Fluid Dynamics: Kinematics and Streamlines

Kinematics

• Kinematics studies motion without considering forces.
• Velocity is crucial in fluid flow analysis to determine pressure and forces.

Streamlines

• Streamlines are imaginary lines tangent to velocity vectors.
• No flow crosses streamlines.
• A differential equation describes streamlines: dx/u = dy/v = ds/w.

Path Lines

• A path line shows the trajectory of a particular fluid particle.
• It tracks the particle's movement over time.

Streak Lines

• Streak lines trace the path of particles passing a fixed point.
• Dye or smoke are typical tracers.
• In steady flow, streamlines, path lines, and streak lines coincide.

Instantaneous Streamlines

• In unsteady flow, streamlines change with time.
• Instantaneous streamlines depict the streamline position at a specific time.

Stream Tubes

• Streamlines forming a closed curve create a stream tube.
• Fluid cannot cross a stream tube's boundary.
• Fluid entering a stream tube equals fluid leaving.

Flow Classifications

• Steady/Unsteady: Steady flow has constant properties over time, while unsteady flow changes with time.

• Uniform/Non-uniform: Uniform flow has constant velocity throughout, while non-uniform flow changes with position.

• Laminar/Turbulent: Laminar flow is smooth and in layers, while turbulent flow is erratic with eddies.

• Compressible/Incompressible: Incompressible fluids have constant density, while compressible fluids do not.

• Rotational/Irrotational: Rotational flow involves particle rotation, while irrotational flow does not.

• One, Two, and Three-Dimensional Flows: One-dimensional flow varies in one direction, two-dimensional in two, and three-dimensional in three.

Discharge (Rate of Flow)

• Discharge measures fluid quantity per second.
• Liquid discharge is volume per second (e.g., m³/s).
• Gas discharge is often weight or force per second (e.g., kgf/s, N/s).