Consider the following statements pertaining to boundary layer on a f...
For laminar boundary layer
For Turbulent boundary layer
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Consider the following statements pertaining to boundary layer on a f...
Reynolds number and boundary layer thickness on a flat plate
The given statements pertain to the boundary layer on a flat plate and the variation of its thickness with distance x from the leading edge. Let's analyze each statement and determine their correctness.
Statement 1: The thickness of the laminar boundary layer at a distance x from the leading edge varies as x^(1/2)
This statement is correct. The thickness of the laminar boundary layer, also known as the momentum boundary layer, increases with the square root of the distance x from the leading edge. This relationship is derived from the boundary layer theory and can be expressed mathematically as δ_laminar = (5x/√Re_x), where δ_laminar is the thickness of the laminar boundary layer and Re_x is the Reynolds number at distance x.
Statement 2: The thickness of the turbulent boundary layer at a distance x from the leading edge varies as x^(4/5)
This statement is correct. The thickness of the turbulent boundary layer, also known as the energy boundary layer, increases with the power of 4/5 of the distance x from the leading edge. This relationship is also derived from the boundary layer theory and can be expressed mathematically as δ_turbulent = (0.37x/Re_x^(1/5)), where δ_turbulent is the thickness of the turbulent boundary layer and Re_x is the Reynolds number at distance x.
Statement 3: The boundary layer is laminar when the Reynolds number is less than 5 × 10^5
This statement is correct. The laminar boundary layer exists when the flow has a low Reynolds number, typically less than 5 × 10^5. At lower Reynolds numbers, the flow is smooth and exhibits a laminar flow pattern. As the Reynolds number increases beyond this threshold, the flow becomes more turbulent, and the laminar boundary layer transitions to a turbulent boundary layer.
In conclusion, all the given statements are correct:
a) 1, 2, and 3.
Consider the following statements pertaining to boundary layer on a f...
For laminar boundary layer
For Turbulent boundary layer