GATE 2016 ME (ME1) – Question 50
Oil of kinematic viscosity $1.0\times10^{-5}$ m²/s flows at 10 m/s through a 0.5 m diameter pipe. Water of viscosity $0.89\times10^{-6}$ m²/s flows through a 20 mm model pipe. The water velocity required for dynamic similarity is ______ m/s.
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Correct answer: 22.0 to 22.5
Explanation
For corresponding incompressible pipe flows, match Reynolds numbers VD/ν. Prototype Re=10·0.5/(1e−5)=500000. Model velocity is Re·νw/Dm=500000·0.89e−6/0.020=**22.25m/s**. Diameter must be converted from20mm to0.020m.