For a liner distribution of velocity profile in the laminar boundary layer on a flat plate given byu/U∞= y/δ, the ratio of displacement thickness (δ*) to the boundary layer thickness (δ) isa)1/5b)1/2c)1/3d)1/4Correct answer is option 'B'. Can you explain this answer?

Question

For a liner distribution of velocity profile in the laminar boundary layer on a flat plate given byu/U&infin;= y/&delta;, the ratio of displacement thickness (&delta;*) to the boundary layer thickness (&delta;) isa)1/5b)1/2c)1/3d)1/4Correct answer is option 'B'. Can you explain this answer?

Answer

The velocity profile in the laminar boundary layer on a flat plate can be approximated by a linear distribution, often referred to as the 'laminar boundary layer velocity profile.' This profile is given by the equation:

u/U = y/δ

where u is the local velocity, U is the freestream velocity, y is the distance from the surface of the flat plate, and δ is the thickness of the boundary layer.

In this equation, the ratio of u/U represents the normalized velocity, which varies linearly with the distance from the surface. As y increases, the normalized velocity u/U also increases, indicating an increase in the local velocity.

This linear distribution of velocity profile is valid within the laminar boundary layer, which is the thin layer of fluid adjacent to the surface where viscosity effects dominate. Beyond the boundary layer, the flow transitions to the freestream flow, where the velocity is equal to U.

It's important to note that this linear velocity profile is an approximation and may not hold true for all cases. In reality, the velocity profile may deviate from linearity due to various factors such as pressure gradients, surface roughness, and transition to turbulence.

Answer

Concept:
Nominal boundary thickness as δ
Displacement thickness is given as

Calculation:

∴ The ratio of displacement thickness to boundary layer thickness will be =

Hence, option 2 is correct.

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