Turbulent Boundary layer thickness on a flat plate

In summary, the conversation discusses the calculation of turbulent boundary layer thickness on a flat plate using two different formulas: the well-known Schlichting formula and the Hansen Formula. The speaker offers to provide the derivation for the Schlichting formula if needed.
  • #1
Mitra
12
0
I am really confused. Would you please tell me what the turbulent boundary layer thickness is on a flat plate?

There is a well-known Schlichting formula in the previous editions of his book “boundary layer theory”, which is:

[tex]\delta = 0.37 X Re^{-0.2}[/tex]

But actually I could not find this relationship in his 8th edition book, instead I found the Hansen Formula, which is:

[tex] \frac {\delta U}{\nu} = 0.14 \frac{Re}{\ln Re} G(\ln Re)[/tex]
 
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  • #2
Well I have the complete derivation for the Schlichting formula for the turbulent boundary layer.
If you need it, just ask. my e-mail id is waqaskhan200@yahoo.com
 
  • #3


Thank you for your question. The turbulent boundary layer thickness on a flat plate refers to the distance from the surface of the flat plate to the point where the velocity of the fluid flow reaches 99% of the free stream velocity. In simpler terms, it is the distance from the surface at which the flow becomes turbulent.

As for the formulas you mentioned, the Schlichting formula is a well-known empirical relation that gives an estimate of the boundary layer thickness for a turbulent flow over a flat plate. However, as you mentioned, it is not included in the latest edition of Schlichting's book. The Hansen formula, on the other hand, is a modified version of the Schlichting formula that takes into account the effect of pressure gradient on the boundary layer. Both formulas are commonly used in engineering applications to estimate the boundary layer thickness.

It is important to note that these formulas are empirical and may not give an exact value for the boundary layer thickness, as it depends on various factors such as the Reynolds number, surface roughness, and pressure gradient. Therefore, it is always recommended to validate these formulas with experimental data for a specific flow situation.
 

1. What is a turbulent boundary layer on a flat plate?

A turbulent boundary layer is a layer of fluid that forms on the surface of a flat plate when it is exposed to a moving stream of fluid. It is characterized by chaotic and irregular flow patterns, which result in increased mixing and energy transfer between the fluid and the surface.

2. How is the thickness of a turbulent boundary layer on a flat plate determined?

The thickness of a turbulent boundary layer on a flat plate is typically determined by measuring the distance from the surface where the velocity of the fluid reaches 99% of the free stream velocity. This distance is known as the boundary layer thickness and can be calculated using theoretical equations or measured experimentally.

3. What factors affect the thickness of a turbulent boundary layer on a flat plate?

The thickness of a turbulent boundary layer on a flat plate is affected by the velocity and viscosity of the fluid, as well as the surface roughness and shape of the flat plate. Other factors such as pressure gradient and temperature differences can also influence the boundary layer thickness.

4. Why is the thickness of a turbulent boundary layer important in fluid dynamics?

The thickness of a turbulent boundary layer is important in fluid dynamics because it affects the drag force on the surface of the flat plate. A thicker boundary layer results in higher drag, which can have implications for the performance and efficiency of various systems such as airplanes, ships, and cars.

5. How can the thickness of a turbulent boundary layer be reduced?

There are several methods for reducing the thickness of a turbulent boundary layer, such as using a smooth and streamlined surface, increasing the velocity of the fluid, or introducing turbulence control devices. Additionally, manipulating the properties of the fluid, such as temperature or viscosity, can also affect the thickness of the boundary layer.

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