Fluid Mechanics............../Kinematics in FM

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

Steady flow:
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.