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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 :

- 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)

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