Topic: Fluid Mechanics
Consider the following statement pertaining to boundary layer on a flat plate.
1. The thickness of laminar boundary layer at a distance x from the leading edge varies as $x^{1/2}$
2. The thickness of turbulent boundary layer at a distance x from the leading edge varies as $x^{4/5}$
3. The boundary layer is laminar when Reynolds number is less than $5\times10^{5}$.
Which of the above statements are correct?
- A. 1, 2 and 3
- B. 1 and 2 only
- C. 1 and 3 only
- D. 2 and 3 only
Answer: A. 1, 2 and 3
Explanation: 1. For a laminar boundary layer, $\delta = \frac{5x}{\sqrt{Re_x}} \propto \frac{x}{\sqrt{x}} = x^{1/2}$.
2. For a turbulent boundary layer, $\delta = \frac{0.376x}{(Re_x)^{1/5}} \propto \frac{x}{x^{1/5}} = x^{4/5}$.
3. The critical Reynolds number for transition from laminar to turbulent flow over a flat plate is widely accepted as $5 \times 10^5$. All three statements are correct.