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

= 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
    Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    (ii) Hydro Dynamically Rough pipe
    Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    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
     Chapter 11 Turbulent Flow - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev
    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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