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Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).

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Chapter 11

TURBULENT FLOW

Velocity distribution is relatively uniform and velocity profile is much flatter than the corresponding laminar flow parabola for the same mean velocity, as shown below :

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Shear stress in turbulent flow

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

where, µ = dynamic coefficient of viscosity (fluid characteristic) h = eddy viscosity coefficient (flow characteristic)

eddy viscosity come into picture due to turbulence effect
Hydro-Dynamically Smooth And Rough Pipes 
If the average height of irregularities (k) is greater than the thickness of laminar sublayer (d'), then the boundary is called hydrodynamically Rough.
If the average height of irregularities (k) is less than the thickness of laminar sublayer (d'), then the boundary is called hydrodynamically smooth.
On the basis of NIKURADSE's EXPERIMENT the boundary is classified as :

Hydrodynamically smooth : k/d < 0.25'

Boundary in transition :6.0 < k/d < 0.25

Hydrodynamically Rough : k/d > 6.0

R/K is known as specific roughness. where ‘k’ is average height of roughness and‘R’ is radius of the pipe.
Velocity Distribution For Turbulent Flow in Pipes

(a) Prandtl’s universal velocity distribution equation :

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
where

= shear or friction velocity..

y = distance from pipe wall R = radius of pipe.

The above equation is valid for both smooth and rough pipe boundaries.
(b) Karman - Prandtl Velocity distribution equation :
(i) Hydro Dynamically Smooth pipe

(ii) Hydro Dynamically Rough pipe

where
V* = shear velocity y = distance from pipe wall k = average height of roughness v = kinematic viscosity.
(c) Velocity distribution in terms of mean velocity

The above equation is for both rough and smooth pipes.
Friction Factor
(a) Friction factor ‘f ’ for laminar flow :

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev where Re = Reynolds number

(b) Friction factor ‘f ’ for transition flow :

There exists no specific relationship between f and Re for transition flow in pipes.

(c) Friction factor (f) for turbulent flow in smooth pipes :

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

(d) Friction factor (f) for turbulent flow in rough pipes

Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

This equation shows that for rough pipes friction factor depends only on R/K (Relative smoothness) and not on Reynolds number (Re)

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