- 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 :
= 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
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)