GATE 2017 ME (ME2) – Question 51
For laminar water flow over a sphere, $C_F=F/(\rho U^2D^2)$. Here F is drag, ρ fluid density, U velocity and D diameter. Water density is 1000 kg/m³. At D = 100 mm and U = 2 m/s, $C_F=0.5$. For a 200 mm sphere under dynamically similar conditions, drag is ______ N.
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Correct answer: 19.9 to 20.1
Explanation
Same fluid and equal Reynolds number require U2D2=U1D1, so U2=1m/s. Dynamic similarity keeps the defined coefficient0.5. Therefore F2=CFρU2²D2²=0.5·1000·1²·0.2²=**20N**. Use the coefficient definition given here rather than inserting a conventional half-dynamic-pressure factor.