Hii,
In fluid dynamics we have to study this theory given by Ludwig Prandtl, known as Boundary Layer Theory.
When a fluid flowing with laminar flow through an infinite thickness with an uniform velocity of U, passes through a boundary which can be the surface of a tube or any bed or wall, the velocity of the the fluid particles near to the boundary is obstructed by the frictional force of the surface and the adhesion of the particle to the surface.
Now these obstructed particles having almost zero velocity are attracting the nearby particles due to the cohesive force known as the viscosity. So the velocity of the particles of the next layers is also retarded.
This way the velocity of the flow changes from the U at the boundary to zero and it increases gradually as we go to the next layer away from the boundary layer.
This increase is almost parabolic in nature and after a certain distance from the boundary layer the flow again gains its uniform velocity U.
This distance at a section depends upon the distance of the section from the starting point of the boundary flow. At the starting point of the boundary flow, the velocity of all the layers is U, but as we go to the further sections, the velocity will decrease near to the boundary layer and gradually increases to its initial value of U at a thickness of 'd'. This 'd' goes on increase with the increase in the distance of the section from the starting point of the boundary section.
Thank You!!
In fluid dynamics we have to study this theory given by Ludwig Prandtl, known as Boundary Layer Theory.
Boundary Layer Theory:
When a fluid flowing with laminar flow through an infinite thickness with an uniform velocity of U, passes through a boundary which can be the surface of a tube or any bed or wall, the velocity of the the fluid particles near to the boundary is obstructed by the frictional force of the surface and the adhesion of the particle to the surface.
Now these obstructed particles having almost zero velocity are attracting the nearby particles due to the cohesive force known as the viscosity. So the velocity of the particles of the next layers is also retarded.
This way the velocity of the flow changes from the U at the boundary to zero and it increases gradually as we go to the next layer away from the boundary layer.
This increase is almost parabolic in nature and after a certain distance from the boundary layer the flow again gains its uniform velocity U.
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| Boundary Layers - Laminar and Turbulent Boundary Layers (Source: Wikipedia.org) |
This distance at a section depends upon the distance of the section from the starting point of the boundary flow. At the starting point of the boundary flow, the velocity of all the layers is U, but as we go to the further sections, the velocity will decrease near to the boundary layer and gradually increases to its initial value of U at a thickness of 'd'. This 'd' goes on increase with the increase in the distance of the section from the starting point of the boundary section.
Remember:
- If the velocity is increased the value of 'd' decreases.
- If viscosity is increased the value of 'd' increases.
- If upstream pressure is increased, the value of 'd' increases
- When Reynold's number R< 2 00 the flow in the boundary layer is laminar and the boundary layer is parabolic and if R > 4 * 10^5 then the boundary layer is turbulent.
Thank You!!
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