Important Dimensionless Numbers in Fluid Mechanics:
| Dimensionless Number | Symbol | Formula | Numerator | Denominator | Importance |
| Reynolds number | NRe | Dvr/m | Inertial force | Viscous force | Fluid flow involving viscous and inertial forces |
| Froude number | NFr | u2/gD | Inertial force | Gravitational force | Fluid flow with free surface |
| Weber number | NWe | u2rD/s | Inertial force | Surface force | Fluid flow with interfacial forces |
| Mach number | NMa | u/c | Local velocity | Sonic velocity | Gas flow at high velocity |
| Drag coefficient | CD | FD/(ru2/2) | Total drag force | Inertial force | Flow around solid bodies |
| Friction factor | f | tw/(ru2/2) | Shear force | Inertial force | Flow though closed conduits |
| Pressure coefficient | CP | Dp/(ru2/2) | Pressure force | Inertial force | Flow though closed conduits. Pressure drop estimation |
When the velocity at each location is constant, the velocity field is invarient with time and the flow is said to be steady.
Uniform flow:
Uniform flow occurs when the magnitude and direction of velocity do not change from point to point in the fluid.
Flow of liquids through long pipelines of constant diameter is uniform whether flow is steady or unsteady.
Non-uniform flow occurs when velocity, pressure etc., change from point to point in the fluid.
Steady, unifrom flow:
Conditions do not change with position or time.
e.g., Flow of liquid through a pipe of uniform bore running completely full at constant velocity.
Steady, non-unifrom flow:
Conditions change from point to point but do not with time.
e.g., Flow of a liquid at constant flow rate through a tapering pipe running completely full.
Unsteady, unifrom Flow: e.g. When a pump starts-up.
Unsteady, non-unifrom Flow: e.g. Conditions of liquid during pipetting out of liquid.
