Question

The thickness of a laminar boundary layer at a distance \( x \) from the leading edge over a flat plate varies as

• A. \( x^{\frac{1}{5}} \)
• B. \( x^{\frac{1}{3}} \)
• C. \( x^{\frac{2}{3}} \)
• D. \( x^{\frac{1}{2}} \)

Hint:

For laminar flow over a flat plate, the boundary layer thickness increases with the square root of the distance from the leading edge.

Answer 1

The Correct Option is C

Step 1: Understanding boundary layer thickness.
For a laminar boundary layer over a flat plate, the thickness of the boundary layer \( \delta \) at a distance \( x \) from the leading edge is given by the formula: \[ \delta \sim x^{\frac{1}{2}} \] This formula is derived from the solution of the Navier-Stokes equations for laminar flow over a flat plate. Step 2: Conclusion.
The boundary layer thickness varies as \( x^{\frac{1}{2}} \) for laminar flow. Final Answer: \[ \boxed{x^{\frac{1}{2}}} \]