11.1

Mass Density

Fluids are materials that can flow, and they include both gases and liquids. Air is the most common gas, and moves from place to place as wind. Water is the most familiar liquid, and flowing water has many uses, from generating hydroelectric power to white-water rafting. The mass density of a liquid or gas is an important factor that determines its behavior as a fluid. As indicated below, the mass density is the mass per unit volume and is denoted by the Greek letter rho ().

| Definition of Mass Density
| The mass density is the mass m of a substance divided by its volume V:

| (11.1)

SI Unit of Mass Density: kg/m3

Equal volumes of different substances generally have different masses, so the density depends on the nature of the material, as Table 11-1 indicates. Gases have the smallest densities because gas molecules are relatively far apart and a gas contains a large fraction of empty space. In contrast, the molecules are much more tightly packed in liquids and solids, and the tighter packing leads to larger densities. The densities of gases are very sensitive to changes in temperature and pressure. However, for the range of temperatures and pressures encountered in this text, the densities of liquids and solids do not differ much from the values in Table 11-1.

Table 11-1 Mass Densities* of Common Substances

Substance | Mass Density (kg/m3)
Solids |
Aluminum | 2700
Brass | 8470
Concrete | 2200
Copper | 8890
Diamond | 3520
Gold | 19 300
Ice | 917
Iron (steel) | 7860
Lead | 11 300
Quartz | 2660
Silver | 10 500
Wood (yellow pine) | 550
Liquids |
Blood (whole, 37 °C) | 1060
Ethyl alcohol | 806
Mercury | 13 600
Oil (hydraulic) | 800
Water (4 °C) |
Gases |
Air | 1.29
Carbon dioxide | 1.98
Helium | 0.179
Hydrogen | 0.0899
Nitrogen | 1.25
Oxygen | 1.43

a) |  | Unless otherwise noted, densities are given at 0 °C and 1 atm pressure.

It is the mass of a substance, not its weight, that enters into the definition of density. In situations where weight is needed, it can be calculated from the mass density, the volume, and the acceleration due to gravity, as Example 1 illustrates.

| Example 1 | | | Blood as a Fraction of Body Weight

The body of a man whose weight is 690 N contains about (5.5 qt) of blood. (a) Find the blood’s weight and (b) express it as a percentage of the body weight. Reasoning To find the weight W of the blood, we need the mass m, since (Equation 4.5), where g is the magnitude of the acceleration due to gravity. According to Table 11-1, the density of blood is 1060 kg/m3, so the mass of the blood can be found by using the given volume of Equation 11.1.
Solution

a. | According to Equation 4.5, the blood’s weight is . Equation 11.1 can be solved for m to show that the mass is . Substituting this result into Equation 4.5 gives

b. | The percentage of body weight contributed by the blood is

A convenient way to compare densities is to use the concept of specific gravity. The specific gravity of a substance is its density divided by the density of a standard reference material, usually chosen to be water at 4 °C.

| (11.2)

Being the ratio of two densities, specific gravity has no units. For example, Table 11-1 reveals that diamond has a specific gravity of 3.52, since the density of diamond is 3.52 times greater than the density of water at 4 °C.
The next two sections deal with the important concept of pressure. We will see that the density of a fluid is one factor determining the pressure that a fluid exerts.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.