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An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.
Correct answer is 'Range: 98 to 99'. Can you explain this answer?
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An elastic air balloon having a diameter of 30 cm is attached to the ...
FBD of balloon
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where FB = Buoyant force T = Tension Clearly T = FB
As the balloon is flexible, and as the pressure changes, the volume of the balloon will also change, so will the buoyant force experienced by it. So
FB1 = ρ × 4 / 3 πr13 × g and FB2 = ρ × 4 / 3 πr23 × g
Given, p = C / D2 ⟹ D = √C / p
⇒ r1 = 1 / 2√ C / p1 and r2 = 1 / 2 √C / p2
% change in Buoyant force
=FB2 − FB1 / FB1× 100
= (FB2 / FB1− 1) × 100
= [(p1 / p2)3/2 − 1] × 100
Putting p1 = 100 kPa and p2 = 1.6 kPa we get the % change in Buoyant Force = −98.4%.
The negative sign indicates that Buoyant Force decreases.
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An elastic air balloon having a diameter of 30 cm is attached to the ...
FBD of balloon
where FB = Buoyant force T = Tension Clearly T = FB
As the balloon is flexible, and as the pressure changes, the volume of the balloon will also change, so will the buoyant force experienced by it. So
FB1 = ρ × 4 / 3 πr13 × g and FB2 = ρ × 4 / 3 πr23 × g
Given, p = C / D2 ⟹ D = √C / p
⇒ r1 = 1 / 2√ C / p1 and r2 = 1 / 2 √C / p2
% change in Buoyant force
=FB2 − FB1 / FB1× 100
= (FB2 / FB1− 1) × 100
= [(p1 / p2)3/2 − 1] × 100
Putting p1 = 100 kPa and p2 = 1.6 kPa we get the % change in Buoyant Force = −98.4%.
The negative sign indicates that Buoyant Force decreases.
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An elastic air balloon having a diameter of 30 cm is attached to the ...
FBD of balloon
where FB = Buoyant force T = Tension Clearly T = FB
As the balloon is flexible, and as the pressure changes, the volume of the balloon will also change, so will the buoyant force experienced by it. So
FB1 = ρ × 4 / 3 πr13 × g and FB2 = ρ × 4 / 3 πr23 × g
Given, p = C / D2 ⟹ D = √C / p
⇒ r1 = 1 / 2√ C / p1 and r2 = 1 / 2 √C / p2
% change in Buoyant force
=FB2 − FB1 / FB1× 100
= (FB2 / FB1− 1) × 100
= [(p1 / p2)3/2 − 1] × 100
Putting p1 = 100 kPa and p2 = 1.6 kPa we get the % change in Buoyant Force = −98.4%.
The negative sign indicates that Buoyant Force decreases.
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An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer?
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An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer?.
An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer?.
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ample number of questions to practice An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Figure. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by p = CDn , where C is a constant and n = −2. The weight of the balloon and the air in it is negligible.Correct answer is 'Range: 98 to 99'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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