Fluid Kinematics

It is defined as, "study of motion of a body without considering the forces acting on it".

• If particle follow path  ⇰  Langrangian Approach (analogous to closed system analysis in thermodynamics).
  

• If follow domain or control volume  ⇰  Eulerian Approach. 

• For Flow field, Material derivative  ⇰  click here.
• Unsteady Effects  ⇰  deals with properties (like velocity, temperature, density) changes with time.
• Convective Effects  ⇰  change in acceleration due to change in space represented by spatial derivative.
• For Flow Pattern and Visualization  ⇰ click here. 

Stream Tube

It consists of a bundle of individual streamlines (like cables) which tells us whether the flow is accelerating or decelerating.

• If steady flow  ⇰  streamlines = pathlines = streaklines.

Potential Lines

These are the lines joining points of equal velocity potentials on streamlines.

Flow Net

A grid obtained by drawing a series of stream lines and equipotential lines.

• Flow net analysis assist design of an efficient boundary shapes.
• Used to calculate the flow at ground level.

Refractive Flow Visualization Technique

Flow visualization method used refractive property of light waves. There are two methods, namely:

1. Shadowgraph Technique
2. Schileren Technique

Plots of Flow Data

It is the representation of flow properties varying in time or space.

1. Profile Plot  ⇰  line graph
2. Vector Plot  ⇰  array of arrows indicating vector properties in time.
3. Contour Plot  ⇰  curves of contact values.

Types of Fluid Flow

1. 1D, 2D and 3D Flow

• 3D Flow  ⇰  Three velocity components are important and of equal magnitude. For eg: flow passes a wing.
• 2D Flow  ⇰  One of the velocity components may be small relative to other two. For eg: flow over an airfoil.
• 1D Flow  ⇰  Two velocity components may be small relative to other one. For eg: flow in open channel.

2. Steady & Unsteady Flow

• Steady Flow  ⇰  flow is not changing with time.
• Unsteady Flow  ⇰  flow is changing with time at a particular cross-section.

3. Uniform & Non-Uniform Flow

• Uniform Flow  ⇰  flow in which velocity is not changing with respect to space.
• Non-Uniform Flow  ⇰  flow in which velocity is changing with space.

4. Laminar & Turbulent Flow

• Laminar Flow  ⇰  Smooth flow and Re < 2300.
• Turbulent Flow  ⇰  Efficient mixing, velocity at any point fluctuates and Re > 4000.

5. Rotational & Irrotational Flow

• Rotational Flow  ⇰  The flow in which fluid particles while flowing along streamlines rotate about their own axis.
• Irrotational Flow  ⇰  Flow in which fluid particles do not rotate about their own axis.

6. Compressible & Incompressible Flow

• Compressible Flow  ⇰  if density is changing with time (mostly gases).
• Incompressible Flow  ⇰  if density is not changing with time (mostly liquids).

Control Volume and System Representation

System Approach (Integral approach)  ↠  no mass crosses the boundary and the total mass of the system remain fixed.

Control Volume Approach (Differential approach)  ↠  mass crosses the boundary (fixed interior volume).

• Control Surfaces  ↠  Boundaries which allow flow in or out.
• Reynolds Transport Theorem (RTT)  ↠  Relation between time rates of change of an extensive property for a system and for a control volume (i.e. relation between system and control volume approach).

Reynolds Transport Theorem (RTT)

The assumptions made during RTT Derivation are given below:

1. Fixed control volume.
2. One inlet and one outlet.
3. Uniform Properties.
4. Normal velocities to I and II sections.

If there were more than one inlet and one outlet:

• Sum the Inlets  ↠  I = I1 + I2 + I3 + . . . + In.
• Sum the Outlets  ↠  II = II1 + II2 + II3 + . . . + IIn.  

If velocity is not normal to the control surface:

The assumptions are: 

1. Time rate of change of extensive parameter of a system mass, momentum, etc.
2. Time rate of change of extensive parameter within CV.
3. Net flow rate of extensive parameter across entire CS.

Relationship between Material Derivative & RTT

• RTT deals with finite size CV (integral analysis).
• Material derivative deals with infinitesimal fluid particles (differential analysis).

Note:

• Langrangian VS Eulerian Approach
• Application of Fluid Mechanics
• Divergence and Curl

References:

• Material from Class Lectures + Book named Fundamentals of Fluid Mechanics by Munson, Young & Okiishi's (8th Edition) + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube (Engineering Sights).