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analysis is based on representing physical quantities with a combination of fundamental dimensions, noting that units of two sides of an equation must be consistent.
In fluid mechanics, as in other branches of engineering sciences, the fundamental dimensions are mass (M), length (L), and time (T). Temperature, if applicable, can be assigned a fundamental dimension such as (θ). These fundamental dimensions can be used to provide qualitative descriptions of physical quantities: for example, velocity can be described as LT−1, density as MT−3, and so on. Table 1.2 lists the symbols, units, and dimensions of common physical quantities. For effective application of dimensional analysis, it is essential to state which independent variables are relevant to the problem.
Table 1.2 Symbols, units, and dimensions of common physical quantities.
| Quantity | Symbol | Units | Dimensions |
| Length | l | m | L |
| Time | t | s | T |
| Mass | m | kg | M |
| Force | F | N | MLT −2 |
| Temperature | T | K | θ |
| Velocity | C or V | m/s | LT −1 |
| Volume | m 3 | m 3 | L 3 |
| Acceleration | a | m/s2 | LT −2 |
| Angular velocity | ω | rad | T −1 |
| Area | m 2 | m 2 | L 2 |
| Volume flow rate |
|
m3/s | L 3 T −1 |
| Mass flow rate |
|
kg/s | MT −1 |
| Pressure | p | N/m2 | ML −1 T −2 |
| Density | ρ | kg/m3 | ML −3 |
| Specific weight | γ | N/m3 | ML −2 T −2 |
| Dynamic viscosity | μ | N. s/m2 | ML −1 T −1 |
| Kinematic viscosity | ν | m2/s | L 2 T −1 |
| Work | W | J | ML 2 T −2 |
| Power |
|
W | ML 2 T −3 |
| Surface tension | σ | N/m | MT −2 |
| Bulk modulus | B | N/m2 | ML −1 T −2 |
| Momentum | G | kg. m/s | MLT −1 |
| Torque, moment of force |
T, M
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