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**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.

τ = ρu'v'

u' and v’ fluctuating component of velocity.

τ = ρl^{2}(du/dy)^{2}

where, l = Mixing length

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

u = u_{max} + 2.5u*log_{e}y/R

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 (umax) and local velocity (u) at any point is given by

u_{max} -u = 5.75u*log_{10R/y}

Hydrodynamically pipe

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

u* = shear velocity =

v = Kinematic viscosity of fluid

y = Distance from the pipe wall

k = Roughness factor

Velocity distribution in terms of average velocity

[(u - u¯) / u*] = 5.75 log_{10} (y/R) + 3.75

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

Coefficient of friction f = 16/R (for laminar flow)

(for smooth pipe)

(for rough pipe)

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