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: Analyze boundary layer relationship.
For laminar flow on a flat plate, the boundary layer thickness \( \delta \) increases with distance \( x \) from the leading edge. The ratio \( \delta/x \) is proportional to the Reynolds number \( Re \) raised to an exponent \( k \).

Step 2: Apply known boundary layer growth equation.
In laminar flow conditions, the relationship governing boundary layer thickness \( \delta \) and Reynolds number \( Re \) is expressed as:\[\frac{\delta}{x} \sim Re^{1/2}\]Therefore, the exponent \( k \) is determined to be \( \frac{1}{2} \).

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