Explain Boundary Layer Concept along a thin plate?

When a real fluid (viscous fluid) flows past a stationary solid boundary, a layer of fluid which comes in contact with the boundary surface, adheres to it (on account of viscosity) and condition of no slip occurs (The no-slip condition implies that the velocity of fluid at a solid boundary must be the same as that of boundary itself). Thus the layer of fluid which cannot slip away from the boundary surface undergoes retardation; this retarded layer further causes retardation for the adjacent layers of the fluid, thereby developing a small region in the immediate vicinity of the boundary surface in which the velocity of the flowing fluid increases rapidly from zero at the boundary surface and approaches the velocity of main stream. The velocity gradient will be set up and this gradient develops shear resistant which retards the fluid. So, the boundary layer develops at the leading edge.

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When a real fluid (viscous fluid) flows past a stationary solid boundary, a layer of fluid which comes in contact with the boundary surface, adheres to it (on account of viscosity) and condition of no slip occurs (The no-slip condition implies that the velocity of fluid at a solid boundary must be the same as that of boundary itself). Thus the layer of fluid which cannot slip away from the boundary surface undergoes retardation; this retarded layer further causes retardation for the adjacent layers of the fluid, thereby developing a small region in the immediate vicinity of the boundary surface in which the velocity of the flowing fluid increases rapidly from zero at the boundary surface and approaches the velocity of main stream. The velocity gradient will be set up and this gradient develops shear resistant which retards the fluid. So, the boundary layer develops at the leading edge.

Near the leading edge of solid surface, where thickness is small, the flow in the boundary layer can be laminar and the layer is said to be laminar boundary layer. The velocity profile in the laminar layer is approximately parabolic.

As the thickness of the boundary layer increases in the downstream direction, the laminar layer becomes unstable and the motion within it will be disturbed and becomes irregular which leads to the transition from laminar to turbulent boundary layer. This zone is called a transition zone.

Further downstream the transition zone, the boundary layer is turbulent and continues to grow in thickness. The velocity profile in the turbulent boundary layer is not parabolic but follows a logarithmic law. The velocity gradient at turbulent layer is larger than that in laminar layer.

If the plate is very smooth, even in the zone of turbulent boundary layer, there exists a very thin layer immediately adjacent to the boundary, in which the flow is laminar. This thin layer is commonly known as laminar sublayer, and its thickness is represented by δ. Hence, exponential or logarithmic velocity distribution law cannot be applied within the laminar sublayer. Nikuradses experimental studies have shown that, for laminar sublayer,

`delta^'=(11.6 nu)/V^*`

Where, `V^*=root()(tau_0/rho)` is known as shear velocity.

The characteristics of a boundary layer may be summarised as follows:

1.  δ (thickness of boundary layer) increases as distance from leading edge x increases.

2.  δ decreases as U increases.

3.  δ increases as kinematic viscosity (`nu`) increases.

4.  `tau_0~~(muU)/delta`; hence `tau_0` decreases as x increases. However, when boundary layer becomes turbulent, it shows a sudden increase and then decreases with increasing x.

5. When U increases in the downward direction, boundary layer growth is reduced. 

6. When U decreases in the downward direction, flow near the boundary is further retarded, boundary layer groExplain the concept of Boundary Layer.

7. The various characteristics of the boundary layer on flat plate (e.g variation of δ, `tau_0` or force F) are governed by inertial and viscous forces; hence they are functions of either `Ux/nu` or  `UL/nu` .

8. If `(Ux)/nu <5`*`10^5`,boundary layer is laminar (velocity distribution is parabolic).  

9. If `(Ux)/nu >5`*`10^5`,boundary layer is turbulent on that portion (velocity distribution follows Log law or a power law).

10. Though the velocity distribution would be a parabolic curve in a laminar sub-layer zone, for small thickness we can assume the velocity distribution to be linear.