Consider a steady, two-dimensional, laminar, incompressible flow of water over a horizontal flat plate of length $L$ with Reynolds number, $Re_L = 10^4$. The flat plate is aligned with the incoming free-stream flow. The $x$-axis is along the length of the plate while the $y$-axis is normal to the plate. The respective velocity components are $u$ and $v$.

Which of the following statements is/are TRUE?

Question

Which of the following statements is/are TRUE?

Answer 1

All four statements describe flow over a flat plate at Reynolds number $10^4$, low enough to stay laminar over the full length. Each claim can be checked against the basic boundary layer picture, a thin viscous layer next to the wall with the free stream almost undisturbed just outside it.

For the flow within the boundary layer, $u \gg v$: true. Flow inside the layer runs mostly parallel to the plate, and the small velocity normal to the wall, $v$, stays far smaller than the streamwise velocity $u$.
For the flow within the boundary layer, $\partial u/\partial y \gg \partial u/\partial x$: true. $u$ rises from zero at the wall to nearly the free stream value across a very thin layer in $y$, a much sharper change than the slow growth of the layer along $x$.
The flow within the boundary layer is irrotational and inviscid: false. The boundary layer is exactly where viscosity acts and where the velocity gradient produces vorticity, so calling it inviscid and irrotational contradicts its own definition.
The thickness of the boundary layer is much less than the length of the flat plate: true. Using $\delta/L \approx 5/\sqrt{Re_L}$ with $Re_L = 10^4$ gives $\delta/L \approx 0.05$, so the layer is only about 5 percent as thick as the plate is long.

So the true statements are the first, second and fourth, giving option A, B, D.

Answer 2

All four statements describe flow over a flat plate at Reynolds number $10^4$, low enough to stay laminar over the full length. Each claim can be checked against the basic boundary layer picture, a thin viscous layer next to the wall with the free stream almost undisturbed just outside it.

For the flow within the boundary layer, $u \gg v$: true. Flow inside the layer runs mostly parallel to the plate, and the small velocity normal to the wall, $v$, stays far smaller than the streamwise velocity $u$.
For the flow within the boundary layer, $\partial u/\partial y \gg \partial u/\partial x$: true. $u$ rises from zero at the wall to nearly the free stream value across a very thin layer in $y$, a much sharper change than the slow growth of the layer along $x$.
The flow within the boundary layer is irrotational and inviscid: false. The boundary layer is exactly where viscosity acts and where the velocity gradient produces vorticity, so calling it inviscid and irrotational contradicts its own definition.
The thickness of the boundary layer is much less than the length of the flat plate: true. Using $\delta/L \approx 5/\sqrt{Re_L}$ with $Re_L = 10^4$ gives $\delta/L \approx 0.05$, so the layer is only about 5 percent as thick as the plate is long.

So the true statements are the first, second and fourth, giving option A, B, D.

Show Hint

The Correct Option is A, B, D

Solution and Explanation

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