Question

A smooth two dimensional flat plate is exposed to a wind velocity of $80kmph$. Laminar boundary layer exists upto Reynolds no.of flow equal to $3\times {10}^5$. The kinematic viscosity of wind is $1.5\times {10}^{-5}{m}^2/sec$. The maximum thickness of laminar boundary layer (in mm) is ___.

• A. 1.75

Answer 1

The correct option is A 1.75
$V_0=80kmph=80\times \frac{5}{18}=22.22m/sec$
Reynolds no, $R_e=\frac{V_{0}x}{\nu }$
$3\times {10}^5=\frac{22.22x}{1.5\times {10}^{-6}}$
$x=0.202m$
So, the boundary layer is laminar upto $x=0.202m$
For laminar flow on smooth plate,
Boundary layer thickness, $\delta =\frac{5x}{\sqrt{R_{e_x}}}$
$\therefore$ Maximum thickness of laminar boundary layer
$=\frac{5\times 0.202}{\sqrt{3\times {10}^5}}$
$=1.844\times {10}^{-3}m$
$=1.844mm$