Turbulence vs Laminar flow: Reynold’s number Explained

Reynold’s Number

The Reynolds number (Re) predicts whether a flow is laminar or turbulent. It’s a dimensionless number comparing inertial and viscous forces:

Where:

• : fluid density (kg/m³)
• v : average velocity (m/s)
• D : characteristic length (e.g., pipe diameter)
• μ : dynamic viscosity (Pa·s)
• : kinematic viscosity (m²/s)

Flow Type

Laminar : Re < 2,000
Transitional Turbulent : 2,000 < Re < 4,000
Turbulent : Re > 4,000

Turbulent vs Laminar Flow

Laminar Flow

Laminar flow is smooth and orderly. Fluid particles flow linearly. In parallel layers with no crossing of paths.

• Smooth streamlines
• Predictable velocity profile
• Low momentum diffusion
• Dominated by viscous forces

Turbulent Flow

Turbulent flow is chaotic. Fluid particles swirl and move in random paths, known as eddies. These vortices stir the flow, enhancing the momentum, thermal, and solute transport.

• Irregular streamlines
• Unpredictable velocity
• High momentum diffusion
• Dominated by inertial forces

Head Loss and Friction Factor

Darcy-Weisbach Equation

Head loss is related to the flow and the properties of the pipe according to the Darcy-Weisbach equation:

Where:
: head loss (m)
f : Darcy friction factor
L : length of pipe (m)
D : diameter of pipe (m)
v : average velocity (m/s)
g : acceleration due to gravity (9.81 m/s²)

The Darcy friction factor f is not something we assume; it’s what we’re trying to solve, basedon measurements and theory (fluid dynamics). It is a measure of the resistance offered by the pipe to the flowing fluid.

It depends on two things:

1. Reynolds number – Is the flow laminar or turbulent?
2. Pipe roughness – Is the pipe smooth like (PVC) or rough like (old cast iron)?

For Laminar Flow

We will use the formula derived from the Reynold’s Number:

For Turbulent Flow

We can use the Moody Chart or
Colebrook Equation:

Note: In most tests like Board Exams, GATE, and PEng, friction factor is given.