(a)
Find the terminal ascent velocity?
Answer to Problem 7.73P
Explanation of Solution
Given information:
Diameter of balloon is equal to
Balloon contains helium at
The total weight of balloon is equal to
The drag force is defined as,
In above equation,
The buoyancy force is defined as,
The specific heat capacity
Assume, the sea level air will have,
Assume,
The specific heat capacity of helium is equal to,
Calculation:
Calculate the density of helium,
For force balance,
Where,
Substitute,
Assume,
Substitute for known values,
Solve for velocity
Conclusion:
The terminal ascent velocity is equal to
(b)
Find the altitude when balloon comes to rest?
Answer to Problem 7.73P
Explanation of Solution
Given information:
Diameter of balloon is equal to
Balloon contains helium at
The total weight of balloon is equal to
According to sub-part a,
We have found,
The buoyancy force is defined as,
Calculation:
If the balloon comes to rest,
The drag will be equal to zero,
Therefore, the force balance equation can be written as,
Substitute,
Substitute for known values,
Solve for
Therefore to find the relevant altitude,
According to table
We can evaluate,
Conclusion:
The final standard altitude is equal to
(c)
Find the minimum diameter of balloon when it begins to rise?
Answer to Problem 7.73P
Explanation of Solution
Given information:
Diameter of balloon is equal to
Balloon contains helium at
The total weight of balloon is equal to
According to sub-part a,
We have found,
The buoyancy force is defined as,
Calculation:
If the balloon begins to rise at sea level,
The buoyancy force will be larger than the weight
Therefore,
Substitute,
Substitute for known values,
Solve for
Conclusion:
The diameter of the balloon needs to be larger than
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Chapter 7 Solutions
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