Concept explainers
The terminal speed of ascent for a spherical
The time required for this bubble to rise
Whether this length of time is consistent with one’s observation.
Answer to Problem 76P
Explanation of Solution
Given:
The drag force on a moving sphere at a very low Reynolds number is
where,
Density of carbonated beverage,
Viscosity of carbonated beverage,
Diameter of the carbon dioxide bubble
Radius of the carbon dioxide bubble,
Formula used:
FIGURE: 1
The forces acting on the bubble before it reaches to its terminal speed are shown in the free body diagram (figure 1).
Applying Newton’s second law,
Where,
Under terminal speed conditions, acceleration
By using Archimedes principle, the buoyant force
Where,
Since
Where,
Mass of the gas bubble can be written as,
Substituting for
Where,
Volume of the carbon dioxide bubble which is spherical in shape can be written as,
Substituting for
Since
The rise time
Where,
Calculation:
Substituting the numerical values in equation
Substituting numerical values in equation
The time is less than a second. It seems reasonable.
Conclusion:
The terminal speed of ascent for a spherical
The time required for this bubble to rise
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Chapter 13 Solutions
Physics for Scientists and Engineers
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