Topic: Fluid Mechanics
For laminar flow over a flat plate, the thickness of the boundary layer at a distance from the leading edge is found to be 5 mm. The thickness of the boundary layer at a downstream section, which is at twice the distance of the previous section from the leading edge, will be-
- A. 10 mm
- B. $5\sqrt{2}mm$
- C. $5/\sqrt{2}mm$
- D. 2.5 mm
Answer: B. $5\sqrt{2}mm$
Explanation: For laminar flow over a flat plate, boundary layer thickness $\delta \propto \sqrt{x}$. Given $\delta_{1} = 5~mm$ at distance $x_{1}$. At $x_{2} = 2x_{1}$, $\frac{\delta_{1}}{\delta_{2}} = \sqrt{\frac{x_{1}}{x_{2}}} = \sqrt{\frac{x_{1}}{2x_{1}}} = \frac{1}{\sqrt{2}}$. Thus, $\delta_{2} = \delta_{1}\sqrt{2} = 5\sqrt{2}mm$.