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,

τ

_{t }= 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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