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1. (a) Given a free-falling sphere, nondimensionalise the equations of continuity and momentum conservation. Hence, state the physical meaning of Reynolds number (Re) together

1. (a) Given a free-falling sphere, nondimensionalise the equations of continuity and momentum conservation. Hence, state the physical meaning of Reynolds number (Re) together with the characteristic dynamics in small-Re and high-Re flows during the free-falling of the sphere. Hints: Take the diameter D and speed U of the sphere as the characteristic scales of length and speed, respectively. (10 marks)

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