Question 1.8: At what velocity should tests be run in a wind tunnel on a m......

Turbomachinery Design and Theory [1005770]

At what velocity should tests be run in a wind tunnel on a model of an airplane wing of 160 mm chord in order that the Reynolds number should be the same as that of the prototype of 1000 mm chord moving at 40.5 m/s. Air is under atmospheric pressure in the wind tunnel.

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Let
Velocity of the model : $V_m$
Length of the model: $L_m$ = 160 mm
Length of the prototype: $L_p$ = 1000 mm
Velocity of the prototype: $V_p$ = 40.5 m/s

According to the given conditions:
$(Re)_m = (Re)_p$
$\frac{V_mL_m} {ν_m} =\frac{V_pL_p} {ν_p}$ , Therefore; $ν_m = ν_p = ν_{air}$
Hence
$V_mL_m = V_pL_p$ ,
or
$V_m = L_pV_p/L_m$ = 40.5 × 1000/160 = 253.13 m/s

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