are shown for a standard temperature of 0.0 °C and a standard pressure of 101.3 kPa, and the density is highly dependent on temperature and pressure. The densities of solids and liquids shown are given for the standard temperature of 0.0 °C and the densities of solids and liquids are temperature dependent. The density of solids and liquids generally increases with decreasing temperature.

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

### Table 14.2 - Water densities

substance $$\rho$$(kg/m3)
Ice (0°C) 9,17x102
water (0°C) 9,998x102
water (4°C) 1,000x103
water (20°C) 9,982 x 102
water (100°C) 9.584x102
Humidityf (100 °C, 101.3 kPa) 1.670x102
sea ​​water (0°C) 1.030x103

The density of a substance is not necessarily constant over the volume of a substance. If the density of a substance is constant, it is said to be homogeneous. A solid iron bar is an example of a homogeneous substance. The density is constant at all times, and the density of each sample of the substance is equal to its average density. If the density of a substance is not constant, it is said to be a heterogeneous substance. A piece of Swiss cheese is an example of a heterogeneous material that contains both solid cheese and gas-filled voids. The density at a specific location within a heterogeneous material is called the local density and is given as a function of location, $$\rho$$ = $$\rho$$(x, y, z) (Figure $$\PageIndex { 3 }$$).

The local density can be obtained by a bounding process based on the mean density in a small volume around the point of interest, taking the boundary where the size of the volume tends to zero.

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

where $$\rho$$ is density, m is mass, and V is volume.

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

Density is a dimensional property; Therefore, when comparing the densities of two substances, units must be considered. For this reason, a more convenient dimensionless quantity is calledspecific weightoften used to compare densities. Specific gravity is defined as the ratio between the density of the material and the density of water at 4.0 °C and one atmosphere of pressure, which corresponds to 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, which is dimensionless, provides an easy comparison between materials without having to worry about the unit of density. For example, 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 in terms of buoyancy, which we will discuss later in this chapter.

(Video) PS 14.2 - Properties of Fluids (Textbook)

(Video) 14.2 Pressure in a Fluid

## Print

You've probably heard the word "pressure" associated with blood (high or low blood pressure) and weather (high and low pressure weather patterns). These are just two of many examples of pressure in liquids. (Remember that we introduced the idea of ​​printing inStatic balance and elasticity., related to stress and bulk strain.)

##### Print

Print(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 given point, the pressure is defined as the force dF exerted by a liquid on an infinitesimally small surface element dA containing the point, resulting in p = $$\frac{dF}{dA }$$ carry.

A given force can have a significantly different effect depending on the area to which the force is applied. For example a force applied to an area of ​​1mm2has a pressure 100 times the same force applied to an area of ​​1 cm2. Therefore, a sharp needle can pierce the skin with little force, but the skin cannot be pierced with the same force with a finger (Figure $$\PageIndex{4}$$).

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

(Video) Phys Sci 9.2 Properties of Fluids

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

There are several other units used for pressure, which we will discuss later in this chapter.

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