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19. Laminar and Turbulent Flow (Contd.)

The chapter focuses on shear stresses in turbulent flow, detailing the Boussinesq model which introduces the concept of eddy viscosity. It discusses Reynolds' shear stress theories and Prandtl's mixing length theory, highlighting how shear stress in turbulent flows is significantly influenced by turbulence. Furthermore, it elucidates the relationship between kinematic quantities and flow characteristics in fluid dynamics, particularly in pipes.

Sections

Hydraulic Engineering

This section delves into the principles of shear stresses in turbulent flow, exploring concepts such as eddy viscosity, Reynolds shear stress, and the mixing length theory introduced by Prandtl.

1 Section Overview

Start current section content and materials

1.1 Lecture- 15
1.2 Laminar and Turbulent Flow (Contd.)

This section discusses the concept of shear stress in turbulent flow and introduces Boussinesq's model, which includes the significance of turbulent viscosity and Reynolds shear stress.

1.3 Shear Stress in Turbulent Flow

This section discusses shear stress in turbulent flow, emphasizing Boussinesq’s model, Reynolds shear stress, and Prandtl’s mixing length theory.

1.4 Boussinesq’s Model

Boussinesq’s model describes the shear stress in turbulent flow, highlighting the concept of eddy viscosity and its significance in hydraulic engineering.

1.5 Eddy Viscosity

Eddy viscosity is a concept in fluid dynamics, particularly relevant to turbulent flow, where it serves as an additional component of shear stress.

1.6 Reynolds Shear Stress

This section explores the concept of Reynolds shear stress in turbulent flow and its relationship with the flow's eddy viscosity and mixing length.

1.7 Prandtl's Mixing Length Theory

Prandtl’s Mixing Length Theory provides a framework for understanding shear stress in turbulent flows by relating fluctuating velocities to a defined mixing length.

1.8 Mixing length (lm)

This section explains the concept of mixing length in fluid dynamics, particularly how it relates to shear stress in turbulent flow.

1.9 Turbulent Flow in Pipes

This section discusses the additional shear stresses in turbulent flow compared to laminar flow and introduces the concepts of Boussinesq's model and Prandtl's mixing length theory.

Learning Objectives

  • Shear stress in turbulent flow includes components from both viscosity and turbulence.

  • Eddy viscosity and kinematic eddy viscosity are crucial in understanding turbulent flow behavior.

  • Reynolds shear stress involves fluctuating velocity components and can be calculated using Prandtl's mixing length theory.

Key Concepts

Eddy Viscosity

A coefficient that describes the turbulent shear stress in a fluid and varies with flow conditions.

Reynolds Shear Stress

The shear stress due to turbulence, expressed as the average of the product of velocity fluctuations in perpendicular directions.

Mixing Length Theory

A concept introduced by Prandtl that relates turbulence characteristics in a fluid to the average velocity gradient and distance from the wall.

Practice Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting
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