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: Boundary Layer Thickness Explained.
For laminar flow over a flat plate, the boundary layer thickness \( \delta \) at a distance \( x \) from the leading edge is defined by:\[\delta \sim x^{\frac{1}{2}}\]This relationship is a result of solving the Navier-Stokes equations for the described conditions.Step 2: Summary.
The laminar boundary layer thickness scales with \( x^{\frac{1}{2}} \). Final Answer: \[ \boxed{x^{\frac{1}{2}}} \]