Turbulent Flow

By Deepanshu Rastogi|Updated : November 24th, 2021

This article contains basic notes on the "Turbulent Flow"  topic of the "Fluid Mechanics & Hydraulics" subject.           

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 τ= 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

12-Elementary-turbulent-flow (2) 

where, l = Mixing length

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

12-Elementary-turbulent-flow (3)

Umax = centre velocity

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

u* = Shear velocity 12-Elementary-turbulent-flow (4)

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

12-Elementary-turbulent-flow (5)

Karman-Prandtl velocity distribution equation.

Hydro dynamically pipe

12-Elementary-turbulent-flow (6)


12-Elementary-turbulent-flow (7)

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

u* = shear velocity = 12-Elementary-turbulent-flow (8)

v = Kinematic viscosity of fluid

y = Distance from pipe wall

k = Roughness factor

Velocity distribution in terms of average velocity

12-Elementary-turbulent-flow (9)

12-Elementary-turbulent-flow (10)

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 12-Elementary-turbulent-flow (12) (for laminar flow)

12-Elementary-turbulent-flow (13) (for smooth pipe)

12-Elementary-turbulent-flow (14)

(for smooth pipe)

12-Elementary-turbulent-flow (15) (for rough pipe)

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write a comment
Manisha Choudhary
Am unable to save the notes ,it's not getting saved by tapping on the bookmark option
Chan Doraemi

Chan DoraemiSep 27, 2019

Velocity distribution in terms of average velocity in smooth pipe  is wrong...it is 1.75 not 5.5

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