Turbulent Flow

Turbulent Flow

Turbulent Flow: Turbulent flow is a flow regime characterized by the following points as given below

Shear stress in the turbulent flow

where, τ_v and τ_t = shear stress due to viscosity and turbulence.

η = eddy viscosity coefficient.

Turbulent shear stress by Reynolds

τ = ρu’v’

u' and v’ fluctuating component of velocity.

Shear stress in turbulent flow by Prandtl

where, l = Mixing length

The velocity distribution in the turbulent flow for pipes is given by the expression.

U_max = centre velocity

where, y = Distance from the pipe wall, R = radius of the pipe

u* = Shear velocity 

Velocity defect is the difference between the maximum velocity (u_max) and local velocity (u) at any point is given by

Karman-Prandtl velocity distribution equation.

Hydro dynamically pipe

where, u = velocity at any point in the turbulent flow

u* = shear velocity = 

v = Kinematic viscosity of fluid

y = Distance from pipe wall

k = Roughness factor

Velocity distribution in terms of average velocity

Common Mean Velocity Distribution Equation: (Very Important for Exams)

[(u-u¯)/ u*]= 5.75 log₁₀ (y/R) + 3.75             

(This is valid for both rough and smooth pipes, that's why it is referred as Common Mean Velocity Distribution Equation) 

Coefficient of friction  (for laminar flow)

 (for smooth pipe)

(for smooth pipe)

 (for rough pipe)

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