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 Hydrodynamically smooth and rough boundaries Fig: Definition of smooth and rough boundaries In general, a boundary with irregularities of large average height 'K' on its surface is considered to  be a rough boundary and one with smaller 'K' value is considered as a smooth boundary. ✓ However, for a proper classification of smooth and rough boundaries, the flow and fluid characteristics are required to be considered in addition to the boundary characteristics. ✓ As the flow outside the laminar sub-layer is turbulent, eddies of various sizes are present which try  to penetrate through the laminar sublayer. But, due to greater thickness of laminar sub-layer ,   eddies can't reach the surface irregularities and thus the boundary acts as a smooth boundary. Such  a boundary is termed as " Hydro-dynamically Smooth Boundary" ✓ With the increase in Reynold's no (Re), the thickness of the laminar sub-layer  decreases and it's  can even become much smaller

  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. Ad: https://happyshirtsnp.com/   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 fl