Turbulent Flow | Fluid Mechanics for Civil Engineering - Civil Engineering (CE) PDF Download

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 = ρl²(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_ey/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 log₁₀ (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)