Turbulent Flow | Mechanical Engineering SSC JE (Technical) PDF Download

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 :

• Shear stress in turbulent flow

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 :

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 :

 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 :

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

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