2.1. DIMENSIONS
23
Table 2.1 gives the dimensions in terms of base units for many of the
common engineering physical parameters. The table also identifies the type
of parameter based on the above definition given by Yalin (1971). Note that
several parameters in Table 2.1 do not strictly fit into one of the four types
defined by Yalin. Angular velocity, angular acceleration, and frequency
have base units consisting of time and angle (or cycles); and therefore,
these should be considered kinematic quantities. The remaining parameters
without a designation all consist of the base unit of mass combined with
either time or length units. These parameters should be considered dynamic
quantities because the exponent of the base unit of mass is not zero even
though the exponent of either time or length is zero (contrary to Yalin’s
definition).
2.1.2 Conversion of Dimensional Units
Within a system of units it is common to have several different dimensions
representing the same physical entity or property. For instance, fluid velocity can be correctly expressed as “meters per second”, “kilometers per
hour”, or centimeters per minute” in the SI System. Each dimension retains the same relationship between the base units making up the dimension
as given in Table 2.1. The only difference is the selected length and time
magnitudes.
Values of dimensional quantities are easily converted within a system
of units or to another system of units using conversion factors. Conversion
factors result from definitions (e.g., 12 inches = 1 foot; 1 foot = 0.3048 meters), or they arise from application of Newton’s 2nd law between different
systems (e.g., 4.448 pounds = 1 newton). A table of commonly used engineering conversion factors for converting dimensions between the American
Engineering System and the SI System is given in Appendix A. Conversion
factors not listed in Appendix A can be constructed by combining several
conversion factors. Conversion of dimensional units is illustrated in the
following examples.
Example 2.1. Conversion of Units
An industrious graduate student has made careful experimental measurements to
determine that the average motivated cat has a top speed of 50 kilometers per hour
(km/h). The student’s numerical simulation model requires a feline top speed input
having units of meters per second. The required conversion is
km [ 1 h 1 [ 1000 ml _
m
5 o — I —~—-1 —I -— i o. y
h [3600 sJ L 1km f
s
conversion factor
23
Table 2.1 gives the dimensions in terms of base units for many of the
common engineering physical parameters. The table also identifies the type
of parameter based on the above definition given by Yalin (1971). Note that
several parameters in Table 2.1 do not strictly fit into one of the four types
defined by Yalin. Angular velocity, angular acceleration, and frequency
have base units consisting of time and angle (or cycles); and therefore,
these should be considered kinematic quantities. The remaining parameters
without a designation all consist of the base unit of mass combined with
either time or length units. These parameters should be considered dynamic
quantities because the exponent of the base unit of mass is not zero even
though the exponent of either time or length is zero (contrary to Yalin’s
definition).
2.1.2 Conversion of Dimensional Units
Within a system of units it is common to have several different dimensions
representing the same physical entity or property. For instance, fluid velocity can be correctly expressed as “meters per second”, “kilometers per
hour”, or centimeters per minute” in the SI System. Each dimension retains the same relationship between the base units making up the dimension
as given in Table 2.1. The only difference is the selected length and time
magnitudes.
Values of dimensional quantities are easily converted within a system
of units or to another system of units using conversion factors. Conversion
factors result from definitions (e.g., 12 inches = 1 foot; 1 foot = 0.3048 meters), or they arise from application of Newton’s 2nd law between different
systems (e.g., 4.448 pounds = 1 newton). A table of commonly used engineering conversion factors for converting dimensions between the American
Engineering System and the SI System is given in Appendix A. Conversion
factors not listed in Appendix A can be constructed by combining several
conversion factors. Conversion of dimensional units is illustrated in the
following examples.
Example 2.1. Conversion of Units
An industrious graduate student has made careful experimental measurements to
determine that the average motivated cat has a top speed of 50 kilometers per hour
(km/h). The student’s numerical simulation model requires a feline top speed input
having units of meters per second. The required conversion is
km [ 1 h 1 [ 1000 ml _
m
5 o — I —~—-1 —I -— i o. y
h [3600 sJ L 1km f
s
conversion factor