Question

Consider a flat plate with a sharp leading edge in a uniform flow of speed \(U\). The free stream is steady, incompressible and laminar. At a fixed streamwise station \(L\) from the leading edge, the boundary–layer thickness is \(\delta\). How does \(\delta\) vary with \(U\)?

• A. \(\delta \propto U\)
• B. \(\delta \propto U^{3/2}\)
• C. \(\delta \propto U^{1/2}\)
• D. \(\delta \propto U^{-1/2}\)

Hint:

Remember the laminar flat-plate rule: \(\delta/x \sim \mathrm{Re}_x^{-1/2}\). At a fixed \(x\), increasing \(U\) thins the layer as \(U^{-1/2}\).

Answer 1

The Correct Option is D

Step 1: Blasius scaling for a laminar flat–plate boundary layer.
For steady incompressible laminar flow over a flat plate, the classical Blasius result gives \[ \delta(x) \approx \frac{5\,x}{\sqrt{\mathrm{Re}_x}}, \qquad \mathrm{Re}_x=\frac{U x}{\nu}, \] where \(\nu\) is kinematic viscosity. 

Step 2: Hold the streamwise location fixed at \(x=L\).
At fixed \(x=L\) and constant fluid properties (\(\nu=\) const.), \[ \delta(L) \;\propto\; \frac{L}{\sqrt{U L/\nu}} \;=\; \frac{L}{\sqrt{L}}\sqrt{\frac{\nu}{U}} \;\propto\; U^{-1/2}. \] \[ \boxed{\delta \propto U^{-1/2}} \]