Blasius Solution for Boundary Layer

In summary, the Blasius solution is only valid for the entrance region of an underdeveloped pipe, where the boundary layer thickness is small compared to the radius of the pipe. This is because the solution assumes a constant pressure across a flat plate, which is not true for pipe flow.
  • #1
ccrook
14
0
Is the Blasius solution valid for internal flow in an underdeveloped pipe? Can the function for the boundary layer thickness be used to calculate when the boundary layers will meet in the center of the pipe? I don't see how it could be valid since the assumption in its derivation is that pressure is constant across the flat plate, so dP/dx = 0 which is not true for pipe flow. Any thoughts?
 
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  • #2
It is valid for the portion of the entrance region in which the Blasius BL thickness is small compared to the radius of the pipe. In this region, the pipe wall looks like an infinite flat plate.
 

1. What is the Blasius Solution for Boundary Layer?

The Blasius Solution for Boundary Layer refers to a mathematical solution proposed by German engineer and physicist Heinrich Blasius in 1908. It is a simplified model that describes the behavior of a boundary layer, which is the thin layer of fluid that forms on the surface of an object moving through a fluid medium.

2. What are the assumptions of the Blasius Solution?

The Blasius Solution assumes that the flow is laminar, incompressible, and steady. It also assumes that the fluid properties are constant and the velocity at the edge of the boundary layer is zero.

3. How is the Blasius Solution derived?

The Blasius Solution is derived by solving the Navier-Stokes equations, which describe the motion of a fluid, for a specific set of boundary conditions. These equations are simplified using the assumptions mentioned above, and the resulting differential equation is solved using the method of similarity.

4. What are the applications of the Blasius Solution?

The Blasius Solution has various applications in the field of fluid dynamics, such as in the design of aircraft wings, wind turbines, and marine vessels. It is also used in the study of heat transfer, as the Blasius Solution can be extended to solve for the temperature profile in a boundary layer.

5. What are the limitations of the Blasius Solution?

The Blasius Solution is only applicable to laminar boundary layers, and cannot accurately model turbulent flows. It also assumes that the fluid properties are constant, which may not hold true for some real-life scenarios. Additionally, the Blasius Solution is limited to two-dimensional flows and cannot be applied to three-dimensional or unsteady flows.

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