Hydro-dynamically smooth and rough boundaries

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(a) Smooth Boundary

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(b) Rough Boundary

Let the average height of the irregularities projecting from the surface of boundary be denoted as ‘K’.

Now, if the value of ‘K’ is large for a boundary then the boundary is called as Rough boundary.

And if the value of ‘K’ is smaller or less, then the boundary is known as Smooth boundary.

This is the classification of rough and smooth boundaries based on boundary characteristics. But for proper classification flow and fluid characteristics are also considered.

Hydro-dynamically smooth boundary

1) For a turbulent flow analysis, the flow is divided into two parts or portions.

2) The first portion consists of a thin layer of fluid in the immediate neighbourhood of the boundary, where the viscous shear stress is stronger whereas the shear stress due to turbulent is negligible. This is known as laminar sublayer.

3) The second portion of flow is the one where shear stress due to turbulence is higher or large as compared to the viscous shear and this zone is called as Turbulent zone.

4) The zone upto which or the height upto which the effect of viscosity predominates is denoted by $δ'$.

5) So, we can say that if the average velocity height ‘K’ is less than ‘$\delta'$’, then the boundary is called as Smooth boundary.

6) This happens because, outside the laminar sub-layer the flow is turbulent and eddies of various sizes present in the turbulent flow try to penetrate through the laminar sub-layer, but due to the great thickness of laminar sub-layer the eddies are unable to reach the surface irregularities and so the boundary behaves as smooth boundary.

Hydro-dynamically rough boundary

1) If the Reynolds number of the flow increases, the thickness of laminar sub-layer decreases.

2) If this happens, then the average height ‘K’ of irregularities is above the laminar sub-layer and thus the eddies present will come in contact with irregularities of the surface and lot of energy will be lost.

3) Such a boundary is known as Hydro-dynamically rough boundary.

Conditions from Nikuradse’s experiment:-

1) If $\left(\dfrac {K’}{\delta'}\right)\lt0.25$, (smooth boundary)

2) If $\left(\dfrac {K’}{\delta'}\right)\gt6.0$, (Rough boundary)

3) If $0.25\lt\left(\dfrac {K’}{\delta'}\right)\lt6.0$, (boundary is in transition)


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