JEE Exam > JEE Questions > When water flows at a rate Q through a capill...
Start Learning for Free
When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomes
- a)p/32
- b)p/8
- c)p
- d)8p
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
When water flows at a rate Q through a capillary tube of radius r that...
If the length of capillary tube is l, the pressure difference is given by
where η is the coefficient of viscosity of water. If r becomes 2r and Q becomes Q/2, we have
Hence the correct choice is (a).
where η is the coefficient of viscosity of water. If r becomes 2r and Q becomes Q/2, we have
Hence the correct choice is (a).
Free Test
FREE
| Start Free Test |
Community Answer
When water flows at a rate Q through a capillary tube of radius r that...
Answer:
To understand why the pressure difference becomes p/32 when the radius of the capillary tube is doubled and the rate of flow is halved, we need to apply the principles of fluid mechanics and the Hagen-Poiseuille equation.
Hagen-Poiseuille Equation:
The Hagen-Poiseuille equation describes the flow of an incompressible and viscous fluid through a cylindrical pipe or tube. It states that the flow rate (Q) through a tube is directly proportional to the fourth power of the radius (r) and the pressure difference (ΔP), and inversely proportional to the viscosity of the fluid (η) and the length of the tube (L).
Mathematically, the Hagen-Poiseuille equation is given by:
Q = (π * r^4 * ΔP) / (8 * η * L)
where:
Q = flow rate
r = radius of the tube
ΔP = pressure difference across the ends of the tube
η = viscosity of the fluid
L = length of the tube
Effect of Doubling the Radius:
When the radius of the capillary tube is doubled, the flow rate (Q) is directly proportional to the fourth power of the radius (r^4). Therefore, the flow rate becomes 2^4 = 16 times the original value.
Effect of Halving the Flow Rate:
When the rate of flow is halved, the flow rate (Q) becomes 1/2 times the original value.
Pressure Difference Calculation:
From the Hagen-Poiseuille equation, we can express the pressure difference (ΔP) in terms of the flow rate (Q) and other variables:
ΔP = (8 * η * L * Q) / (π * r^4)
Now, let's calculate the pressure difference for the original scenario and the new scenario.
Original Scenario:
Q_original = Q
ΔP_original = (8 * η * L * Q_original) / (π * r^4)
New Scenario:
Q_new = Q_original / 2
r_new = 2 * r
ΔP_new = (8 * η * L * Q_new) / (π * (r_new)^4)
= (8 * η * L * (Q_original / 2)) / (π * (2r)^4)
= (8 * η * L * Q_original) / (π * 16r^4)
= (1/2) * (8 * η * L * Q_original) / (π * r^4)
= (1/2) * ΔP_original
The pressure difference in the new scenario is half of the original pressure difference. Therefore, the correct answer is option 'A': p/32.
To understand why the pressure difference becomes p/32 when the radius of the capillary tube is doubled and the rate of flow is halved, we need to apply the principles of fluid mechanics and the Hagen-Poiseuille equation.
Hagen-Poiseuille Equation:
The Hagen-Poiseuille equation describes the flow of an incompressible and viscous fluid through a cylindrical pipe or tube. It states that the flow rate (Q) through a tube is directly proportional to the fourth power of the radius (r) and the pressure difference (ΔP), and inversely proportional to the viscosity of the fluid (η) and the length of the tube (L).
Mathematically, the Hagen-Poiseuille equation is given by:
Q = (π * r^4 * ΔP) / (8 * η * L)
where:
Q = flow rate
r = radius of the tube
ΔP = pressure difference across the ends of the tube
η = viscosity of the fluid
L = length of the tube
Effect of Doubling the Radius:
When the radius of the capillary tube is doubled, the flow rate (Q) is directly proportional to the fourth power of the radius (r^4). Therefore, the flow rate becomes 2^4 = 16 times the original value.
Effect of Halving the Flow Rate:
When the rate of flow is halved, the flow rate (Q) becomes 1/2 times the original value.
Pressure Difference Calculation:
From the Hagen-Poiseuille equation, we can express the pressure difference (ΔP) in terms of the flow rate (Q) and other variables:
ΔP = (8 * η * L * Q) / (π * r^4)
Now, let's calculate the pressure difference for the original scenario and the new scenario.
Original Scenario:
Q_original = Q
ΔP_original = (8 * η * L * Q_original) / (π * r^4)
New Scenario:
Q_new = Q_original / 2
r_new = 2 * r
ΔP_new = (8 * η * L * Q_new) / (π * (r_new)^4)
= (8 * η * L * (Q_original / 2)) / (π * (2r)^4)
= (8 * η * L * Q_original) / (π * 16r^4)
= (1/2) * (8 * η * L * Q_original) / (π * r^4)
= (1/2) * ΔP_original
The pressure difference in the new scenario is half of the original pressure difference. Therefore, the correct answer is option 'A': p/32.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer?
Question Description
When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer?.
When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer?.
Solutions for When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice When water flows at a rate Q through a capillary tube of radius r that is placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference becomesa)p/32b)p/8c)pd)8pCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup