Boundary Layer displacement thickness

In summary, the displacement thickness, \delta*, pushes the streamlines outside a boundary layer away from the wall. This can be calculated using the formula \delta*=\int^{\infty}_{0}(1-\frac{u}{U})dy for flow over a plate with length x=4m. To find the equation of the streamline that touches the boundary layer at x=4 and y=\delta^{b}, the boundary layer displacement thickness needs to be calculated. However, it is unclear how to do this without a clear understanding of the given problem.
  • #1
VooDoo
59
0
Hey guys,


The streamlines just outside a boundary layer are pushed away from the wall by the displacement thickness [tex]\delta[/tex]* and I understand that;

[tex]\delta[/tex]*=[tex]\int^{\infty}_{0}[/tex](1-[tex]\frac{u}{U}[/tex])dy

Now this is for flow over a plate with length x=4m. At x=0 is the leading edge and at x=4 [tex]\delta[/tex] = [tex]\delta^{b}[/tex]

Now been told to find the equation of the streamline i.e. y=y(x) that touches the boundary layer at x=4 (and y = [tex]\delta^{b}[/tex] I guess).

I know I have to calculate the boundary layer displacement thickness...but I am unsure of how to do that and what I should do after that.
 
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  • #2
delta = delta ^ b is a mathematical inequality? Therefore if you rewrite the problem literally from your homework a bit more clearly I might be able to help you with this one.
 

What is Boundary Layer Displacement Thickness?

Boundary Layer Displacement Thickness is a measurement of the distance between the physical surface of an object and the point at which the flow of a fluid is no longer affected by the presence of the object. It is often used to study the interactions between a solid surface and a moving fluid, such as air over an airplane wing.

How is Boundary Layer Displacement Thickness calculated?

Boundary Layer Displacement Thickness is typically calculated by integrating the velocity profile of the fluid flow over the surface of the object. This can be done using mathematical models or through experimental methods such as hot wire anemometry.

Why is Boundary Layer Displacement Thickness important?

Boundary Layer Displacement Thickness is an important parameter in fluid dynamics as it can influence the drag and lift forces acting on an object. It is also used in the design of aerodynamic surfaces and to understand the effects of surface roughness on fluid flow.

How does Boundary Layer Displacement Thickness change with flow conditions?

The value of Boundary Layer Displacement Thickness can vary depending on the flow conditions, such as the speed and viscosity of the fluid. It also increases as the Reynolds number (a ratio of inertial forces to viscous forces) increases.

What are some real-world applications of Boundary Layer Displacement Thickness?

Boundary Layer Displacement Thickness is used in a wide range of industries, including aerospace, automotive, and marine engineering. It is used to optimize the design of vehicles and structures to reduce drag and improve performance. It is also used in hydrodynamics research to understand the movement of fluids around objects in motion.

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