Turbulent Flow – free study notes for Diploma / BTech.

1. Introduction

Turbulent flow is a type of fluid motion characterized by irregular fluctuations, eddies, and mixing of fluid particles. Unlike laminar flow (smooth and orderly), turbulent flow is chaotic and highly energetic.

It is commonly observed in:

• Rivers and oceans
• Airflow over aircraft wings
• Flow in large pipes at high velocity

2. Nature of Turbulent Flow

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Key characteristics:

• Random and irregular motion
• Presence of eddies and vortices
• High mixing of fluid particles
• Velocity at a point fluctuates with time

3. Reynolds Number and Turbulence

The nature of flow is determined using Reynolds number:$$Re = \frac{\rho V D}{\mu}$$Re=μρVD​

Where:

• $\rho$ρ = density
• $V$V = velocity
• $D$D = characteristic length (diameter)
• $\mu$μ = viscosity

Flow Regimes:

• $Re < 2000$Re<2000 → Laminar flow
• $2000 < Re < 4000$2000<Re<4000 → Transitional flow
• $Re > 4000$Re>4000 → Turbulent flow

4. Velocity Distribution in Turbulent Flow

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• Velocity profile is flatter (fuller) compared to laminar flow
• High velocity gradient near the wall
• Described by logarithmic laws

5. Characteristics of Turbulent Flow

(a) Irregularity

• Motion is unpredictable and random

(b) Diffusivity

• High mixing enhances heat and mass transfer

(c) Rotationality

• Flow contains vorticity and circulation

(d) Energy Dissipation

• Mechanical energy converts into heat due to friction

6. Turbulent Shear Stress

In turbulent flow, shear stress has two components:$$\tau = \mu \frac{du}{dy} + \rho u’v’$$τ=μdydu​+ρu′v′

Where:

• $\mu \frac{du}{dy}$μdydu​ → Viscous shear stress
• $\rho u’v’$ρu′v′ → Turbulent (Reynolds) stress

7. Reynolds Stresses

• Caused by velocity fluctuations
• Represent momentum transfer due to turbulence
• Important in analyzing turbulent flow mathematically

8. Boundary Layer in Turbulent Flow

• Boundary layer becomes thicker
• Higher shear stress at wall
• More resistance but better mixing

Comparison with Laminar Boundary Layer:

Property	Laminar	Turbulent
Flow nature	Smooth	Chaotic
Mixing	Low	High
Energy loss	Low	High
Velocity profile	Parabolic	Fuller

9. Energy Loss in Turbulent Flow

Energy losses are higher due to:

• Increased friction
• Formation of eddies
• Continuous energy dissipation

This is important in:

• Pipe design
• Pump selection
• Hydraulic systems

10. Darcy–Weisbach Equation

Used to calculate head loss in turbulent pipe flow:$$h_f = \frac{f L V^2}{2gD}$$hf​=2gDfLV2​

Where:

• $f$f = friction factor
• $L$L = pipe length
• $D$D = diameter

11. Turbulence Models

Due to complexity, turbulence is studied using models:

• Reynolds Averaged Navier–Stokes (RANS)
• k–ε model
• k–ω model

Used in Computational Fluid Dynamics (CFD).

12. Applications of Turbulent Flow

• Mixing of fluids in chemical industries
• Combustion processes
• Aerodynamics (aircraft, automobiles)
• Heat exchangers
• River and environmental engineering

13. Advantages and Disadvantages

Advantages:

• Better mixing
• Improved heat transfer
• Efficient chemical reactions

Disadvantages:

• Higher energy loss
• Increased drag
• Noise and vibration

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