Development of the boundary layer
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The thickness of the boundary layer on a flat plate can be estimated using the following formulas: For a laminar boundary layer: δ/x = 4.64/Rex0.5; for a turbulent boundary layer: δ/x = 0.376/Rex0.2. Here, Rex = usxρ/μ, where us is the velocity in the main flow region and x is the distance from the leading edge of the plate. When Rex ≤ 2×105, the flow within the boundary layer is laminar; when Rex ≥ 3×106, the flow within the boundary layer is turbulent. Even when x becomes infinite, Rex does not become infinite, and if us is small, the flow remains turbulent.??????
Guys, let’s talk about it; I have a question!
That's how it is. The Reynolds number of fluid flow on the plate increases as the plate length increases. As the plate length tends to infinity, the Reynolds number also tends to infinity. When the Reynolds number is less than 2000, it is laminar flow. When the Reynolds number exceeds 2000, the boundary layer begins to separate. As the plate length tends to infinity, the Reynolds number also tends to infinity.
The boundary layer is the region where the velocity drops to within 99% of the incoming flow velocity, so X cannot be infinite. That’s how I understand it
I think your concept of boundary layer separation might be incorrect; please verify it. Additionally, your critical Rex value of 2000 applies to pipe flow; for flat plate flow, refer to the value provided by the original poster. This post was last edited by I love rainy days on 2009-3-5 08:26.]
We do indeed rarely consider the case where x is infinitely large, but I think your analysis is correct; theoretically, when x is infinitely large, turbulence will develop even if us is very small. But in reality, x cannot be infinitely large. Also, is it possible for turbulence to develop even when us is small, if the viscosity is very high? x is the distance in the flow direction from the leading edge of the plate. The distance over which the velocity changes, as you mentioned, is the distance perpendicular to the plate. Last edited by zhangyong6404 on 2009-3-5 09:45.]
Since the decelerating effect of the boundary layer gradually fades away, its boundary should extend to infinity away from the wall surface.
I agree with what was said on floor 6: when x is infinitely large, turbulence will develop even if us is very small. But in reality, x cannot be infinitely large
During flow over a flat plate, there are two types of boundary layers: laminar boundary layers and turbulent boundary layers； The distance at which the laminar boundary layer begins to transition into a turbulent boundary layer is called the critical distance, denoted by X. The size of Xc is related to the shape and roughness of the wall front edge, the properties of the fluid, and the flow velocity. For smooth flat wall surfaces, the range of the critical Reynolds number is 2×10^5 to 3×10^6. -------------This is the discussion from \"Fundamentals of Chemical Engineering Transport Processes\" (2nd edition) by Chen Tao. According to this reasoning, it is inevitable for flow over a flat plate to develop into turbulence; it’s just that the critical distance required varies? ? ! !