1.3-Dimensions, Units.pdf

Dimensions, Units, and Resources

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1.3 Dimensions, Units, and Resources

This section describes the dimensions and units that are used in fluid mechanics. This information is essential

for understanding most aspects of fluid mechanics. In addition, this section describes useful resources that are

presented in the front and back of this text.

Dimensions

A dimension is a category that represents a physical quantity such as mass, length, time, momentum, force,

acceleration, and energy. To simplify matters, engineers express dimensions using a limited set that are called

primary dimensions . Table 1.2 lists one common set of primary dimensions.

Table 1.2 PRIMARY DIMESIOS

Dimension

Symbol Unit (SI)

Length

L meter (m)

Mass

M kilogram (kg)

Time

T second (s)

Temperature θ kelvin (K)

Electric current i ampere (A)

Amount of light C candela (cd)

Amount of matter mole (mol)

Secondary dimensions such as momentum and energy can be related to primary dimensions by using equations.

For example, the secondary dimension “force” is expressed in primary dimensions by using Newton's second

law of motion, F = ma . The primary dimensions of acceleration are L / T 2 , so

(1.1)

In Eq. 1.1, the square brackets mean “dimensions of.” This equation reads “the primary dimensions of force are

mass times length divided by time squared.” Note that primary dimensions are not enclosed in brackets.

Units

While a dimension expresses a specific type of physical quantity, a unit assigns a number so that the dimension

can be measured. For example, measurement of volume (a dimension) can be expressed using units of liters.

Similarly, measurement of energy (a dimension) can be expressed using units of joules. Most dimensions have

multiple units that are used for measurement. For example, the dimension of “force” can be expressed using

units of newtons, poundsforce, or dynes.

Unit Systems

In practice, there are several unit systems in use. The International System of Units (abbreviated SI from the

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Dimensions, Units, and Resources

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French “Le Système International d'Unités”) is based on the meter, kilogram, and second. Although the SI

system is intended to serve as an international standard, there are other systems in common use in the United

States. The U.S. Customary System (USCS), sometimes called English Engineering System, uses the poundmass

(lbm) for mass, the foot (ft) for length, the poundforce (lbf) for force, and the second (s) for time. The British

Gravitational (BG) System is similar to the USCS system that the unit of mass is the slug. To convert between

poundsmass and kg or slugs, the relationships are

Thus, a gallon of milk, which has mass of approximately 8 lbm, will have a mass of about 0.25 slugs, which is

about 3.6 kg.

For simplicity, this text uses two categories for units. The first category is the familiar SI unit system. The second

category contains units from both the USCS and the BG systems of units and is called the “Traditional Unit

System.”

Resources Available in This Text

To support calculations and design tasks, formulas and data are presented in the front and back of this text.

Table F.1 (the notation “F.x” means a table in the front of the text) presents data for converting units. For

example, this table presents the factor for converting meters to feet (1 m = 3.281 ft) and the factor for converting

horsepower to kilowatts (1 hp = 745.7 W). Notice that a given parameter such as viscosity will have one set of

primary dimensions ( M / LT ) and several possible units, including pascalsecond (Pa · s), poise, and lbf ·

s/ft 2 .Table F.1 lists unit conversion formulas , where each formula is a relationship between units expressed

using the equal sign. Examples of unit conversion formulas are 1.0 m = 3.281 ft and 3.281 ft = km/1000. Notice

that each row of Table F.1 provides multiple conversion formulas. For example, the row for length conversions,

(1.2)

has the usual conversion formulas such as 1 m = 39.37 in, and the less common formulas such as 1.094 yd = 10 6

Table F.2 presents equations that are commonly used in fluid mechanics. To make them easier to remember,

equations are given descriptive names such as the “hydrostatic equation.” Also, notice that each equation is given

an equation number and page number corresponding to where it is introduced in this text.

Tables F.3, F.4, and F.5 present commonly used constants and fluid properties. Other fluid properties are

presented in the appendix. For example, Table A.3 (the notation “A.x” means a table in the appendix) gives

properties of air.

Table A.6 lists the variables that are used in this text. Notice that this table gives the symbol, the primary

dimensions, and the name of the variable.

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