Turbulent Flow | Velocity and shear stress in turbulent flow

Turbulent Flow in Circular Pipe

• In laminar flow ( <2000) any disturbance produced is quickly damped out by the viscous resistance.

• At higher Re (Re>4000), the fluid motion is irregular and random. There is complete mixing of fluid due to collision of fluid masses with each other. The resulting flow is known as turbulent flow. The phenomenon of turbulent motion is known as turbulence.

• In turbulent flow, velocity fluctuation causes a continuous interchange of fluid masses between neighboring layers, which is accompanied by a transfer of momentum. This momentum transfers results in developing additional shear stress besides viscous shear stress. The additional shear stress is known as turbulent shear stress.

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Velocity in turbulent flow

In turbulent flow, velocity does not remain constant with time. The velocity at any instant is considered to be made up of a mean value and a fluctuating component.

Fig: Velocity variation in turbulent flow

Over large time 'T', mean of fluctuating component = 0 & the mean value is taken for computation purpose.

Similarly, in other directions,

v(t) = v + v' and w(t) = w + w'

Fluctuating component = mean velocity of layer 1- mean velocity of layer 2

Features of Turbulent Flow in Pipe

Fig: Comparison of velocity profile for laminar and turbulent flow

•Flatter velocity (more uniform) profile due to mixing of fluid layers and exchange of momentum
•Large velocity gradient (du/dy) near the wall resulting in more shear
•Additional shear stresses due to turbulence
•Higher frictional loss due to the formation of eddies, mixing and curving of path lines.

Shear stress in turbulent flow

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