Problem 4 20 pt Convection Flow Boundary Layer Transition A

Problem 4 (20 pt) (Convection - Flow Boundary Layer Transition) A wind tunnel is used to study the flat plate boundary layer behavior for the range of Reynolds numbers up to Re = 107. The tunnel setup uses a fan that provides air flow speed of 75 m/s, and the air temperature is 20 C. (a) At what distance from the leading edge of the plate the transition zone (between the laminar and turbulent flow conditions) occurs in this system? Consider the critical Reynolds number at Re_x,c = 5 x 105. (b) What minimum length of the plate should be used to cover the entire targeted Re range in this study?

Solution

Assumption Taken:(Standard Data)

Density of air()=1.225 kg/m^3

Kineamtic viscosity( ) of air at 20°C =15.11*10^-6 (m^2/s)

=>Dynamic Viscosity (µ)= *=1.851*10^-5(N-s/m^2)

a)Transition occurs at critical length(x) which is obtained from critical Reynolds number(5*10^5)

Re(Critical)=( *U*x)/ µ

=> 5*10^5 =(11.225*75*x)/(1.851*10^-5)

Therefore x= 0.1007 m from the leading edge.

b)For entire targeted Re no.,length of the plate(L) is obtained by

Re=( *U*L)/ µ

10^7=(11.225*75*L)/(1.851*10^-5)

=>L=2.0147 m