Question

A fan that can provide air speeds of up to 40 m/s is to be used in a low-speed wind tunnel with atmospheric air at 17◦C. If one wishes to use the wind tunnel to study flat-plate boundary layer behaviour up to Reynolds numbers of Rex = 107 , what is the minimum plate length that should be used? At what distance from the leading edge would transition, from laminar to turbulent flow, occur if the critical Reynolds number were Rex,c = 5 × 105 ?

Answer 1

Answer with Explanation:

We are given that

Speed of  fan=$u_\infty}=40 m/s$

T=$17^{\circ} C=273+17=290 K$

Kinematic viscosity of air at  17 degree Celsius=$\nu=1.51\times 10^{-5}m^2/s$

Reynolds number =$Re_{x}=10^7$

We have to find the minimum length of plate should be used.

$L_{min}=\frac{Re_{x}\nu}{u_{\infty}}$

Substitute the values then we get

$L_min}=\frac{10^7\times 1.51\times 10^{-5}}{40}=3.775 m$

Hence, the minimum length of plate=3.775 m

Now, $Re_{x,c}=5\times 10^{5}$

The point of transition is given by

$x_c=\frac{Re_{x,c}\nu}{u_{\infty}}$

$x_c=\frac{5\times 10^5\times 1.51\times 10^{-5}}{40}=0.18875 m$

Hence, the transition point from the leading edge =0.18875 m