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1.3 Dimensions, Units, and ResourcesThis 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 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
areL/T2, 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 dimensioncan 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, pounds-force, 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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French Le Systme International d'Units) 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 pound-mass
(lbm) for mass, the foot (ft) for length, the pound-force (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
pounds-mass 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 isabout 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
pascal-second (Pa s), poise, and lbf
s/ft2.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 = 106
m.
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.
Copyright 2009 John Wiley & Sons, Inc. All rights
reserved.
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