Question

A fan that can provide air speeds up to 45 m/s is to be used in a low-speed wind tunnel with atmospheric air at 25ºC. If one wishes to use the wind tunnel to study flatplate boundary layer behavior up to Reynolds numbers of Rex = 108, what is the minimum plate length that should be used? At what distance from the leading edge would transition occur if the critical Reynolds number were Rex,c= 5 x105?

Answer 1

a) L(min) = 31.4 m

b) L(min) = 0.157 m

Step-by-step explanation:

KNOWN: Air speed and temperature in a wind tunnel.

FIND: Minimum plate length to achieve a Reynolds number of 10^8

Distance from leading edge at which transition would occur. ASSUMPTIONS: Isothermal conditions
`T_(s) = T_(infinity)`

PROPERTIES: Air (25°C = 29810 : v = 15.71 x 10^-6m^2/s

ANALYSIS: The Reynolds number is

`E_(rx) = p*u(inifinty)*x/u = u(inifinty)*x/v`

To achieve a Reynolds number of 1 x 10^8, the minimum plate length is then

`L_(min) = Re_x*v/u(inifinity) = 1*10^8(15.71*10^-6)/45\\ L_(min) =31.4m`

(b) For a transition Reynolds number of 5 x 10^5

`x_(c)= Re_x,_c*v/u(infinty)\\ L_(min) =0.157`

COMMENTS: Note that

`x_(c)/L= Re_x,_c/R_e_L`

This expression may be used to quickly establish the location of transition from knowledge of
`Re_x,_c andR_e_L`