1 of 10

Fluid Mechanics: Types of Flows and Important Dimensionless Numbers

2 of 10

Introduction to Fluid Mechanics

  • - Definition: Fluid mechanics is the study of fluids (liquids and gases) in motion and at rest.
  • - Applications: Aerospace, automotive, energy systems, biomedical engineering.

3 of 10

Types of Fluid Flows (Classification by Characteristics)

  • 1. Laminar Flow: Smooth, orderly layers of fluid.
  • - Example: Slow-moving water in a pipe.
  • 2. Turbulent Flow: Chaotic, irregular motion with eddies and vortices.
  • - Example: Fast-moving river.
  • 3. Transitional Flow: Mixture of laminar and turbulent flow.
  • - Example: Flow at intermediate speeds.

4 of 10

Types of Fluid Flows (Other Classifications)

  • 1. Compressible vs. Incompressible Flow:
  • - Compressible: Density changes significantly (e.g., supersonic jets).
  • - Incompressible: Density remains constant (e.g., water in pipelines).
  • 2. Steady vs. Unsteady Flow:
  • - Steady: Properties do not change with time (e.g., constant water flow).
  • - Unsteady: Properties vary with time (e.g., pulsating blood flow).

5 of 10

Reynolds Number (Re)

  • - Definition: Ratio of inertial forces to viscous forces.
  • Re = ρvL / μ
  • - Interpretation:
  • - Re < 2000: Laminar Flow
  • - 2000 < Re < 4000: Transitional Flow
  • - Re > 4000: Turbulent Flow
  • - Applications: Pipe flow, aerodynamic studies.

6 of 10

Mach Number (Ma)

  • - Definition: Ratio of fluid velocity to the speed of sound.
  • Ma = v / c
  • - Interpretation:
  • - Ma < 1: Subsonic Flow
  • - Ma = 1: Sonic Flow
  • - Ma > 1: Supersonic Flow
  • - Ma > 5: Hypersonic Flow
  • - Applications: Aircraft design, compressible flow analysis.

7 of 10

Froude Number (Fr)

  • - Definition: Ratio of inertial forces to gravitational forces.
  • Fr = v / sqrt(gL)
  • - Interpretation:
  • - Fr < 1: Subcritical Flow (dominated by gravity)
  • - Fr = 1: Critical Flow
  • - Fr > 1: Supercritical Flow (dominated by inertia)
  • - Applications: Open channel flows, ship hydrodynamics.

8 of 10

Weber Number (We)

  • - Definition: Ratio of inertial forces to surface tension forces.
  • We = ρv²L / σ
  • - Interpretation:
  • - High We: Surface tension effects are negligible.
  • - Low We: Surface tension effects are significant.
  • - Applications: Droplet formation, liquid sprays.

9 of 10

Euler Number (Eu)

  • - Definition: Ratio of pressure forces to inertial forces.
  • Eu = p / (ρv²)
  • - Interpretation: Measures pressure differences in flow fields.
  • - Applications: Flow in pipelines, pressure drop analysis.

10 of 10

Summary

  • - Fluid flow is classified based on velocity, compressibility, and time dependence.
  • - Key dimensionless numbers:
  • - Reynolds Number (Re): Laminar vs. Turbulent
  • - Mach Number (Ma): Compressibility
  • - Froude Number (Fr): Gravity effects
  • - Weber Number (We): Surface tension
  • - Euler Number (Eu): Pressure forces

​

  • Thank You!