Question

Required information Air at 25°C and 1 atm is flowing over a long flat plate with a velocity of 7 m/s. The density and kinematic viscosity of air at 1 atm and 25°C are p= 1.184 kg/m3 and V = 1.562x10-5 m2/s. Calculate the distance from the leading edge of the plate where the flow becomes turbulent. The distance from the leading edge of the plate is m.

Answer 1

1. The flow is considered to transit to turbulent in the boundary layer when the local Reynolds number reaches a critical value i.e. at Re_critical.

and the value of Re_critical for flow over a plate is 5*10⁵

Thus, Re_critical = {(U*x)/v} = 5*10⁵ , where U = 7 m/s, x = distance along the plate from the leading edge of the plate and v = 1.562*10^-5

So, x = (5*10⁵*1.562*10^-5) / 7 = 1.1157 m is the distance from the leading edge where flow becomes turbulent.

2. Unto the point of the Re_critical the boundary layer grows as laminar, therefore, the thickness of the layer at point where the flow becomes turbulent is given by $\delta = 4.91 x/(Re_c_r_i_t_i_c_a_l)^1^/^2$

Then, $\delta$ = 4.91 * 1.1157 / (5*10⁵) ^1/2 = 0.00775 m = 0.775 cm

Thus boundary layer thickness at start of turbulent boundary layer is 0.775 cm.