Question

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is ${\delta }_L$. When the plate length is increased to twice of its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to ${\delta }_L$) is_____(correct to two decimal places).

• A. 41.42

Answer 1

The correct option is A 41.42

For laminar flow over flat plate,
As per Blasius equation,

$\delta =\frac{5x}{\sqrt{\frac{\rho V_{\infty }x}{\mu }}}$

$\delta \propto \sqrt{x}$

${\delta }_L\propto \sqrt{L}$

${\delta }_{2L}\propto \sqrt{2L}$

$\frac{{\delta }_{2L}-{\delta }_L}{{\delta }_L}\times =\left[\frac{\sqrt{2L}-\sqrt{L}}{\sqrt{L}}\right]\times 100$

$=(\sqrt{2}-1)\times 100=41.42\%$