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The terminal speed of an air bubble rising through water.
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Answer to Problem 76P
The terminal speed of an air bubble rising through water is
Explanation of Solution
Given that the specific gravity of aluminium sphere is
The free-body diagram of the aluminium sphere and the air bubble is given in Figure 1.
Write the equilibrium condition on forces in
Apply the condition in equation (I) to the aluminium sphere.
Here,
Apply the condition in equation (I) to the air bubble.
Here,
Divide equation (III) by (II).
Write the expression for the drag force on the aluminium sphere.
Here,
Write the expression for the drag force on the air bubble.
Here,
Divide equation (VI) by (V).
Equate the right hand sides of equations (IV) and (VII).
The buoyant force on aluminium sphere and the air bubble is equal to
Replace ratios of mass in equation (IX) with densities.
Here,
Since the specific gravity of aluminium is
Conclusion:
Substitute
Therefore, the terminal speed of an air bubble rising through water is
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Physics - Connect Access (2 Semester)
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