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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?

Respuesta :

Hashirriaz830

Answer:

a) L(min) = 31.4 m

b) L(min) = 0.157 m

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  [tex]T_{s} = T_{infinity}[/tex]

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

ANALYSIS:  The Reynolds number is  

[tex]E_{rx} = p*u(inifinty)*x/u = u(inifinty)*x/v[/tex]

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

[tex]L_{min} = Re_x*v/u(inifinity) = 1*10^8(15.71*10^-6)/45\\ L_{min} =31.4m[/tex]

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

[tex]x_{c}= Re_x,_c*v/u(infinty)\\ L_(min) =0.157[/tex]

COMMENTS: Note that  

[tex]x_{c}/L= Re_x,_c/R_e_L[/tex]

This expression may be used to quickly establish the location of transition from knowledge of  [tex]Re_x,_c andR_e_L[/tex]

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