In order to understand all issues regarding the analysis of flow around a sphere, first (a) Argue why force equilibrium occurs both in the case of a rising and a falling sphere fully submerged in a fluid. Take into consideration that the drag force depends on the velocity of the sphere. Can you sketch how the velocity of the sphere changes with respect to time? The prove the following: (b) The validity of eq. 4.12 (Textbook, p. 198). By the way, this result has beenfirst proven theoretically and verified with a laboratory experiment by G.G. Stokes, one of the two men who formulated the governing equations in Fluid Mechanics. (c) The validity of eq’s 4.17 and 4.18 (Textbook, p. 200).
In order to understand all issues regarding the analysis of flow around a sphere, first
(a) Argue why force equilibrium occurs both in the case of a rising and a falling sphere fully submerged in a fluid. Take into consideration that the drag force depends on the velocity of the sphere. Can you sketch how the velocity of the sphere changes with respect to time?
The prove the following:
(b) The validity of eq. 4.12 (Textbook, p. 198). By the way, this result has beenfirst proven theoretically and verified with a laboratory experiment by G.G. Stokes, one of the two men who formulated the governing equations in Fluid
(c) The validity of eq’s 4.17 and 4.18 (Textbook, p. 200).
(d) The validity of the result in eq. E4.2.5 (Textbook, p. 204).
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(4.12)
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CD
gu
– Ps).
(4.18)
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3 p?u (Po - pr).
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dx
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dt
eat +1'
(E4.2.5)
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