Question

In the laminar boundary layer over a flat plate, the ratio of \( \delta/x \) varies as \( Re^k \) (Where, \( Re \) is Reynolds number). The value of \( k \) is:

• A. 1
• B. \( \frac{1}{2} \)
• C. -1
• D. \( -\frac{1}{2} \)

Hint:

For laminar flow over a flat plate, the boundary layer thickness grows as \( x^{1/2} \), and this is proportional to \( Re^{1/2} \).

Answer 1

The Correct Option is B

Step 1: Understanding the relationship.
In laminar flow over a flat plate, the boundary layer thickness \( \delta \) grows with the distance \( x \) from the leading edge of the plate. The ratio \( \delta/x \) is known to vary with the Reynolds number \( Re \) raised to a power \( k \).

Step 2: Known relationship for boundary layer growth.
For laminar flow, the relationship between the boundary layer thickness \( \delta \) and the Reynolds number \( Re \) is given by: \[ \frac{\delta}{x} \sim Re^{1/2} \] Thus, the exponent \( k \) is \( \frac{1}{2} \).

Final Answer: \[ \boxed{\frac{1}{2}} \]