20
CHAPTER 2. DIMENSIONAL ANALYSIS
porting a measurement introduces uncertainty in the interpretation of the
value. Although there are instances where local custom enables a reasonable assumption to be made of the dimensional units that accompany a
numerical value, there is still an inherent risk in blindly assuming that the
local custom has been applied in every specific case. This is particularly
true in hydraulic laboratories in the United States where often more than
one system of units are routinely used.
Scientific thinking involves abstract concepts such as force, mass, length,
area, volume, time, acceleration, velocity, temperature, specific heat and
electric charge. To each of these conceptual entities we have assigned a
unit of measure. Some entities (mass, length, time, temperature, and electric charge) are independent of each other, and their dimensions can be
considered fundamental dimensions and their units base units. Other
properties, such as force, area, volume, acceleration, velocity, pressure, and
specific heat, arise from definitions or from physical laws, and they have
derived dimensions that represent combinations of the fundamental dimensions, resulting in derived units. Finally, there are a few supplementary
units, such as plane angle and solid angle that do not contain any of the
fundamental dimensions.
Langhaar (1951) stated that dimensions serve a mathematical purpose
because “They are a code for telling us how the numerical value of a quantity changes when the basic units of measurement are subjected to prescribed
changes.” Although his statement is somewhat philosophical, Langhaar’s
remark can be interpreted to mean “dimensions and dimensional units provide a known reference frame from which to observe relative change in a
physical quantity.”
Different types of conventional measurement systems have been developed based on Newton’s second law (given in its simplest form as F = ma).
Systems of units utilizing Newton’s law specify acceleration as a derived
quantity having units composed of the base units of length (L) and time
(T). Then either mass (M) or force (F) is specified as a fundamental quantity, leaving the final quantity (either force or mass) as a derived quantity
having units determined from Newton’s second law. Depending on which
variable is chosen as the fundamental quantity, we can have either a length,
time, mass system or a length, time, force system.
Common mass systems of measurement and their corresponding dimensions of length, mass, and time are:
• CGS System (centimeter-gram-second), with force unit
defined as dyne
• SI System (meter-kilogram-second), with force unit defined as newton
CHAPTER 2. DIMENSIONAL ANALYSIS
porting a measurement introduces uncertainty in the interpretation of the
value. Although there are instances where local custom enables a reasonable assumption to be made of the dimensional units that accompany a
numerical value, there is still an inherent risk in blindly assuming that the
local custom has been applied in every specific case. This is particularly
true in hydraulic laboratories in the United States where often more than
one system of units are routinely used.
Scientific thinking involves abstract concepts such as force, mass, length,
area, volume, time, acceleration, velocity, temperature, specific heat and
electric charge. To each of these conceptual entities we have assigned a
unit of measure. Some entities (mass, length, time, temperature, and electric charge) are independent of each other, and their dimensions can be
considered fundamental dimensions and their units base units. Other
properties, such as force, area, volume, acceleration, velocity, pressure, and
specific heat, arise from definitions or from physical laws, and they have
derived dimensions that represent combinations of the fundamental dimensions, resulting in derived units. Finally, there are a few supplementary
units, such as plane angle and solid angle that do not contain any of the
fundamental dimensions.
Langhaar (1951) stated that dimensions serve a mathematical purpose
because “They are a code for telling us how the numerical value of a quantity changes when the basic units of measurement are subjected to prescribed
changes.” Although his statement is somewhat philosophical, Langhaar’s
remark can be interpreted to mean “dimensions and dimensional units provide a known reference frame from which to observe relative change in a
physical quantity.”
Different types of conventional measurement systems have been developed based on Newton’s second law (given in its simplest form as F = ma).
Systems of units utilizing Newton’s law specify acceleration as a derived
quantity having units composed of the base units of length (L) and time
(T). Then either mass (M) or force (F) is specified as a fundamental quantity, leaving the final quantity (either force or mass) as a derived quantity
having units determined from Newton’s second law. Depending on which
variable is chosen as the fundamental quantity, we can have either a length,
time, mass system or a length, time, force system.
Common mass systems of measurement and their corresponding dimensions of length, mass, and time are:
• CGS System (centimeter-gram-second), with force unit
defined as dyne
• SI System (meter-kilogram-second), with force unit defined as newton