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Friday, 7 September 2018

SHEAR STRESS IN TURBULENT FLOW

We were discussing the concept of laminar and turbulent flow, Reynolds experiment, frictional loss in pipes, derivation of expression for loss of head due to friction in pipes and  also co-efficient of friction in terms of shear stress, in the subject of fluid mechanics, in our recent posts. 

Now we will go ahead to see the basics of shear stress in turbulent flow, in the subject of fluid mechanics, with the help of this post. 

As we know that shear stress in case of viscous flow is provided by Newton’s law of viscosity and it is as mentioned here. 

Similarly, J Boussinesq has explained the turbulent shear as mentioned here 
Where,
τt = Shear stress due to turbulence
η = Eddy viscosity
ữ = Average velocity at a distance y from boundary 

Ratio of eddy viscosity and mass density will be called as kinematic eddy viscosity and will be displayed by ε. We can write kinematic eddy viscosity as mentioned here. 

ε = η /ρ 

If shear stress due to viscous flow will also be considered then we will have following equation for the total shear stress and it is as mentioned here. 
For laminar flow, η = 0 

For any other case, the value of η might be several thousand times the value of μ. 

Further we will go ahead to see the minor head losses in pipe flow, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal  
Image courtesy: Google  

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