A cylinder of diameter 1 m moves through air at STP at 1 m/s. A geometrically similar model has diameter 0.1 m and is tested in air at STP. What speed (m/s) gives Reynolds-number similarity?
The same fluid at the same state has the same kinematic viscosity. Equate $VD/\nu=V_mD_m/\nu$: $V_m=1(1/0.1)=10$ m/s. Matching size alone would not preserve the viscous-to-inertial force ratio.
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