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, τv and τt = 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.
Umax = 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
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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Comments
write a commentManisha ChoudharyJul 20, 2018
Chan DoraemiSep 27, 2019
Dev RupAug 9, 2021