In order to describe the variety of fluid characteristics that are involved in fluid mechanics a system was developed to describe the qualitative and quantitative aspects of these characteristics. When you are looking at the qualitative aspects of a problem, you are describing the length, time, stress, or velocity. Basically the qualitative aspects identities the nature or type of characteristic. On the other hand the quantitative aspect represents the numerical value of the characteristic. A quantitative aspect will require both a number and a standard, such as 1 kg. The number 1 is the number, and kg (kilogram) represents the standard. These standards are known as units.
Basic Dimensions
There are qualitative values that are primary quantities. This means that a combination of these values create other qualitative values such as velocity, but they themselves cannot be created. For example, length (L), time (T), mass (M), and temperature (Θ) are all primary quantities. All other quantities are derived from these primary quantities. Primary quantities are also called basic dimensions.
Most fluid mechanic problems will only require the use of the three basic dimensions length, mass, and time. However, force is also used quite often to describe the results of a fluid dynamics problem. Due to this for simplicity Force (F) is sometimes considered a basic dimension even though it is a product of length, mass, and time.
$ F = MLT^{-2}$
Common Physical Quantities Dimensions
Physical Quantities |
FLT System |
MLT System |
Acceleration |
$LT^{-2}$ |
$LT^{-2}$ |
Angle |
$F^0L^0T^0$ |
$M^0L^0T^0$ |
Angular Acceleration |
$T^{-2}$ |
$T^{-2}$ |
Area |
$L^2$ |
$L^2$ |
Density |
$FL^{-4}T^2$ |
$ML^{-3}$ |
Energy |
$FL$ |
$ML^2T^{-2}$ |
Frequency |
$T^{-1}$ |
$T^{-1}$ |
Heat |
$FL$ |
$ML^2T^{-2}$ |
Modulus of Elasticity |
$FL^{-2}$ |
$ML^{-1}T^{-2}$ |
Area Moment of Inertia |
$L^4$ |
$L^4$ |
Mass Moment of Inertia |
$FLT^2$ |
$ML^2$ |
Momentum |
$FT$ |
$MLT^{-1}$ |
Power |
$FLT^{-1}$ |
$ML^2T^{-3}$ |
Pressure |
$FL^{-2}$ |
$ML^{-1}T^{-2}$ |
Specific Heat |
$L^2T^{-2} Θ^{-1}$ |
$L^2T^{-2} Θ^{-1}$ |
Specific Weight |
$FL^{-3}$ |
$ML^{-2}T^{-2}$ |
Strain |
$F^0L^0T^0$ |
$M^0L^0T^0$ |
Stress |
$FL^{-2}$ |
$ML^{-1}T^{-2}$ |
Surface Tension |
$FL^{-1}$ |
$MT^{-2}$ |
Velocity |
$LT^{-1}$ |
$LT^{-1}$ |
Dynamic Viscosity |
$FL^{-2}T$ |
$ML^{-1}T^{-1}$ |
Kinematic Viscosity |
$L^2T^{-1}$ |
$L^2T^{-1}$ |
Volume |
$L^3$ |
$L^3$ |
Work | $FL$ |
$ML^2T^{-2}$ |
System of Units
The above information will apply to the qualitative aspect regardless of the system of units. On the other hand the system of units that is used will affect the quantitative aspect of the problem. As mention above the quantitative aspect is based off of a number and a standard. The standard that is used is based off of the system of units that is chosen. One system of units which is used all over the world is the International System, or SI units. Other systems that are also used are the British Gravitational system, and the English Engineering system. The system that is chosen will determine what units are used to describe the quantitative aspect of the problem.